From 50d1542f830b7ceb73efd34573b6b56b4971a114 Mon Sep 17 00:00:00 2001 From: Son Ho Date: Tue, 9 May 2023 10:40:19 +0200 Subject: Regenerate the translated files for Lean --- tests/lean/betree/Base/Primitives.lean | 392 ------- tests/lean/betree/BetreeMain.lean | 1 - tests/lean/betree/BetreeMain/Clauses/Template.lean | 185 ---- tests/lean/betree/BetreeMain/Funs.lean | 1167 -------------------- tests/lean/betree/BetreeMain/Opaque.lean | 33 - tests/lean/betree/BetreeMain/Types.lean | 55 - tests/lean/betree/lake-manifest.json | 27 - tests/lean/betree/lakefile.lean | 12 - tests/lean/betree/lean-toolchain | 1 - tests/lean/hashmap/Base/Primitives.lean | 622 +++++++---- tests/lean/hashmap/Hashmap/Clauses/Clauses.lean | 18 +- tests/lean/hashmap/Hashmap/Clauses/Template.lean | 16 +- tests/lean/hashmap/Hashmap/Funs.lean | 183 ++- tests/lean/hashmap/Hashmap/Types.lean | 8 +- tests/lean/hashmap_on_disk/Base/Primitives.lean | 622 +++++++---- .../HashmapMain/Clauses/Clauses.lean | 44 +- .../HashmapMain/Clauses/Template.lean | 16 +- .../hashmap_on_disk/HashmapMain/ExternalFuns.lean | 5 + tests/lean/hashmap_on_disk/HashmapMain/Funs.lean | 205 ++-- tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean | 4 +- tests/lean/hashmap_on_disk/HashmapMain/Types.lean | 8 +- tests/lean/misc-constants/Base/Primitives.lean | 622 +++++++---- tests/lean/misc-constants/Constants.lean | 267 +++-- tests/lean/misc-external/Base/Primitives.lean | 622 +++++++---- .../lean/misc-external/External/ExternalFuns.lean | 5 + tests/lean/misc-external/External/Funs.lean | 35 +- tests/lean/misc-external/External/Opaque.lean | 3 +- tests/lean/misc-loops/Base/Primitives.lean | 622 +++++++---- tests/lean/misc-loops/Loops/Clauses/Clauses.lean | 42 +- tests/lean/misc-loops/Loops/Clauses/Template.lean | 45 +- tests/lean/misc-loops/Loops/Funs.lean | 281 +++-- .../misc-no_nested_borrows/Base/Primitives.lean | 622 +++++++---- .../misc-no_nested_borrows/NoNestedBorrows.lean | 1050 +++++++++--------- tests/lean/misc-paper/Base/Primitives.lean | 622 +++++++---- tests/lean/misc-paper/Paper.lean | 240 ++-- tests/lean/misc-polonius_list/Base/Primitives.lean | 622 +++++++---- tests/lean/misc-polonius_list/PoloniusList.lean | 59 +- 37 files changed, 4452 insertions(+), 4931 deletions(-) delete mode 100644 tests/lean/betree/Base/Primitives.lean delete mode 100644 tests/lean/betree/BetreeMain.lean delete mode 100644 tests/lean/betree/BetreeMain/Clauses/Template.lean delete mode 100644 tests/lean/betree/BetreeMain/Funs.lean delete mode 100644 tests/lean/betree/BetreeMain/Opaque.lean delete mode 100644 tests/lean/betree/BetreeMain/Types.lean delete mode 100644 tests/lean/betree/lake-manifest.json delete mode 100644 tests/lean/betree/lakefile.lean delete mode 100644 tests/lean/betree/lean-toolchain create mode 100644 tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean create mode 100644 tests/lean/misc-external/External/ExternalFuns.lean (limited to 'tests/lean') diff --git a/tests/lean/betree/Base/Primitives.lean b/tests/lean/betree/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/betree/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -def ret? {α: Type} (r: Result α): Bool := - match r with - | Result.ret _ => true - | Result.fail _ => false - -def massert (b:Bool) : Result Unit := - if b then .ret () else fail assertionFailure - -def eval_global {α: Type} (x: Result α) (_: ret? x): α := - match x with - | Result.fail _ => by contradiction - | Result.ret x => x - -/- DO-DSL SUPPORT -/ - -def bind (x: Result α) (f: α -> Result β) : Result β := - match x with - | ret v => f v - | fail v => fail v - --- Allows using Result in do-blocks -instance : Bind Result where - bind := bind - --- Allows using return x in do-blocks -instance : Pure Result where - pure := fun x => ret x - -/- CUSTOM-DSL SUPPORT -/ - --- Let-binding the Result of a monadic operation is oftentimes not sufficient, --- because we may need a hypothesis for equational reasoning in the scope. We --- rely on subtype, and a custom let-binding operator, in effect recreating our --- own variant of the do-dsl - -def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := - match o with - | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e - -macro "let" e:term " ⟵ " f:term : doElem => - `(doElem| let ⟨$e, h⟩ ← Result.attach $f) - --- TODO: any way to factorize both definitions? -macro "let" e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, h⟩ ← Result.attach $f) - --- We call the hypothesis `h`, in effect making it unavailable to the user --- (because too much shadowing). But in practice, once can use the French single --- quote notation (input with f< and f>), where `‹ h ›` finds a suitable --- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` -#eval do - let y <-- .ret (0: Nat) - let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide - let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ - .ret r - ----------------------- --- MACHINE INTEGERS -- ----------------------- - --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. - --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) - --- Note from Chris Bailey: "If there's more than one salient property of your --- definition then the subtyping strategy might get messy, and the property part --- of a subtype is less discoverable by the simplifier or tactics like --- library_search." So, we will not add refinements on the return values of the --- operations defined on Primitives, but will rather rely on custom lemmas to --- invert on possible return values of the primitive operations. - --- Machine integer constants, done via `ofNatCore`, which requires a proof that --- the `Nat` fits within the desired integer type. We provide a custom tactic. - -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- Further thoughts: look at what has been done here: --- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean --- and --- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean --- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow - -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- Aeneas-translated function -- useful to reduce non-recursive definitions. - Use with `simp [ aeneas ]` -/ -register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/betree/BetreeMain.lean b/tests/lean/betree/BetreeMain.lean deleted file mode 100644 index 5f307877..00000000 --- a/tests/lean/betree/BetreeMain.lean +++ /dev/null @@ -1 +0,0 @@ -import BetreeMain.Funs diff --git a/tests/lean/betree/BetreeMain/Clauses/Template.lean b/tests/lean/betree/BetreeMain/Clauses/Template.lean deleted file mode 100644 index 1d18174e..00000000 --- a/tests/lean/betree/BetreeMain/Clauses/Template.lean +++ /dev/null @@ -1,185 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: templates for the decreases clauses -import Base.Primitives -import BetreeMain.Types - -/- [betree_main::betree::List::{1}::len]: termination measure -/ -@[simp] -def betree_list_len_terminates (T : Type) (self : betree_list_t T) := self - -/- [betree_main::betree::List::{1}::len]: decreases_by tactic -/ -syntax "betree_list_len_decreases" term+ : tactic -macro_rules -| `(tactic| betree_list_len_decreases $self) =>`(tactic| sorry) - -/- [betree_main::betree::List::{1}::split_at]: termination measure -/ -@[simp] -def betree_list_split_at_terminates (T : Type) (self : betree_list_t T) - (n : UInt64) := - (self, n) - -/- [betree_main::betree::List::{1}::split_at]: decreases_by tactic -/ -syntax "betree_list_split_at_decreases" term+ : tactic -macro_rules -| `(tactic| betree_list_split_at_decreases $self $n) =>`(tactic| sorry) - -/- [betree_main::betree::List::{2}::partition_at_pivot]: termination measure -/ -@[simp] -def betree_list_partition_at_pivot_terminates (T : Type) - (self : betree_list_t (UInt64 × T)) (pivot : UInt64) := - (self, pivot) - -/- [betree_main::betree::List::{2}::partition_at_pivot]: decreases_by tactic -/ -syntax "betree_list_partition_at_pivot_decreases" term+ : tactic -macro_rules -| `(tactic| betree_list_partition_at_pivot_decreases $self $pivot) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::lookup_in_bindings]: termination measure -/ -@[simp] -def betree_node_lookup_in_bindings_terminates (key : UInt64) - (bindings : betree_list_t (UInt64 × UInt64)) := - (key, bindings) - -/- [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases_by tactic -/ -syntax "betree_node_lookup_in_bindings_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_lookup_in_bindings_decreases $key $bindings) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: termination measure -/ -@[simp] -def betree_node_lookup_first_message_for_key_terminates (key : UInt64) - (msgs : betree_list_t (UInt64 × betree_message_t)) := - (key, msgs) - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases_by tactic -/ -syntax "betree_node_lookup_first_message_for_key_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_lookup_first_message_for_key_decreases $key $msgs) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::apply_upserts]: termination measure -/ -@[simp] -def betree_node_apply_upserts_terminates - (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64) - (key : UInt64) (st : State) := - (msgs, prev, key, st) - -/- [betree_main::betree::Node::{5}::apply_upserts]: decreases_by tactic -/ -syntax "betree_node_apply_upserts_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_apply_upserts_decreases $msgs $prev $key $st) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::lookup]: termination measure -/ -@[simp] -def betree_node_lookup_terminates (self : betree_node_t) (key : UInt64) - (st : State) := - (self, key, st) - -/- [betree_main::betree::Node::{5}::lookup]: decreases_by tactic -/ -syntax "betree_node_lookup_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_lookup_decreases $self $key $st) =>`(tactic| sorry) - -/- [betree_main::betree::Internal::{4}::lookup_in_children]: termination measure -/ -@[simp] -def betree_internal_lookup_in_children_terminates (self : betree_internal_t) - (key : UInt64) (st : State) := - (self, key, st) - -/- [betree_main::betree::Internal::{4}::lookup_in_children]: decreases_by tactic -/ -syntax "betree_internal_lookup_in_children_decreases" term+ : tactic -macro_rules -| `(tactic| betree_internal_lookup_in_children_decreases $self $key $st) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: termination measure -/ -@[simp] -def betree_node_lookup_mut_in_bindings_terminates (key : UInt64) - (bindings : betree_list_t (UInt64 × UInt64)) := - (key, bindings) - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases_by tactic -/ -syntax "betree_node_lookup_mut_in_bindings_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_lookup_mut_in_bindings_decreases $key $bindings) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: termination measure -/ -@[simp] -def betree_node_apply_messages_to_leaf_terminates - (bindings : betree_list_t (UInt64 × UInt64)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) := - (bindings, new_msgs) - -/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases_by tactic -/ -syntax "betree_node_apply_messages_to_leaf_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_apply_messages_to_leaf_decreases $bindings -$new_msgs) =>`(tactic| sorry) - -/- [betree_main::betree::Node::{5}::filter_messages_for_key]: termination measure -/ -@[simp] -def betree_node_filter_messages_for_key_terminates (key : UInt64) - (msgs : betree_list_t (UInt64 × betree_message_t)) := - (key, msgs) - -/- [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases_by tactic -/ -syntax "betree_node_filter_messages_for_key_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_filter_messages_for_key_decreases $key $msgs) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: termination measure -/ -@[simp] -def betree_node_lookup_first_message_after_key_terminates (key : UInt64) - (msgs : betree_list_t (UInt64 × betree_message_t)) := - (key, msgs) - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases_by tactic -/ -syntax "betree_node_lookup_first_message_after_key_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_lookup_first_message_after_key_decreases $key $msgs) => - `(tactic| sorry) - -/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: termination measure -/ -@[simp] -def betree_node_apply_messages_to_internal_terminates - (msgs : betree_list_t (UInt64 × betree_message_t)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) := - (msgs, new_msgs) - -/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases_by tactic -/ -syntax "betree_node_apply_messages_to_internal_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_apply_messages_to_internal_decreases $msgs -$new_msgs) =>`(tactic| sorry) - -/- [betree_main::betree::Node::{5}::apply_messages]: termination measure -/ -@[simp] -def betree_node_apply_messages_terminates (self : betree_node_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) := - (self, params, node_id_cnt, msgs, st) - -/- [betree_main::betree::Node::{5}::apply_messages]: decreases_by tactic -/ -syntax "betree_node_apply_messages_decreases" term+ : tactic -macro_rules -| `(tactic| betree_node_apply_messages_decreases $self $params $node_id_cnt -$msgs $st) =>`(tactic| sorry) - -/- [betree_main::betree::Internal::{4}::flush]: termination measure -/ -@[simp] -def betree_internal_flush_terminates (self : betree_internal_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (UInt64 × betree_message_t)) (st : State) := - (self, params, node_id_cnt, content, st) - -/- [betree_main::betree::Internal::{4}::flush]: decreases_by tactic -/ -syntax "betree_internal_flush_decreases" term+ : tactic -macro_rules -| `(tactic| betree_internal_flush_decreases $self $params $node_id_cnt $content -$st) =>`(tactic| sorry) - diff --git a/tests/lean/betree/BetreeMain/Funs.lean b/tests/lean/betree/BetreeMain/Funs.lean deleted file mode 100644 index 7177e2ec..00000000 --- a/tests/lean/betree/BetreeMain/Funs.lean +++ /dev/null @@ -1,1167 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: function definitions -import Base.Primitives -import BetreeMain.Types -import BetreeMain.Opaque -import BetreeMain.Clauses.Clauses - -section variable (opaque_defs: OpaqueDefs) - -/- [betree_main::betree::load_internal_node] -/ -def betree_load_internal_node_fwd - (id : UInt64) (st : State) : - Result (State × (betree_list_t (UInt64 × betree_message_t))) - := - opaque_defs.betree_utils_load_internal_node_fwd id st - -/- [betree_main::betree::store_internal_node] -/ -def betree_store_internal_node_fwd - (id : UInt64) (content : betree_list_t (UInt64 × betree_message_t)) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - opaque_defs.betree_utils_store_internal_node_fwd id content st - Result.ret (st0, ()) - -/- [betree_main::betree::load_leaf_node] -/ -def betree_load_leaf_node_fwd - (id : UInt64) (st : State) : - Result (State × (betree_list_t (UInt64 × UInt64))) - := - opaque_defs.betree_utils_load_leaf_node_fwd id st - -/- [betree_main::betree::store_leaf_node] -/ -def betree_store_leaf_node_fwd - (id : UInt64) (content : betree_list_t (UInt64 × UInt64)) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← opaque_defs.betree_utils_store_leaf_node_fwd id content st - Result.ret (st0, ()) - -/- [betree_main::betree::fresh_node_id] -/ -def betree_fresh_node_id_fwd (counter : UInt64) : Result UInt64 := - do - let _ ← UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit)) - Result.ret counter - -/- [betree_main::betree::fresh_node_id] -/ -def betree_fresh_node_id_back (counter : UInt64) : Result UInt64 := - UInt64.checked_add counter (UInt64.ofNatCore 1 (by intlit)) - -/- [betree_main::betree::NodeIdCounter::{0}::new] -/ -def betree_node_id_counter_new_fwd : Result betree_node_id_counter_t := - Result.ret - { betree_node_id_counter_next_node_id := (UInt64.ofNatCore 0 (by intlit)) } - -/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/ -def betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : Result UInt64 := - do - let _ ← UInt64.checked_add self.betree_node_id_counter_next_node_id - (UInt64.ofNatCore 1 (by intlit)) - Result.ret self.betree_node_id_counter_next_node_id - -/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/ -def betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : Result betree_node_id_counter_t := - do - let i ← UInt64.checked_add self.betree_node_id_counter_next_node_id - (UInt64.ofNatCore 1 (by intlit)) - Result.ret { betree_node_id_counter_next_node_id := i } - -/- [core::num::u64::{10}::MAX] -/ -def core_num_u64_max_body : Result UInt64 := - Result.ret (UInt64.ofNatCore 18446744073709551615 (by intlit)) -def core_num_u64_max_c : UInt64 := eval_global core_num_u64_max_body (by simp) - -/- [betree_main::betree::upsert_update] -/ -def betree_upsert_update_fwd - (prev : Option UInt64) (st : betree_upsert_fun_state_t) : Result UInt64 := - match h: prev with - | Option.none => - match h: st with - | betree_upsert_fun_state_t.Add v => Result.ret v - | betree_upsert_fun_state_t.Sub i => - Result.ret (UInt64.ofNatCore 0 (by intlit)) - | Option.some prev0 => - match h: st with - | betree_upsert_fun_state_t.Add v => - do - let margin ← UInt64.checked_sub core_num_u64_max_c prev0 - if h: margin >= v - then UInt64.checked_add prev0 v - else Result.ret core_num_u64_max_c - | betree_upsert_fun_state_t.Sub v => - if h: prev0 >= v - then UInt64.checked_sub prev0 v - else Result.ret (UInt64.ofNatCore 0 (by intlit)) - -/- [betree_main::betree::List::{1}::len] -/ -def betree_list_len_fwd - (T : Type) (self : betree_list_t T) : (Result UInt64) := - match h: self with - | betree_list_t.Cons t tl => - do - let i ← betree_list_len_fwd T tl - UInt64.checked_add (UInt64.ofNatCore 1 (by intlit)) i - | betree_list_t.Nil => Result.ret (UInt64.ofNatCore 0 (by intlit)) -termination_by betree_list_len_fwd self => betree_list_len_terminates T self -decreasing_by betree_list_len_decreases self - -/- [betree_main::betree::List::{1}::split_at] -/ -def betree_list_split_at_fwd - (T : Type) (self : betree_list_t T) (n : UInt64) : - (Result ((betree_list_t T) × (betree_list_t T))) - := - if h: n = (UInt64.ofNatCore 0 (by intlit)) - then Result.ret (betree_list_t.Nil, self) - else - match h: self with - | betree_list_t.Cons hd tl => - do - let i ← UInt64.checked_sub n (UInt64.ofNatCore 1 (by intlit)) - let p ← betree_list_split_at_fwd T tl i - let (ls0, ls1) := p - let l := ls0 - Result.ret (betree_list_t.Cons hd l, ls1) - | betree_list_t.Nil => Result.fail Error.panic -termination_by betree_list_split_at_fwd self n => - betree_list_split_at_terminates T self n -decreasing_by betree_list_split_at_decreases self n - -/- [betree_main::betree::List::{1}::push_front] -/ -def betree_list_push_front_fwd_back - (T : Type) (self : betree_list_t T) (x : T) : Result (betree_list_t T) := - let tl := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - let l := tl - Result.ret (betree_list_t.Cons x l) - -/- [betree_main::betree::List::{1}::pop_front] -/ -def betree_list_pop_front_fwd (T : Type) (self : betree_list_t T) : Result T := - let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - match h: ls with - | betree_list_t.Cons x tl => Result.ret x - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{1}::pop_front] -/ -def betree_list_pop_front_back - (T : Type) (self : betree_list_t T) : Result (betree_list_t T) := - let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil - match h: ls with - | betree_list_t.Cons x tl => Result.ret tl - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{1}::hd] -/ -def betree_list_hd_fwd (T : Type) (self : betree_list_t T) : Result T := - match h: self with - | betree_list_t.Cons hd l => Result.ret hd - | betree_list_t.Nil => Result.fail Error.panic - -/- [betree_main::betree::List::{2}::head_has_key] -/ -def betree_list_head_has_key_fwd - (T : Type) (self : betree_list_t (UInt64 × T)) (key : UInt64) : - Result Bool - := - match h: self with - | betree_list_t.Cons hd l => let (i, _) := hd - Result.ret (i = key) - | betree_list_t.Nil => Result.ret false - -/- [betree_main::betree::List::{2}::partition_at_pivot] -/ -def betree_list_partition_at_pivot_fwd - (T : Type) (self : betree_list_t (UInt64 × T)) (pivot : UInt64) : - (Result ((betree_list_t (UInt64 × T)) × (betree_list_t (UInt64 × T)))) - := - match h: self with - | betree_list_t.Cons hd tl => - let (i, t) := hd - if h: i >= pivot - then Result.ret (betree_list_t.Nil, betree_list_t.Cons (i, t) tl) - else - do - let p ← betree_list_partition_at_pivot_fwd T tl pivot - let (ls0, ls1) := p - let l := ls0 - Result.ret (betree_list_t.Cons (i, t) l, ls1) - | betree_list_t.Nil => Result.ret (betree_list_t.Nil, betree_list_t.Nil) -termination_by betree_list_partition_at_pivot_fwd self pivot => - betree_list_partition_at_pivot_terminates T self pivot -decreasing_by betree_list_partition_at_pivot_decreases self pivot - -/- [betree_main::betree::Leaf::{3}::split] -/ -def betree_leaf_split_fwd - (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : State) : - Result (State × betree_internal_t) - := - do - let p ← - betree_list_split_at_fwd (UInt64 × UInt64) content - params.betree_params_split_size - let (content0, content1) := p - let p0 ← betree_list_hd_fwd (UInt64 × UInt64) content1 - let (pivot, _) := p0 - let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0 - let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st - let (st1, _) ← betree_store_leaf_node_fwd id1 content1 st0 - let n := betree_node_t.Leaf - { - betree_leaf_id := id0, - betree_leaf_size := params.betree_params_split_size - } - let n0 := betree_node_t.Leaf - { - betree_leaf_id := id1, - betree_leaf_size := params.betree_params_split_size - } - Result.ret (st1, mkbetree_internal_t self.betree_leaf_id pivot n n0) - -/- [betree_main::betree::Leaf::{3}::split] -/ -def betree_leaf_split_back - (self : betree_leaf_t) (content : betree_list_t (UInt64 × UInt64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : State) : - Result betree_node_id_counter_t - := - do - let p ← - betree_list_split_at_fwd (UInt64 × UInt64) content - params.betree_params_split_size - let (content0, content1) := p - let _ ← betree_list_hd_fwd (UInt64 × UInt64) content1 - let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0 - let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st - let _ ← betree_store_leaf_node_fwd id1 content1 st0 - betree_node_id_counter_fresh_id_back node_id_cnt0 - -/- [betree_main::betree::Node::{5}::lookup_in_bindings] -/ -def betree_node_lookup_in_bindings_fwd - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) : - (Result (Option UInt64)) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i = key - then Result.ret (Option.some i0) - else - if h: i > key - then Result.ret Option.none - else betree_node_lookup_in_bindings_fwd key tl - | betree_list_t.Nil => Result.ret Option.none -termination_by betree_node_lookup_in_bindings_fwd key bindings => - betree_node_lookup_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/ -def betree_node_lookup_first_message_for_key_fwd - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons x next_msgs => - let (i, m) := x - if h: i >= key - then Result.ret (betree_list_t.Cons (i, m) next_msgs) - else betree_node_lookup_first_message_for_key_fwd key next_msgs - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_first_message_for_key_fwd key msgs => - betree_node_lookup_first_message_for_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/ -def betree_node_lookup_first_message_for_key_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) - (ret0 : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons x next_msgs => - let (i, m) := x - if h: i >= key - then Result.ret ret0 - else - do - let next_msgs0 ← - betree_node_lookup_first_message_for_key_back key next_msgs ret0 - Result.ret (betree_list_t.Cons (i, m) next_msgs0) - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_first_message_for_key_back key msgs ret0 => - betree_node_lookup_first_message_for_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::apply_upserts] -/ -def betree_node_apply_upserts_fwd - (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64) - (key : UInt64) (st : State) : - (Result (State × UInt64)) - := - do - let b ← betree_list_head_has_key_fwd betree_message_t msgs key - if h: b - then - do - let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs - let (_, m) := msg - match h: m with - | betree_message_t.Insert i => Result.fail Error.panic - | betree_message_t.Delete => Result.fail Error.panic - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd prev s - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs - betree_node_apply_upserts_fwd msgs0 (Option.some v) key st - else - do - let (st0, v) ← - opaque_defs.core_option_option_unwrap_fwd UInt64 prev st - let _ ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs - (key, betree_message_t.Insert v) - Result.ret (st0, v) -termination_by betree_node_apply_upserts_fwd msgs prev key st => - betree_node_apply_upserts_terminates msgs prev key st -decreasing_by betree_node_apply_upserts_decreases msgs prev key st - -/- [betree_main::betree::Node::{5}::apply_upserts] -/ -def betree_node_apply_upserts_back - (msgs : betree_list_t (UInt64 × betree_message_t)) (prev : Option UInt64) - (key : UInt64) (st : State) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - do - let b ← betree_list_head_has_key_fwd betree_message_t msgs key - if h: b - then - do - let msg ← betree_list_pop_front_fwd (UInt64 × betree_message_t) msgs - let (_, m) := msg - match h: m with - | betree_message_t.Insert i => Result.fail Error.panic - | betree_message_t.Delete => Result.fail Error.panic - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd prev s - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs - betree_node_apply_upserts_back msgs0 (Option.some v) key st - else - do - let (_, v) ← opaque_defs.core_option_option_unwrap_fwd UInt64 prev st - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs (key, - betree_message_t.Insert v) -termination_by betree_node_apply_upserts_back msgs prev key st => - betree_node_apply_upserts_terminates msgs prev key st -decreasing_by betree_node_apply_upserts_decreases msgs prev key st - -/- [betree_main::betree::Node::{5}::lookup] -/ -mutual def betree_node_lookup_fwd - (self : betree_node_t) (key : UInt64) (st : State) : - (Result (State × (Option UInt64))) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, msgs) ← betree_load_internal_node_fwd i st - let pending ← betree_node_lookup_first_message_for_key_fwd key msgs - match h: pending with - | betree_list_t.Cons p l => - let (k, msg) := p - if h: k != key - then - do - let (st1, opt) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 - n n0) key st0 - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, msg) l) - Result.ret (st1, opt) - else - match h: msg with - | betree_message_t.Insert v => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Insert v) l) - Result.ret (st0, Option.some v) - | betree_message_t.Delete => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Delete) l) - Result.ret (st0, Option.none) - | betree_message_t.Upsert ufs => - do - let (st1, v) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i - i0 n n0) key st0 - let (st2, v0) ← - betree_node_apply_upserts_fwd (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i - i0 n n0) key st0 - let (mkbetree_internal_t i1 _ _ _) := node0 - let pending0 ← - betree_node_apply_upserts_back (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let msgs0 ← - betree_node_lookup_first_message_for_key_back key msgs pending0 - let (st3, _) ← betree_store_internal_node_fwd i1 msgs0 st2 - Result.ret (st3, Option.some v0) - | betree_list_t.Nil => - do - let (st1, opt) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 n - n0) key st0 - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - betree_list_t.Nil - Result.ret (st1, opt) - | betree_node_t.Leaf node => - do - let (st0, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let opt ← betree_node_lookup_in_bindings_fwd key bindings - Result.ret (st0, opt) -termination_by betree_node_lookup_fwd self key st => - betree_node_lookup_terminates self key st -decreasing_by betree_node_lookup_decreases self key st - -/- [betree_main::betree::Node::{5}::lookup] -/ -def betree_node_lookup_back - (self : betree_node_t) (key : UInt64) (st : State) : - (Result betree_node_t) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, msgs) ← betree_load_internal_node_fwd i st - let pending ← betree_node_lookup_first_message_for_key_fwd key msgs - match h: pending with - | betree_list_t.Cons p l => - let (k, msg) := p - if h: k != key - then - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, msg) l) - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 - n n0) key st0 - Result.ret (betree_node_t.Internal node0) - else - match h: msg with - | betree_message_t.Insert v => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Insert v) l) - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n - n0)) - | betree_message_t.Delete => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - (betree_list_t.Cons (k, betree_message_t.Delete) l) - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n - n0)) - | betree_message_t.Upsert ufs => - do - let (st1, v) ← - betree_internal_lookup_in_children_fwd (mkbetree_internal_t i - i0 n n0) key st0 - let (st2, _) ← - betree_node_apply_upserts_fwd (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i - i0 n n0) key st0 - let (mkbetree_internal_t i1 i2 n1 n2) := node0 - let pending0 ← - betree_node_apply_upserts_back (betree_list_t.Cons (k, - betree_message_t.Upsert ufs) l) v key st1 - let msgs0 ← - betree_node_lookup_first_message_for_key_back key msgs pending0 - let _ ← betree_store_internal_node_fwd i1 msgs0 st2 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 - n2)) - | betree_list_t.Nil => - do - let _ ← - betree_node_lookup_first_message_for_key_back key msgs - betree_list_t.Nil - let node0 ← - betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 n - n0) key st0 - Result.ret (betree_node_t.Internal node0) - | betree_node_t.Leaf node => - do - let (_, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let _ ← betree_node_lookup_in_bindings_fwd key bindings - Result.ret (betree_node_t.Leaf node) -termination_by betree_node_lookup_back self key st => - betree_node_lookup_terminates self key st -decreasing_by betree_node_lookup_decreases self key st - -/- [betree_main::betree::Internal::{4}::lookup_in_children] -/ -def betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : UInt64) (st : State) : - (Result (State × (Option UInt64))) - := - let (mkbetree_internal_t _ i n n0) := self - if h: key < i - then betree_node_lookup_fwd n key st - else betree_node_lookup_fwd n0 key st -termination_by betree_internal_lookup_in_children_fwd self key st => - betree_internal_lookup_in_children_terminates self key st -decreasing_by betree_internal_lookup_in_children_decreases self key st - -/- [betree_main::betree::Internal::{4}::lookup_in_children] -/ -def betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : UInt64) (st : State) : - (Result betree_internal_t) - := - let (mkbetree_internal_t i i0 n n0) := self - if h: key < i0 - then - do - let n1 ← betree_node_lookup_back n key st - Result.ret (mkbetree_internal_t i i0 n1 n0) - else - do - let n1 ← betree_node_lookup_back n0 key st - Result.ret (mkbetree_internal_t i i0 n n1) -termination_by betree_internal_lookup_in_children_back self key st => - betree_internal_lookup_in_children_terminates self key st -decreasing_by betree_internal_lookup_in_children_decreases self key st - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/ -def betree_node_lookup_mut_in_bindings_fwd - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i >= key - then Result.ret (betree_list_t.Cons (i, i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_mut_in_bindings_fwd key bindings => - betree_node_lookup_mut_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/ -def betree_node_lookup_mut_in_bindings_back - (key : UInt64) (bindings : betree_list_t (UInt64 × UInt64)) - (ret0 : betree_list_t (UInt64 × UInt64)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: bindings with - | betree_list_t.Cons hd tl => - let (i, i0) := hd - if h: i >= key - then Result.ret ret0 - else - do - let tl0 ← betree_node_lookup_mut_in_bindings_back key tl ret0 - Result.ret (betree_list_t.Cons (i, i0) tl0) - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_mut_in_bindings_back key bindings ret0 => - betree_node_lookup_mut_in_bindings_terminates key bindings -decreasing_by betree_node_lookup_mut_in_bindings_decreases key bindings - -/- [betree_main::betree::Node::{5}::apply_to_leaf] -/ -def betree_node_apply_to_leaf_fwd_back - (bindings : betree_list_t (UInt64 × UInt64)) (key : UInt64) - (new_msg : betree_message_t) : - Result (betree_list_t (UInt64 × UInt64)) - := - do - let bindings0 ← betree_node_lookup_mut_in_bindings_fwd key bindings - let b ← betree_list_head_has_key_fwd UInt64 bindings0 key - if h: b - then - do - let hd ← betree_list_pop_front_fwd (UInt64 × UInt64) bindings0 - match h: new_msg with - | betree_message_t.Insert v => - do - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - let bindings2 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1 - (key, v) - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - | betree_message_t.Delete => - do - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | betree_message_t.Upsert s => - do - let (_, i) := hd - let v ← betree_upsert_update_fwd (Option.some i) s - let bindings1 ← - betree_list_pop_front_back (UInt64 × UInt64) bindings0 - let bindings2 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings1 - (key, v) - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - else - match h: new_msg with - | betree_message_t.Insert v => - do - let bindings1 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key, - v) - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | betree_message_t.Delete => - betree_node_lookup_mut_in_bindings_back key bindings bindings0 - | betree_message_t.Upsert s => - do - let v ← betree_upsert_update_fwd Option.none s - let bindings1 ← - betree_list_push_front_fwd_back (UInt64 × UInt64) bindings0 (key, - v) - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - -/- [betree_main::betree::Node::{5}::apply_messages_to_leaf] -/ -def betree_node_apply_messages_to_leaf_fwd_back - (bindings : betree_list_t (UInt64 × UInt64)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × UInt64))) - := - match h: new_msgs with - | betree_list_t.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let bindings0 ← betree_node_apply_to_leaf_fwd_back bindings i m - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl - | betree_list_t.Nil => Result.ret bindings -termination_by betree_node_apply_messages_to_leaf_fwd_back bindings new_msgs => - betree_node_apply_messages_to_leaf_terminates bindings new_msgs -decreasing_by betree_node_apply_messages_to_leaf_decreases bindings new_msgs - -/- [betree_main::betree::Node::{5}::filter_messages_for_key] -/ -def betree_node_filter_messages_for_key_fwd_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p l => - let (k, m) := p - if h: k = key - then - do - let msgs0 ← - betree_list_pop_front_back (UInt64 × betree_message_t) - (betree_list_t.Cons (k, m) l) - betree_node_filter_messages_for_key_fwd_back key msgs0 - else Result.ret (betree_list_t.Cons (k, m) l) - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_filter_messages_for_key_fwd_back key msgs => - betree_node_filter_messages_for_key_terminates key msgs -decreasing_by betree_node_filter_messages_for_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/ -def betree_node_lookup_first_message_after_key_fwd - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p next_msgs => - let (k, m) := p - if h: k = key - then betree_node_lookup_first_message_after_key_fwd key next_msgs - else Result.ret (betree_list_t.Cons (k, m) next_msgs) - | betree_list_t.Nil => Result.ret betree_list_t.Nil -termination_by betree_node_lookup_first_message_after_key_fwd key msgs => - betree_node_lookup_first_message_after_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/ -def betree_node_lookup_first_message_after_key_back - (key : UInt64) (msgs : betree_list_t (UInt64 × betree_message_t)) - (ret0 : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: msgs with - | betree_list_t.Cons p next_msgs => - let (k, m) := p - if h: k = key - then - do - let next_msgs0 ← - betree_node_lookup_first_message_after_key_back key next_msgs ret0 - Result.ret (betree_list_t.Cons (k, m) next_msgs0) - else Result.ret ret0 - | betree_list_t.Nil => Result.ret ret0 -termination_by betree_node_lookup_first_message_after_key_back key msgs ret0 => - betree_node_lookup_first_message_after_key_terminates key msgs -decreasing_by betree_node_lookup_first_message_after_key_decreases key msgs - -/- [betree_main::betree::Node::{5}::apply_to_internal] -/ -def betree_node_apply_to_internal_fwd_back - (msgs : betree_list_t (UInt64 × betree_message_t)) (key : UInt64) - (new_msg : betree_message_t) : - Result (betree_list_t (UInt64 × betree_message_t)) - := - do - let msgs0 ← betree_node_lookup_first_message_for_key_fwd key msgs - let b ← betree_list_head_has_key_fwd betree_message_t msgs0 key - if h: b - then - match h: new_msg with - | betree_message_t.Insert i => - do - let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1 - (key, betree_message_t.Insert i) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Delete => - do - let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs1 - (key, betree_message_t.Delete) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Upsert s => - do - let p ← betree_list_hd_fwd (UInt64 × betree_message_t) msgs0 - let (_, m) := p - match h: m with - | betree_message_t.Insert prev => - do - let v ← betree_upsert_update_fwd (Option.some prev) s - let msgs1 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Insert v) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Delete => - do - let v ← betree_upsert_update_fwd Option.none s - let msgs1 ← - betree_list_pop_front_back (UInt64 × betree_message_t) msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Insert v) - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | betree_message_t.Upsert ufs => - do - let msgs1 ← - betree_node_lookup_first_message_after_key_fwd key msgs0 - let msgs2 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) - msgs1 (key, betree_message_t.Upsert s) - let msgs3 ← - betree_node_lookup_first_message_after_key_back key msgs0 msgs2 - betree_node_lookup_first_message_for_key_back key msgs msgs3 - else - do - let msgs1 ← - betree_list_push_front_fwd_back (UInt64 × betree_message_t) msgs0 - (key, new_msg) - betree_node_lookup_first_message_for_key_back key msgs msgs1 - -/- [betree_main::betree::Node::{5}::apply_messages_to_internal] -/ -def betree_node_apply_messages_to_internal_fwd_back - (msgs : betree_list_t (UInt64 × betree_message_t)) - (new_msgs : betree_list_t (UInt64 × betree_message_t)) : - (Result (betree_list_t (UInt64 × betree_message_t))) - := - match h: new_msgs with - | betree_list_t.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let msgs0 ← betree_node_apply_to_internal_fwd_back msgs i m - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl - | betree_list_t.Nil => Result.ret msgs -termination_by betree_node_apply_messages_to_internal_fwd_back msgs new_msgs => - betree_node_apply_messages_to_internal_terminates msgs new_msgs -decreasing_by betree_node_apply_messages_to_internal_decreases msgs new_msgs - -/- [betree_main::betree::Node::{5}::apply_messages] -/ -mutual def betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (State × Unit)) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, content) ← betree_load_internal_node_fwd i st - let content0 ← - betree_node_apply_messages_to_internal_fwd_back content msgs - let num_msgs ← - betree_list_len_fwd (UInt64 × betree_message_t) content0 - if h: num_msgs >= params.betree_params_min_flush_size - then - do - let (st1, content1) ← - betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (node0, _) ← - betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (mkbetree_internal_t i1 _ _ _) := node0 - let (st2, _) ← betree_store_internal_node_fwd i1 content1 st1 - Result.ret (st2, ()) - else - do - let (st1, _) ← betree_store_internal_node_fwd i content0 st0 - Result.ret (st1, ()) - | betree_node_t.Leaf node => - do - let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs - let len ← betree_list_len_fwd (UInt64 × UInt64) content0 - let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit)) - params.betree_params_split_size - if h: len >= i - then - do - let (st1, _) ← - betree_leaf_split_fwd node content0 params node_id_cnt st0 - let (st2, _) ← - betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil - st1 - Result.ret (st2, ()) - else - do - let (st1, _) ← - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - Result.ret (st1, ()) -termination_by betree_node_apply_messages_fwd self params node_id_cnt msgs st - => - betree_node_apply_messages_terminates self params node_id_cnt msgs st -decreasing_by - betree_node_apply_messages_decreases self params node_id_cnt msgs st - -/- [betree_main::betree::Node::{5}::apply_messages] -/ -def betree_node_apply_messages_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (betree_node_t × betree_node_id_counter_t)) - := - match h: self with - | betree_node_t.Internal node => - do - let (mkbetree_internal_t i i0 n n0) := node - let (st0, content) ← betree_load_internal_node_fwd i st - let content0 ← - betree_node_apply_messages_to_internal_fwd_back content msgs - let num_msgs ← - betree_list_len_fwd (UInt64 × betree_message_t) content0 - if h: num_msgs >= params.betree_params_min_flush_size - then - do - let (st1, content1) ← - betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (node0, node_id_cnt0) ← - betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params - node_id_cnt content0 st0 - let (mkbetree_internal_t i1 i2 n1 n2) := node0 - let _ ← betree_store_internal_node_fwd i1 content1 st1 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 n2), - node_id_cnt0) - else - do - let _ ← betree_store_internal_node_fwd i content0 st0 - Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n n0), - node_id_cnt) - | betree_node_t.Leaf node => - do - let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st - let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs - let len ← betree_list_len_fwd (UInt64 × UInt64) content0 - let i ← UInt64.checked_mul (UInt64.ofNatCore 2 (by intlit)) - params.betree_params_split_size - if h: len >= i - then - do - let (st1, new_node) ← - betree_leaf_split_fwd node content0 params node_id_cnt st0 - let _ ← - betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil - st1 - let node_id_cnt0 ← - betree_leaf_split_back node content0 params node_id_cnt st0 - Result.ret (betree_node_t.Internal new_node, node_id_cnt0) - else - do - let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - Result.ret (betree_node_t.Leaf { node with betree_leaf_size := len }, - node_id_cnt) -termination_by betree_node_apply_messages_back self params node_id_cnt msgs st - => - betree_node_apply_messages_terminates self params node_id_cnt msgs st -decreasing_by - betree_node_apply_messages_decreases self params node_id_cnt msgs st - -/- [betree_main::betree::Internal::{4}::flush] -/ -def betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (State × (betree_list_t (UInt64 × betree_message_t)))) - := - do - let (mkbetree_internal_t _ i n n0) := self - let p ← betree_list_partition_at_pivot_fwd betree_message_t content i - let (msgs_left, msgs_right) := p - let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left - if h: len_left >= params.betree_params_min_flush_size - then - do - let (st0, _) ← - betree_node_apply_messages_fwd n params node_id_cnt msgs_left st - let (_, node_id_cnt0) ← - betree_node_apply_messages_back n params node_id_cnt msgs_left st - let len_right ← - betree_list_len_fwd (UInt64 × betree_message_t) msgs_right - if h: len_right >= params.betree_params_min_flush_size - then - do - let (st1, _) ← - betree_node_apply_messages_fwd n0 params node_id_cnt0 msgs_right - st0 - let _ ← - betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right - st0 - Result.ret (st1, betree_list_t.Nil) - else Result.ret (st0, msgs_right) - else - do - let (st0, _) ← - betree_node_apply_messages_fwd n0 params node_id_cnt msgs_right st - let _ ← - betree_node_apply_messages_back n0 params node_id_cnt msgs_right st - Result.ret (st0, msgs_left) -termination_by betree_internal_flush_fwd self params node_id_cnt content st => - betree_internal_flush_terminates self params node_id_cnt content st -decreasing_by - betree_internal_flush_decreases self params node_id_cnt content st - -/- [betree_main::betree::Internal::{4}::flush] -/ -def betree_internal_flush_back - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (UInt64 × betree_message_t)) (st : State) : - (Result (betree_internal_t × betree_node_id_counter_t)) - := - do - let (mkbetree_internal_t i i0 n n0) := self - let p ← betree_list_partition_at_pivot_fwd betree_message_t content i0 - let (msgs_left, msgs_right) := p - let len_left ← betree_list_len_fwd (UInt64 × betree_message_t) msgs_left - if h: len_left >= params.betree_params_min_flush_size - then - do - let (st0, _) ← - betree_node_apply_messages_fwd n params node_id_cnt msgs_left st - let (n1, node_id_cnt0) ← - betree_node_apply_messages_back n params node_id_cnt msgs_left st - let len_right ← - betree_list_len_fwd (UInt64 × betree_message_t) msgs_right - if h: len_right >= params.betree_params_min_flush_size - then - do - let (n2, node_id_cnt1) ← - betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right - st0 - Result.ret (mkbetree_internal_t i i0 n1 n2, node_id_cnt1) - else Result.ret (mkbetree_internal_t i i0 n1 n0, node_id_cnt0) - else - do - let (n1, node_id_cnt0) ← - betree_node_apply_messages_back n0 params node_id_cnt msgs_right st - Result.ret (mkbetree_internal_t i i0 n n1, node_id_cnt0) -termination_by betree_internal_flush_back self params node_id_cnt content st => - betree_internal_flush_terminates self params node_id_cnt content st -decreasing_by - betree_internal_flush_decreases self params node_id_cnt content st - -/- [betree_main::betree::Node::{5}::apply] -/ -def betree_node_apply_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : UInt64) - (new_msg : betree_message_t) (st : State) : - Result (State × Unit) - := - do - let l := betree_list_t.Nil - let (st0, _) ← - betree_node_apply_messages_fwd self params node_id_cnt - (betree_list_t.Cons (key, new_msg) l) st - let _ ← - betree_node_apply_messages_back self params node_id_cnt - (betree_list_t.Cons (key, new_msg) l) st - Result.ret (st0, ()) - -/- [betree_main::betree::Node::{5}::apply] -/ -def betree_node_apply_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : UInt64) - (new_msg : betree_message_t) (st : State) : - Result (betree_node_t × betree_node_id_counter_t) - := - let l := betree_list_t.Nil - betree_node_apply_messages_back self params node_id_cnt (betree_list_t.Cons - (key, new_msg) l) st - -/- [betree_main::betree::BeTree::{6}::new] -/ -def betree_be_tree_new_fwd - (min_flush_size : UInt64) (split_size : UInt64) (st : State) : - Result (State × betree_be_tree_t) - := - do - let node_id_cnt ← betree_node_id_counter_new_fwd - let id ← betree_node_id_counter_fresh_id_fwd node_id_cnt - let (st0, _) ← betree_store_leaf_node_fwd id betree_list_t.Nil st - let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt - Result.ret (st0, - { - betree_be_tree_params := - { - betree_params_min_flush_size := min_flush_size, - betree_params_split_size := split_size - }, - betree_be_tree_node_id_cnt := node_id_cnt0, - betree_be_tree_root := - (betree_node_t.Leaf - { - betree_leaf_id := id, - betree_leaf_size := (UInt64.ofNatCore 0 (by intlit)) - }) - }) - -/- [betree_main::betree::BeTree::{6}::apply] -/ -def betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st - let _ ← - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::apply] -/ -def betree_be_tree_apply_back - (self : betree_be_tree_t) (key : UInt64) (msg : betree_message_t) - (st : State) : - Result betree_be_tree_t - := - do - let (n, nic) ← - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st - Result.ret - { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n } - -/- [betree_main::betree::BeTree::{6}::insert] -/ -def betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key (betree_message_t.Insert value) st - let _ ← - betree_be_tree_apply_back self key (betree_message_t.Insert value) st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::insert] -/ -def betree_be_tree_insert_back - (self : betree_be_tree_t) (key : UInt64) (value : UInt64) (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key (betree_message_t.Insert value) st - -/- [betree_main::betree::BeTree::{6}::delete] -/ -def betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key betree_message_t.Delete st - let _ ← betree_be_tree_apply_back self key betree_message_t.Delete st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::delete] -/ -def betree_be_tree_delete_back - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key betree_message_t.Delete st - -/- [betree_main::betree::BeTree::{6}::upsert] -/ -def betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t) - (st : State) : - Result (State × Unit) - := - do - let (st0, _) ← - betree_be_tree_apply_fwd self key (betree_message_t.Upsert upd) st - let _ ← - betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st - Result.ret (st0, ()) - -/- [betree_main::betree::BeTree::{6}::upsert] -/ -def betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : UInt64) (upd : betree_upsert_fun_state_t) - (st : State) : - Result betree_be_tree_t - := - betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st - -/- [betree_main::betree::BeTree::{6}::lookup] -/ -def betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result (State × (Option UInt64)) - := - betree_node_lookup_fwd self.betree_be_tree_root key st - -/- [betree_main::betree::BeTree::{6}::lookup] -/ -def betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : UInt64) (st : State) : - Result betree_be_tree_t - := - do - let n ← betree_node_lookup_back self.betree_be_tree_root key st - Result.ret { self with betree_be_tree_root := n } - -/- [betree_main::main] -/ -def main_fwd : Result Unit := - Result.ret () - -/- Unit test for [betree_main::main] -/ -#assert (main_fwd == .ret ()) - diff --git a/tests/lean/betree/BetreeMain/Opaque.lean b/tests/lean/betree/BetreeMain/Opaque.lean deleted file mode 100644 index b3db37c2..00000000 --- a/tests/lean/betree/BetreeMain/Opaque.lean +++ /dev/null @@ -1,33 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: opaque function definitions -import Base.Primitives -import BetreeMain.Types - -structure OpaqueDefs where - - /- [betree_main::betree_utils::load_internal_node] -/ - betree_utils_load_internal_node_fwd - : - UInt64 -> State -> Result (State × (betree_list_t (UInt64 × - betree_message_t))) - - /- [betree_main::betree_utils::store_internal_node] -/ - betree_utils_store_internal_node_fwd - : - UInt64 -> betree_list_t (UInt64 × betree_message_t) -> State -> Result - (State × Unit) - - /- [betree_main::betree_utils::load_leaf_node] -/ - betree_utils_load_leaf_node_fwd - : UInt64 -> State -> Result (State × (betree_list_t (UInt64 × UInt64))) - - /- [betree_main::betree_utils::store_leaf_node] -/ - betree_utils_store_leaf_node_fwd - : - UInt64 -> betree_list_t (UInt64 × UInt64) -> State -> Result (State × - Unit) - - /- [core::option::Option::{0}::unwrap] -/ - core_option_option_unwrap_fwd - (T : Type) : Option T -> State -> Result (State × T) - diff --git a/tests/lean/betree/BetreeMain/Types.lean b/tests/lean/betree/BetreeMain/Types.lean deleted file mode 100644 index 32634e30..00000000 --- a/tests/lean/betree/BetreeMain/Types.lean +++ /dev/null @@ -1,55 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: type definitions -import Base.Primitives - -/- [betree_main::betree::List] -/ -inductive betree_list_t (T : Type) := -| Cons : T -> betree_list_t T -> betree_list_t T -| Nil : betree_list_t T - -/- [betree_main::betree::UpsertFunState] -/ -inductive betree_upsert_fun_state_t := -| Add : UInt64 -> betree_upsert_fun_state_t -| Sub : UInt64 -> betree_upsert_fun_state_t - -/- [betree_main::betree::Message] -/ -inductive betree_message_t := -| Insert : UInt64 -> betree_message_t -| Delete : betree_message_t -| Upsert : betree_upsert_fun_state_t -> betree_message_t - -/- [betree_main::betree::Leaf] -/ -structure betree_leaf_t where - betree_leaf_id : UInt64 - betree_leaf_size : UInt64 - -/- [betree_main::betree::Node] -/ -mutual inductive betree_node_t := -| Internal : betree_internal_t -> betree_node_t -| Leaf : betree_leaf_t -> betree_node_t - -/- [betree_main::betree::Internal] -/ -inductive betree_internal_t := - betree_internal_id : UInt64 - betree_internal_pivot : UInt64 - betree_internal_left : betree_node_t - betree_internal_right : betree_node_t - -/- [betree_main::betree::Params] -/ -structure betree_params_t where - betree_params_min_flush_size : UInt64 - betree_params_split_size : UInt64 - -/- [betree_main::betree::NodeIdCounter] -/ -structure betree_node_id_counter_t where - betree_node_id_counter_next_node_id : UInt64 - -/- [betree_main::betree::BeTree] -/ -structure betree_be_tree_t where - betree_be_tree_params : betree_params_t - betree_be_tree_node_id_cnt : betree_node_id_counter_t - betree_be_tree_root : betree_node_t - -/- The state type used in the state-error monad -/ -axiom State : Type - diff --git a/tests/lean/betree/lake-manifest.json b/tests/lean/betree/lake-manifest.json deleted file mode 100644 index 57b071ca..00000000 --- a/tests/lean/betree/lake-manifest.json +++ /dev/null @@ -1,27 +0,0 @@ -{"version": 4, - "packagesDir": "./lake-packages", - "packages": - [{"git": - {"url": "https://github.com/leanprover-community/mathlib4.git", - "subDir?": null, - "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece", - "name": "mathlib", - "inputRev?": null}}, - {"git": - {"url": "https://github.com/gebner/quote4", - "subDir?": null, - "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa", - "name": "Qq", - "inputRev?": "master"}}, - {"git": - {"url": "https://github.com/JLimperg/aesop", - "subDir?": null, - "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690", - "name": "aesop", - "inputRev?": "master"}}, - {"git": - {"url": "https://github.com/leanprover/std4", - "subDir?": null, - "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee", - "name": "std", - "inputRev?": "main"}}]} diff --git a/tests/lean/betree/lakefile.lean b/tests/lean/betree/lakefile.lean deleted file mode 100644 index ac2cc2d8..00000000 --- a/tests/lean/betree/lakefile.lean +++ /dev/null @@ -1,12 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «betree_main» {} - -lean_lib «Base» {} - -@[default_target] -lean_lib «BetreeMain» {} diff --git a/tests/lean/betree/lean-toolchain b/tests/lean/betree/lean-toolchain deleted file mode 100644 index bbf57f10..00000000 --- a/tests/lean/betree/lean-toolchain +++ /dev/null @@ -1 +0,0 @@ -leanprover/lean4:nightly-2023-01-21 diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/hashmap/Base/Primitives.lean +++ b/tests/lean/hashmap/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean index fad5c11a..197b0a6a 100644 --- a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean +++ b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean @@ -1,11 +1,11 @@ --- [hashmap]: the decreases clauses +-- [hashmap]: templates for the decreases clauses import Base.Primitives import Hashmap.Types /- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/ @[simp] def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T)) - (n : USize) := + (n : Usize) := (slots, n) /- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/ @@ -16,7 +16,7 @@ macro_rules /- [hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T)) - (i : USize) := + (i : Usize) := (slots, i) /- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/ @@ -26,7 +26,7 @@ macro_rules /- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/ @[simp] -def hash_map_insert_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize) (value : T) (ls : list_t T) := (key, value, ls) @@ -51,7 +51,7 @@ macro_rules /- [hashmap::HashMap::{0}::move_elements]: termination measure -/ @[simp] def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T) - (slots : Vec (list_t T)) (i : USize) := + (slots : Vec (list_t T)) (i : Usize) := (ntable, slots, i) /- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/ @@ -62,7 +62,7 @@ macro_rules /- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/ @[simp] -def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) @@ -74,7 +74,7 @@ macro_rules /- [hashmap::HashMap::{0}::get_in_list]: termination measure -/ @[simp] -def hash_map_get_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) @@ -86,7 +86,7 @@ macro_rules /- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/ @[simp] def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T) - (key : USize) := + (key : Usize) := (ls, key) /- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/ @@ -96,7 +96,7 @@ macro_rules /- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/ @[simp] -def hash_map_remove_from_list_loop_terminates (T : Type) (key : USize) +def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean index 7ba079f2..560592c8 100644 --- a/tests/lean/hashmap/Hashmap/Clauses/Template.lean +++ b/tests/lean/hashmap/Hashmap/Clauses/Template.lean @@ -6,7 +6,7 @@ import Hashmap.Types /- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/ @[simp] def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T)) - (n : USize) := + (n : Usize) := (slots, n) /- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/ @@ -17,7 +17,7 @@ macro_rules /- [hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T)) - (i : USize) := + (i : Usize) := (slots, i) /- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/ @@ -27,7 +27,7 @@ macro_rules /- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/ @[simp] -def hash_map_insert_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize) (value : T) (ls : list_t T) := (key, value, ls) @@ -52,7 +52,7 @@ macro_rules /- [hashmap::HashMap::{0}::move_elements]: termination measure -/ @[simp] def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T) - (slots : Vec (list_t T)) (i : USize) := + (slots : Vec (list_t T)) (i : Usize) := (ntable, slots, i) /- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/ @@ -63,7 +63,7 @@ macro_rules /- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/ @[simp] -def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) @@ -75,7 +75,7 @@ macro_rules /- [hashmap::HashMap::{0}::get_in_list]: termination measure -/ @[simp] -def hash_map_get_in_list_loop_terminates (T : Type) (key : USize) +def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) @@ -87,7 +87,7 @@ macro_rules /- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/ @[simp] def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T) - (key : USize) := + (key : Usize) := (ls, key) /- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/ @@ -97,7 +97,7 @@ macro_rules /- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/ @[simp] -def hash_map_remove_from_list_loop_terminates (T : Type) (key : USize) +def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize) (ls : list_t T) := (key, ls) diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean index 535ac9b2..77b1a157 100644 --- a/tests/lean/hashmap/Hashmap/Funs.lean +++ b/tests/lean/hashmap/Hashmap/Funs.lean @@ -5,19 +5,19 @@ import Hashmap.Types import Hashmap.Clauses.Clauses /- [hashmap::hash_key] -/ -def hash_key_fwd (k : USize) : Result USize := +def hash_key_fwd (k : Usize) : Result Usize := Result.ret k /- [hashmap::HashMap::{0}::allocate_slots] -/ def hash_map_allocate_slots_loop_fwd - (T : Type) (slots : Vec (list_t T)) (n : USize) : + (T : Type) (slots : Vec (list_t T)) (n : Usize) : (Result (Vec (list_t T))) := - if h: n > (USize.ofNatCore 0 (by intlit)) + if h: n > (Usize.ofInt 0 (by intlit)) then do let slots0 ← vec_push_back (list_t T) slots list_t.Nil - let n0 ← USize.checked_sub n (USize.ofNatCore 1 (by intlit)) + let n0 ← n - (Usize.ofInt 1 (by intlit)) hash_map_allocate_slots_loop_fwd T slots0 n0 else Result.ret slots termination_by hash_map_allocate_slots_loop_fwd slots n => @@ -26,23 +26,23 @@ decreasing_by hash_map_allocate_slots_loop_decreases slots n /- [hashmap::HashMap::{0}::allocate_slots] -/ def hash_map_allocate_slots_fwd - (T : Type) (slots : Vec (list_t T)) (n : USize) : Result (Vec (list_t T)) := + (T : Type) (slots : Vec (list_t T)) (n : Usize) : Result (Vec (list_t T)) := hash_map_allocate_slots_loop_fwd T slots n /- [hashmap::HashMap::{0}::new_with_capacity] -/ def hash_map_new_with_capacity_fwd - (T : Type) (capacity : USize) (max_load_dividend : USize) - (max_load_divisor : USize) : + (T : Type) (capacity : Usize) (max_load_dividend : Usize) + (max_load_divisor : Usize) : Result (hash_map_t T) := do let v := vec_new (list_t T) let slots ← hash_map_allocate_slots_fwd T v capacity - let i ← USize.checked_mul capacity max_load_dividend - let i0 ← USize.checked_div i max_load_divisor + let i ← capacity * max_load_dividend + let i0 ← i / max_load_divisor Result.ret { - hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), + hash_map_num_entries := (Usize.ofInt 0 (by intlit)), hash_map_max_load_factor := (max_load_dividend, max_load_divisor), hash_map_max_load := i0, hash_map_slots := slots @@ -50,19 +50,19 @@ def hash_map_new_with_capacity_fwd /- [hashmap::HashMap::{0}::new] -/ def hash_map_new_fwd (T : Type) : Result (hash_map_t T) := - hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit)) - (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit)) + hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit)) + (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit)) /- [hashmap::HashMap::{0}::clear] -/ def hash_map_clear_loop_fwd_back - (T : Type) (slots : Vec (list_t T)) (i : USize) : + (T : Type) (slots : Vec (list_t T)) (i : Usize) : (Result (Vec (list_t T))) := let i0 := vec_len (list_t T) slots if h: i < i0 then do - let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let i1 ← i + (Usize.ofInt 1 (by intlit)) let slots0 ← vec_index_mut_back (list_t T) slots i list_t.Nil hash_map_clear_loop_fwd_back T slots0 i1 else Result.ret slots @@ -76,22 +76,22 @@ def hash_map_clear_fwd_back do let v ← hash_map_clear_loop_fwd_back T self.hash_map_slots - (USize.ofNatCore 0 (by intlit)) + (Usize.ofInt 0 (by intlit)) Result.ret { self with - hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), + hash_map_num_entries := (Usize.ofInt 0 (by intlit)), hash_map_slots := v } /- [hashmap::HashMap::{0}::len] -/ -def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result USize := +def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result Usize := Result.ret self.hash_map_num_entries /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_loop_fwd - (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result Bool) := + (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result Bool) := match h: ls with | list_t.Cons ckey cvalue tl => if h: ckey = key @@ -104,12 +104,12 @@ decreasing_by hash_map_insert_in_list_loop_decreases key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_fwd - (T : Type) (key : USize) (value : T) (ls : list_t T) : Result Bool := + (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result Bool := hash_map_insert_in_list_loop_fwd T key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_loop_back - (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result (list_t T)) := + (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result (list_t T)) := match h: ls with | list_t.Cons ckey cvalue tl => if h: ckey = key @@ -126,25 +126,24 @@ decreasing_by hash_map_insert_in_list_loop_decreases key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_back - (T : Type) (key : USize) (value : T) (ls : list_t T) : Result (list_t T) := + (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result (list_t T) := hash_map_insert_in_list_loop_back T key value ls /- [hashmap::HashMap::{0}::insert_no_resize] -/ def hash_map_insert_no_resize_fwd_back - (T : Type) (self : hash_map_t T) (key : USize) (value : T) : + (T : Type) (self : hash_map_t T) (key : Usize) (value : T) : Result (hash_map_t T) := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod let inserted ← hash_map_insert_in_list_fwd T key value l if h: inserted then do - let i0 ← USize.checked_add self.hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let i0 ← self.hash_map_num_entries + (Usize.ofInt 1 (by intlit)) let l0 ← hash_map_insert_in_list_back T key value l let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 Result.ret @@ -156,9 +155,9 @@ def hash_map_insert_no_resize_fwd_back Result.ret { self with hash_map_slots := v } /- [core::num::u32::{9}::MAX] -/ -def core_num_u32_max_body : Result UInt32 := - Result.ret (UInt32.ofNatCore 4294967295 (by intlit)) -def core_num_u32_max_c : UInt32 := eval_global core_num_u32_max_body (by simp) +def core_num_u32_max_body : Result U32 := + Result.ret (U32.ofInt 4294967295 (by intlit)) +def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp) /- [hashmap::HashMap::{0}::move_elements_from_list] -/ def hash_map_move_elements_from_list_loop_fwd_back @@ -182,7 +181,7 @@ def hash_map_move_elements_from_list_fwd_back /- [hashmap::HashMap::{0}::move_elements] -/ def hash_map_move_elements_loop_fwd_back - (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : USize) : + (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) : (Result ((hash_map_t T) × (Vec (list_t T)))) := let i0 := vec_len (list_t T) slots @@ -192,7 +191,7 @@ def hash_map_move_elements_loop_fwd_back let l ← vec_index_mut_fwd (list_t T) slots i let ls := mem_replace_fwd (list_t T) l list_t.Nil let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls - let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let i1 ← i + (Usize.ofInt 1 (by intlit)) let l0 := mem_replace_back (list_t T) l list_t.Nil let slots0 ← vec_index_mut_back (list_t T) slots i l0 hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1 @@ -203,7 +202,7 @@ decreasing_by hash_map_move_elements_loop_decreases ntable slots i /- [hashmap::HashMap::{0}::move_elements] -/ def hash_map_move_elements_fwd_back - (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : USize) : + (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) : Result ((hash_map_t T) × (Vec (list_t T))) := hash_map_move_elements_loop_fwd_back T ntable slots i @@ -212,19 +211,19 @@ def hash_map_move_elements_fwd_back def hash_map_try_resize_fwd_back (T : Type) (self : hash_map_t T) : Result (hash_map_t T) := do - let max_usize ← scalar_cast USize core_num_u32_max_c + let max_usize ← Scalar.cast .Usize core_num_u32_max_c let capacity := vec_len (list_t T) self.hash_map_slots - let n1 ← USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) + let n1 ← max_usize / (Usize.ofInt 2 (by intlit)) let (i, i0) := self.hash_map_max_load_factor - let i1 ← USize.checked_div n1 i + let i1 ← n1 / i if h: capacity <= i1 then do - let i2 ← USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) + let i2 ← capacity * (Usize.ofInt 2 (by intlit)) let ntable ← hash_map_new_with_capacity_fwd T i2 i i0 let (ntable0, _) ← hash_map_move_elements_fwd_back T ntable self.hash_map_slots - (USize.ofNatCore 0 (by intlit)) + (Usize.ofInt 0 (by intlit)) Result.ret { ntable0 @@ -236,7 +235,7 @@ def hash_map_try_resize_fwd_back /- [hashmap::HashMap::{0}::insert] -/ def hash_map_insert_fwd_back - (T : Type) (self : hash_map_t T) (key : USize) (value : T) : + (T : Type) (self : hash_map_t T) (key : Usize) (value : T) : Result (hash_map_t T) := do @@ -248,7 +247,7 @@ def hash_map_insert_fwd_back /- [hashmap::HashMap::{0}::contains_key_in_list] -/ def hash_map_contains_key_in_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (Result Bool) := + (T : Type) (key : Usize) (ls : list_t T) : (Result Bool) := match h: ls with | list_t.Cons ckey t tl => if h: ckey = key @@ -261,22 +260,22 @@ decreasing_by hash_map_contains_key_in_list_loop_decreases key ls /- [hashmap::HashMap::{0}::contains_key_in_list] -/ def hash_map_contains_key_in_list_fwd - (T : Type) (key : USize) (ls : list_t T) : Result Bool := + (T : Type) (key : Usize) (ls : list_t T) : Result Bool := hash_map_contains_key_in_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::contains_key] -/ def hash_map_contains_key_fwd - (T : Type) (self : hash_map_t T) (key : USize) : Result Bool := + (T : Type) (self : hash_map_t T) (key : Usize) : Result Bool := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod hash_map_contains_key_in_list_fwd T key l /- [hashmap::HashMap::{0}::get_in_list] -/ def hash_map_get_in_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (Result T) := + (T : Type) (key : Usize) (ls : list_t T) : (Result T) := match h: ls with | list_t.Cons ckey cvalue tl => if h: ckey = key @@ -289,22 +288,22 @@ decreasing_by hash_map_get_in_list_loop_decreases key ls /- [hashmap::HashMap::{0}::get_in_list] -/ def hash_map_get_in_list_fwd - (T : Type) (key : USize) (ls : list_t T) : Result T := + (T : Type) (key : Usize) (ls : list_t T) : Result T := hash_map_get_in_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::get] -/ def hash_map_get_fwd - (T : Type) (self : hash_map_t T) (key : USize) : Result T := + (T : Type) (self : hash_map_t T) (key : Usize) : Result T := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod hash_map_get_in_list_fwd T key l /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_loop_fwd - (T : Type) (ls : list_t T) (key : USize) : (Result T) := + (T : Type) (ls : list_t T) (key : Usize) : (Result T) := match h: ls with | list_t.Cons ckey cvalue tl => if h: ckey = key @@ -317,12 +316,12 @@ decreasing_by hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_fwd - (T : Type) (ls : list_t T) (key : USize) : Result T := + (T : Type) (ls : list_t T) (key : Usize) : Result T := hash_map_get_mut_in_list_loop_fwd T ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_loop_back - (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : (Result (list_t T)) := + (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : (Result (list_t T)) := match h: ls with | list_t.Cons ckey cvalue tl => if h: ckey = key @@ -338,28 +337,28 @@ decreasing_by hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_back - (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : Result (list_t T) := + (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : Result (list_t T) := hash_map_get_mut_in_list_loop_back T ls key ret0 /- [hashmap::HashMap::{0}::get_mut] -/ def hash_map_get_mut_fwd - (T : Type) (self : hash_map_t T) (key : USize) : Result T := + (T : Type) (self : hash_map_t T) (key : Usize) : Result T := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod hash_map_get_mut_in_list_fwd T l key /- [hashmap::HashMap::{0}::get_mut] -/ def hash_map_get_mut_back - (T : Type) (self : hash_map_t T) (key : USize) (ret0 : T) : + (T : Type) (self : hash_map_t T) (key : Usize) (ret0 : T) : Result (hash_map_t T) := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod let l0 ← hash_map_get_mut_in_list_back T l key ret0 let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 @@ -367,7 +366,7 @@ def hash_map_get_mut_back /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (Result (Option T)) := + (T : Type) (key : Usize) (ls : list_t T) : (Result (Option T)) := match h: ls with | list_t.Cons ckey t tl => if h: ckey = key @@ -385,12 +384,12 @@ decreasing_by hash_map_remove_from_list_loop_decreases key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_fwd - (T : Type) (key : USize) (ls : list_t T) : Result (Option T) := + (T : Type) (key : Usize) (ls : list_t T) : Result (Option T) := hash_map_remove_from_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_loop_back - (T : Type) (key : USize) (ls : list_t T) : (Result (list_t T)) := + (T : Type) (key : Usize) (ls : list_t T) : (Result (list_t T)) := match h: ls with | list_t.Cons ckey t tl => if h: ckey = key @@ -411,33 +410,32 @@ decreasing_by hash_map_remove_from_list_loop_decreases key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_back - (T : Type) (key : USize) (ls : list_t T) : Result (list_t T) := + (T : Type) (key : Usize) (ls : list_t T) : Result (list_t T) := hash_map_remove_from_list_loop_back T key ls /- [hashmap::HashMap::{0}::remove] -/ def hash_map_remove_fwd - (T : Type) (self : hash_map_t T) (key : USize) : Result (Option T) := + (T : Type) (self : hash_map_t T) (key : Usize) : Result (Option T) := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod let x ← hash_map_remove_from_list_fwd T key l match h: x with | Option.none => Result.ret Option.none | Option.some x0 => do - let _ ← USize.checked_sub self.hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let _ ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit)) Result.ret (Option.some x0) /- [hashmap::HashMap::{0}::remove] -/ def hash_map_remove_back - (T : Type) (self : hash_map_t T) (key : USize) : Result (hash_map_t T) := + (T : Type) (self : hash_map_t T) (key : Usize) : Result (hash_map_t T) := do let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod let x ← hash_map_remove_from_list_fwd T key l match h: x with @@ -448,8 +446,7 @@ def hash_map_remove_back Result.ret { self with hash_map_slots := v } | Option.some x0 => do - let i0 ← USize.checked_sub self.hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let i0 ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit)) let l0 ← hash_map_remove_from_list_back T key l let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 Result.ret @@ -458,65 +455,59 @@ def hash_map_remove_back /- [hashmap::test1] -/ def test1_fwd : Result Unit := do - let hm ← hash_map_new_fwd UInt64 + let hm ← hash_map_new_fwd U64 let hm0 ← - hash_map_insert_fwd_back UInt64 hm (USize.ofNatCore 0 (by intlit)) - (UInt64.ofNatCore 42 (by intlit)) + hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit)) + (U64.ofInt 42 (by intlit)) let hm1 ← - hash_map_insert_fwd_back UInt64 hm0 (USize.ofNatCore 128 (by intlit)) - (UInt64.ofNatCore 18 (by intlit)) + hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit)) + (U64.ofInt 18 (by intlit)) let hm2 ← - hash_map_insert_fwd_back UInt64 hm1 (USize.ofNatCore 1024 (by intlit)) - (UInt64.ofNatCore 138 (by intlit)) + hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit)) + (U64.ofInt 138 (by intlit)) let hm3 ← - hash_map_insert_fwd_back UInt64 hm2 (USize.ofNatCore 1056 (by intlit)) - (UInt64.ofNatCore 256 (by intlit)) - let i ← hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) - if h: not (i = (UInt64.ofNatCore 18 (by intlit))) + hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit)) + (U64.ofInt 256 (by intlit)) + let i ← hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit)) + if h: not (i = (U64.ofInt 18 (by intlit))) then Result.fail Error.panic else do let hm4 ← - hash_map_get_mut_back UInt64 hm3 (USize.ofNatCore 1024 (by intlit)) - (UInt64.ofNatCore 56 (by intlit)) - let i0 ← - hash_map_get_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit)) - if h: not (i0 = (UInt64.ofNatCore 56 (by intlit))) + hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit)) + (U64.ofInt 56 (by intlit)) + let i0 ← hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit)) + if h: not (i0 = (U64.ofInt 56 (by intlit))) then Result.fail Error.panic else do let x ← - hash_map_remove_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit)) + hash_map_remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit)) match h: x with | Option.none => Result.fail Error.panic | Option.some x0 => - if h: not (x0 = (UInt64.ofNatCore 56 (by intlit))) + if h: not (x0 = (U64.ofInt 56 (by intlit))) then Result.fail Error.panic else do let hm5 ← - hash_map_remove_back UInt64 hm4 - (USize.ofNatCore 1024 (by intlit)) + hash_map_remove_back U64 hm4 (Usize.ofInt 1024 (by intlit)) let i1 ← - hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 0 (by intlit)) - if h: not (i1 = (UInt64.ofNatCore 42 (by intlit))) + hash_map_get_fwd U64 hm5 (Usize.ofInt 0 (by intlit)) + if h: not (i1 = (U64.ofInt 42 (by intlit))) then Result.fail Error.panic else do let i2 ← - hash_map_get_fwd UInt64 hm5 - (USize.ofNatCore 128 (by intlit)) - if h: not (i2 = (UInt64.ofNatCore 18 (by intlit))) + hash_map_get_fwd U64 hm5 (Usize.ofInt 128 (by intlit)) + if h: not (i2 = (U64.ofInt 18 (by intlit))) then Result.fail Error.panic else do let i3 ← - hash_map_get_fwd UInt64 hm5 - (USize.ofNatCore 1056 (by intlit)) - if h: not (i3 = (UInt64.ofNatCore 256 (by intlit))) + hash_map_get_fwd U64 hm5 + (Usize.ofInt 1056 (by intlit)) + if h: not (i3 = (U64.ofInt 256 (by intlit))) then Result.fail Error.panic else Result.ret () -/- Unit test for [hashmap::test1] -/ -#assert (test1_fwd == .ret ()) - diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean index 9e9e5c03..6eabf7da 100644 --- a/tests/lean/hashmap/Hashmap/Types.lean +++ b/tests/lean/hashmap/Hashmap/Types.lean @@ -4,13 +4,13 @@ import Base.Primitives /- [hashmap::List] -/ inductive list_t (T : Type) := -| Cons : USize -> T -> list_t T -> list_t T +| Cons : Usize -> T -> list_t T -> list_t T | Nil : list_t T /- [hashmap::HashMap] -/ structure hash_map_t (T : Type) where - hash_map_num_entries : USize - hash_map_max_load_factor : (USize × USize) - hash_map_max_load : USize + hash_map_num_entries : Usize + hash_map_max_load_factor : (Usize × Usize) + hash_map_max_load : Usize hash_map_slots : Vec (list_t T) diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/hashmap_on_disk/Base/Primitives.lean +++ b/tests/lean/hashmap_on_disk/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean index 1b69eb2f..a4dc996a 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean @@ -1,39 +1,37 @@ --- [hashmap_main]: the decreases clauses import Base.Primitives import HashmapMain.Types /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/ @[simp] def hashmap_hash_map_allocate_slots_loop_terminates (T : Type) - (slots : Vec (hashmap_list_t T)) (n : USize) := + (slots : Vec (hashmap_list_t T)) (n : Usize) := (slots, n) +/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/ syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) => `(tactic| sorry) -/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/ +/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] -def hashmap_hash_map_clear_slots_loop_terminates (T : Type) - (slots : Vec (hashmap_list_t T)) (i : USize) := +def hashmap_hash_map_clear_loop_terminates (T : Type) + (slots : Vec (hashmap_list_t T)) (i : Usize) := (slots, i) -syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic - +/- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/ +syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic macro_rules -| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) => - `(tactic| sorry) +| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/ @[simp] -def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) := (key, value, ls) +/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/ syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) => `(tactic| sorry) @@ -44,8 +42,8 @@ def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) := (ntable, ls) +/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/ syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>`(tactic| sorry) @@ -53,12 +51,12 @@ $ls) =>`(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/ @[simp] def hashmap_hash_map_move_elements_loop_terminates (T : Type) - (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : USize) + (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize) := (ntable, slots, i) +/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/ syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) => `(tactic| sorry) @@ -66,46 +64,46 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/ @[simp] def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type) - (key : USize) (ls : hashmap_list_t T) := + (key : Usize) (ls : hashmap_list_t T) := (key, ls) +/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/ syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) => `(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/ @[simp] -def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize) (ls : hashmap_list_t T) := (key, ls) +/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/ syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/ @[simp] def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type) - (ls : hashmap_list_t T) (key : USize) := + (ls : hashmap_list_t T) (key : Usize) := (ls, key) +/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/ syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) => `(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/ @[simp] -def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize) (ls : hashmap_list_t T) := (key, ls) +/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/ syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic - macro_rules | `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) => `(tactic| sorry) diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean index 753c92ac..33802597 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean @@ -6,7 +6,7 @@ import HashmapMain.Types /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/ @[simp] def hashmap_hash_map_allocate_slots_loop_terminates (T : Type) - (slots : Vec (hashmap_list_t T)) (n : USize) := + (slots : Vec (hashmap_list_t T)) (n : Usize) := (slots, n) /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/ @@ -18,7 +18,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] def hashmap_hash_map_clear_loop_terminates (T : Type) - (slots : Vec (hashmap_list_t T)) (i : USize) := + (slots : Vec (hashmap_list_t T)) (i : Usize) := (slots, i) /- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/ @@ -28,7 +28,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/ @[simp] -def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) := (key, value, ls) @@ -53,7 +53,7 @@ $ls) =>`(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/ @[simp] def hashmap_hash_map_move_elements_loop_terminates (T : Type) - (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : USize) + (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize) := (ntable, slots, i) @@ -66,7 +66,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/ @[simp] def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type) - (key : USize) (ls : hashmap_list_t T) := + (key : Usize) (ls : hashmap_list_t T) := (key, ls) /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/ @@ -77,7 +77,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/ @[simp] -def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize) (ls : hashmap_list_t T) := (key, ls) @@ -89,7 +89,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/ @[simp] def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type) - (ls : hashmap_list_t T) (key : USize) := + (ls : hashmap_list_t T) (key : Usize) := (ls, key) /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/ @@ -100,7 +100,7 @@ macro_rules /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/ @[simp] -def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : USize) +def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize) (ls : hashmap_list_t T) := (key, ls) diff --git a/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean b/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean new file mode 100644 index 00000000..a5103acc --- /dev/null +++ b/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean @@ -0,0 +1,5 @@ +import Base.Primitives +import HashmapMain.Types +import HashmapMain.Opaque + +def opaque_defs : OpaqueDefs := by sorry diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean index 2be03d98..342c3833 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean @@ -2,25 +2,23 @@ -- [hashmap_main]: function definitions import Base.Primitives import HashmapMain.Types -import HashmapMain.Opaque +import HashmapMain.ExternalFuns import HashmapMain.Clauses.Clauses -section variable (opaque_defs: OpaqueDefs) - /- [hashmap_main::hashmap::hash_key] -/ -def hashmap_hash_key_fwd (k : USize) : Result USize := +def hashmap_hash_key_fwd (k : Usize) : Result Usize := Result.ret k /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/ def hashmap_hash_map_allocate_slots_loop_fwd - (T : Type) (slots : Vec (hashmap_list_t T)) (n : USize) : + (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) : (Result (Vec (hashmap_list_t T))) := - if h: n > (USize.ofNatCore 0 (by intlit)) + if h: n > (Usize.ofInt 0 (by intlit)) then do let slots0 ← vec_push_back (hashmap_list_t T) slots hashmap_list_t.Nil - let n0 ← USize.checked_sub n (USize.ofNatCore 1 (by intlit)) + let n0 ← n - (Usize.ofInt 1 (by intlit)) hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0 else Result.ret slots termination_by hashmap_hash_map_allocate_slots_loop_fwd slots n => @@ -29,25 +27,25 @@ decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/ def hashmap_hash_map_allocate_slots_fwd - (T : Type) (slots : Vec (hashmap_list_t T)) (n : USize) : + (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) : Result (Vec (hashmap_list_t T)) := hashmap_hash_map_allocate_slots_loop_fwd T slots n /- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] -/ def hashmap_hash_map_new_with_capacity_fwd - (T : Type) (capacity : USize) (max_load_dividend : USize) - (max_load_divisor : USize) : + (T : Type) (capacity : Usize) (max_load_dividend : Usize) + (max_load_divisor : Usize) : Result (hashmap_hash_map_t T) := do let v := vec_new (hashmap_list_t T) let slots ← hashmap_hash_map_allocate_slots_fwd T v capacity - let i ← USize.checked_mul capacity max_load_dividend - let i0 ← USize.checked_div i max_load_divisor + let i ← capacity * max_load_dividend + let i0 ← i / max_load_divisor Result.ret { - hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), + hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)), hashmap_hash_map_max_load_factor := (max_load_dividend, max_load_divisor), hashmap_hash_map_max_load := i0, @@ -56,19 +54,19 @@ def hashmap_hash_map_new_with_capacity_fwd /- [hashmap_main::hashmap::HashMap::{0}::new] -/ def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) := - hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit)) - (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit)) + hashmap_hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit)) + (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit)) /- [hashmap_main::hashmap::HashMap::{0}::clear] -/ def hashmap_hash_map_clear_loop_fwd_back - (T : Type) (slots : Vec (hashmap_list_t T)) (i : USize) : + (T : Type) (slots : Vec (hashmap_list_t T)) (i : Usize) : (Result (Vec (hashmap_list_t T))) := let i0 := vec_len (hashmap_list_t T) slots if h: i < i0 then do - let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let i1 ← i + (Usize.ofInt 1 (by intlit)) let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i hashmap_list_t.Nil hashmap_hash_map_clear_loop_fwd_back T slots0 i1 @@ -83,23 +81,23 @@ def hashmap_hash_map_clear_fwd_back do let v ← hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots - (USize.ofNatCore 0 (by intlit)) + (Usize.ofInt 0 (by intlit)) Result.ret { self with - hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), + hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)), hashmap_hash_map_slots := v } /- [hashmap_main::hashmap::HashMap::{0}::len] -/ def hashmap_hash_map_len_fwd - (T : Type) (self : hashmap_hash_map_t T) : Result USize := + (T : Type) (self : hashmap_hash_map_t T) : Result Usize := Result.ret self.hashmap_hash_map_num_entries /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/ def hashmap_hash_map_insert_in_list_loop_fwd - (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : + (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : (Result Bool) := match h: ls with @@ -114,12 +112,12 @@ decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/ def hashmap_hash_map_insert_in_list_fwd - (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : Result Bool := + (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result Bool := hashmap_hash_map_insert_in_list_loop_fwd T key value ls /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/ def hashmap_hash_map_insert_in_list_loop_back - (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : + (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : (Result (hashmap_list_t T)) := match h: ls with @@ -139,28 +137,28 @@ decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/ def hashmap_hash_map_insert_in_list_back - (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : + (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result (hashmap_list_t T) := hashmap_hash_map_insert_in_list_loop_back T key value ls /- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/ def hashmap_hash_map_insert_no_resize_fwd_back - (T : Type) (self : hashmap_hash_map_t T) (key : USize) (value : T) : + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) : Result (hashmap_hash_map_t T) := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod let inserted ← hashmap_hash_map_insert_in_list_fwd T key value l if h: inserted then do - let i0 ← USize.checked_add self.hashmap_hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let i0 ← self.hashmap_hash_map_num_entries + + (Usize.ofInt 1 (by intlit)) let l0 ← hashmap_hash_map_insert_in_list_back T key value l let v ← vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots @@ -180,9 +178,9 @@ def hashmap_hash_map_insert_no_resize_fwd_back Result.ret { self with hashmap_hash_map_slots := v } /- [core::num::u32::{9}::MAX] -/ -def core_num_u32_max_body : Result UInt32 := - Result.ret (UInt32.ofNatCore 4294967295 (by intlit)) -def core_num_u32_max_c : UInt32 := eval_global core_num_u32_max_body (by simp) +def core_num_u32_max_body : Result U32 := + Result.ret (U32.ofInt 4294967295 (by intlit)) +def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp) /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/ def hashmap_hash_map_move_elements_from_list_loop_fwd_back @@ -210,7 +208,7 @@ def hashmap_hash_map_move_elements_from_list_fwd_back /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/ def hashmap_hash_map_move_elements_loop_fwd_back (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) - (i : USize) : + (i : Usize) : (Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))) := let i0 := vec_len (hashmap_list_t T) slots @@ -221,7 +219,7 @@ def hashmap_hash_map_move_elements_loop_fwd_back let ls := mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.Nil let ntable0 ← hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls - let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let i1 ← i + (Usize.ofInt 1 (by intlit)) let l0 := mem_replace_back (hashmap_list_t T) l hashmap_list_t.Nil let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i l0 hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1 @@ -233,7 +231,7 @@ decreasing_by hashmap_hash_map_move_elements_loop_decreases ntable slots i /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/ def hashmap_hash_map_move_elements_fwd_back (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) - (i : USize) : + (i : Usize) : Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T))) := hashmap_hash_map_move_elements_loop_fwd_back T ntable slots i @@ -242,19 +240,19 @@ def hashmap_hash_map_move_elements_fwd_back def hashmap_hash_map_try_resize_fwd_back (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) := do - let max_usize ← scalar_cast USize core_num_u32_max_c + let max_usize ← Scalar.cast .Usize core_num_u32_max_c let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let n1 ← USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) + let n1 ← max_usize / (Usize.ofInt 2 (by intlit)) let (i, i0) := self.hashmap_hash_map_max_load_factor - let i1 ← USize.checked_div n1 i + let i1 ← n1 / i if h: capacity <= i1 then do - let i2 ← USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) + let i2 ← capacity * (Usize.ofInt 2 (by intlit)) let ntable ← hashmap_hash_map_new_with_capacity_fwd T i2 i i0 let (ntable0, _) ← hashmap_hash_map_move_elements_fwd_back T ntable - self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit)) + self.hashmap_hash_map_slots (Usize.ofInt 0 (by intlit)) Result.ret { ntable0 @@ -266,7 +264,7 @@ def hashmap_hash_map_try_resize_fwd_back /- [hashmap_main::hashmap::HashMap::{0}::insert] -/ def hashmap_hash_map_insert_fwd_back - (T : Type) (self : hashmap_hash_map_t T) (key : USize) (value : T) : + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) : Result (hashmap_hash_map_t T) := do @@ -278,7 +276,7 @@ def hashmap_hash_map_insert_fwd_back /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/ def hashmap_hash_map_contains_key_in_list_loop_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result Bool) := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result Bool) := match h: ls with | hashmap_list_t.Cons ckey t tl => if h: ckey = key @@ -291,23 +289,23 @@ decreasing_by hashmap_hash_map_contains_key_in_list_loop_decreases key ls /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/ def hashmap_hash_map_contains_key_in_list_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : Result Bool := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result Bool := hashmap_hash_map_contains_key_in_list_loop_fwd T key ls /- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/ def hashmap_hash_map_contains_key_fwd - (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result Bool := + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result Bool := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod hashmap_hash_map_contains_key_in_list_fwd T key l /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/ def hashmap_hash_map_get_in_list_loop_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result T) := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result T) := match h: ls with | hashmap_list_t.Cons ckey cvalue tl => if h: ckey = key @@ -320,23 +318,23 @@ decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/ def hashmap_hash_map_get_in_list_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : Result T := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result T := hashmap_hash_map_get_in_list_loop_fwd T key ls /- [hashmap_main::hashmap::HashMap::{0}::get] -/ def hashmap_hash_map_get_fwd - (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result T := + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod hashmap_hash_map_get_in_list_fwd T key l /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/ def hashmap_hash_map_get_mut_in_list_loop_fwd - (T : Type) (ls : hashmap_list_t T) (key : USize) : (Result T) := + (T : Type) (ls : hashmap_list_t T) (key : Usize) : (Result T) := match h: ls with | hashmap_list_t.Cons ckey cvalue tl => if h: ckey = key @@ -349,12 +347,12 @@ decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/ def hashmap_hash_map_get_mut_in_list_fwd - (T : Type) (ls : hashmap_list_t T) (key : USize) : Result T := + (T : Type) (ls : hashmap_list_t T) (key : Usize) : Result T := hashmap_hash_map_get_mut_in_list_loop_fwd T ls key /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/ def hashmap_hash_map_get_mut_in_list_loop_back - (T : Type) (ls : hashmap_list_t T) (key : USize) (ret0 : T) : + (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) : (Result (hashmap_list_t T)) := match h: ls with @@ -372,31 +370,31 @@ decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/ def hashmap_hash_map_get_mut_in_list_back - (T : Type) (ls : hashmap_list_t T) (key : USize) (ret0 : T) : + (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) : Result (hashmap_list_t T) := hashmap_hash_map_get_mut_in_list_loop_back T ls key ret0 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/ def hashmap_hash_map_get_mut_fwd - (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result T := + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod hashmap_hash_map_get_mut_in_list_fwd T l key /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/ def hashmap_hash_map_get_mut_back - (T : Type) (self : hashmap_hash_map_t T) (key : USize) (ret0 : T) : + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (ret0 : T) : Result (hashmap_hash_map_t T) := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod let l0 ← hashmap_hash_map_get_mut_in_list_back T l key ret0 @@ -407,7 +405,7 @@ def hashmap_hash_map_get_mut_back /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/ def hashmap_hash_map_remove_from_list_loop_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result (Option T)) := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result (Option T)) := match h: ls with | hashmap_list_t.Cons ckey t tl => if h: ckey = key @@ -426,12 +424,12 @@ decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/ def hashmap_hash_map_remove_from_list_fwd - (T : Type) (key : USize) (ls : hashmap_list_t T) : Result (Option T) := + (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (Option T) := hashmap_hash_map_remove_from_list_loop_fwd T key ls /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/ def hashmap_hash_map_remove_from_list_loop_back - (T : Type) (key : USize) (ls : hashmap_list_t T) : + (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result (hashmap_list_t T)) := match h: ls with @@ -455,18 +453,18 @@ decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/ def hashmap_hash_map_remove_from_list_back - (T : Type) (key : USize) (ls : hashmap_list_t T) : + (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (hashmap_list_t T) := hashmap_hash_map_remove_from_list_loop_back T key ls /- [hashmap_main::hashmap::HashMap::{0}::remove] -/ def hashmap_hash_map_remove_fwd - (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result (Option T) := + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result (Option T) := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod let x ← hashmap_hash_map_remove_from_list_fwd T key l @@ -474,19 +472,19 @@ def hashmap_hash_map_remove_fwd | Option.none => Result.ret Option.none | Option.some x0 => do - let _ ← USize.checked_sub self.hashmap_hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let _ ← self.hashmap_hash_map_num_entries - + (Usize.ofInt 1 (by intlit)) Result.ret (Option.some x0) /- [hashmap_main::hashmap::HashMap::{0}::remove] -/ def hashmap_hash_map_remove_back - (T : Type) (self : hashmap_hash_map_t T) (key : USize) : + (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result (hashmap_hash_map_t T) := do let hash ← hashmap_hash_key_fwd key let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots - let hash_mod ← USize.checked_rem hash i + let hash_mod ← hash % i let l ← vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod let x ← hashmap_hash_map_remove_from_list_fwd T key l @@ -500,8 +498,8 @@ def hashmap_hash_map_remove_back Result.ret { self with hashmap_hash_map_slots := v } | Option.some x0 => do - let i0 ← USize.checked_sub self.hashmap_hash_map_num_entries - (USize.ofNatCore 1 (by intlit)) + let i0 ← self.hashmap_hash_map_num_entries - + (Usize.ofInt 1 (by intlit)) let l0 ← hashmap_hash_map_remove_from_list_back T key l let v ← vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots @@ -516,79 +514,73 @@ def hashmap_hash_map_remove_back /- [hashmap_main::hashmap::test1] -/ def hashmap_test1_fwd : Result Unit := do - let hm ← hashmap_hash_map_new_fwd UInt64 + let hm ← hashmap_hash_map_new_fwd U64 let hm0 ← - hashmap_hash_map_insert_fwd_back UInt64 hm - (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit)) + hashmap_hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit)) + (U64.ofInt 42 (by intlit)) let hm1 ← - hashmap_hash_map_insert_fwd_back UInt64 hm0 - (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit)) + hashmap_hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit)) + (U64.ofInt 18 (by intlit)) let hm2 ← - hashmap_hash_map_insert_fwd_back UInt64 hm1 - (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit)) + hashmap_hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit)) + (U64.ofInt 138 (by intlit)) let hm3 ← - hashmap_hash_map_insert_fwd_back UInt64 hm2 - (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit)) - let i ← - hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) - if h: not (i = (UInt64.ofNatCore 18 (by intlit))) + hashmap_hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit)) + (U64.ofInt 256 (by intlit)) + let i ← hashmap_hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit)) + if h: not (i = (U64.ofInt 18 (by intlit))) then Result.fail Error.panic else do let hm4 ← - hashmap_hash_map_get_mut_back UInt64 hm3 - (USize.ofNatCore 1024 (by intlit)) - (UInt64.ofNatCore 56 (by intlit)) + hashmap_hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit)) + (U64.ofInt 56 (by intlit)) let i0 ← - hashmap_hash_map_get_fwd UInt64 hm4 - (USize.ofNatCore 1024 (by intlit)) - if h: not (i0 = (UInt64.ofNatCore 56 (by intlit))) + hashmap_hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit)) + if h: not (i0 = (U64.ofInt 56 (by intlit))) then Result.fail Error.panic else do let x ← - hashmap_hash_map_remove_fwd UInt64 hm4 - (USize.ofNatCore 1024 (by intlit)) + hashmap_hash_map_remove_fwd U64 hm4 + (Usize.ofInt 1024 (by intlit)) match h: x with | Option.none => Result.fail Error.panic | Option.some x0 => - if h: not (x0 = (UInt64.ofNatCore 56 (by intlit))) + if h: not (x0 = (U64.ofInt 56 (by intlit))) then Result.fail Error.panic else do let hm5 ← - hashmap_hash_map_remove_back UInt64 hm4 - (USize.ofNatCore 1024 (by intlit)) + hashmap_hash_map_remove_back U64 hm4 + (Usize.ofInt 1024 (by intlit)) let i1 ← - hashmap_hash_map_get_fwd UInt64 hm5 - (USize.ofNatCore 0 (by intlit)) - if h: not (i1 = (UInt64.ofNatCore 42 (by intlit))) + hashmap_hash_map_get_fwd U64 hm5 + (Usize.ofInt 0 (by intlit)) + if h: not (i1 = (U64.ofInt 42 (by intlit))) then Result.fail Error.panic else do let i2 ← - hashmap_hash_map_get_fwd UInt64 hm5 - (USize.ofNatCore 128 (by intlit)) - if h: not (i2 = (UInt64.ofNatCore 18 (by intlit))) + hashmap_hash_map_get_fwd U64 hm5 + (Usize.ofInt 128 (by intlit)) + if h: not (i2 = (U64.ofInt 18 (by intlit))) then Result.fail Error.panic else do let i3 ← - hashmap_hash_map_get_fwd UInt64 hm5 - (USize.ofNatCore 1056 (by intlit)) - if h: not (i3 = (UInt64.ofNatCore 256 (by intlit))) + hashmap_hash_map_get_fwd U64 hm5 + (Usize.ofInt 1056 (by intlit)) + if h: not (i3 = (U64.ofInt 256 (by intlit))) then Result.fail Error.panic else Result.ret () -/- Unit test for [hashmap_main::hashmap::test1] -/ -#assert (hashmap_test1_fwd == .ret ()) - /- [hashmap_main::insert_on_disk] -/ def insert_on_disk_fwd - (key : USize) (value : UInt64) (st : State) : Result (State × Unit) := + (key : Usize) (value : U64) (st : State) : Result (State × Unit) := do let (st0, hm) ← opaque_defs.hashmap_utils_deserialize_fwd st - let hm0 ← hashmap_hash_map_insert_fwd_back UInt64 hm key value + let hm0 ← hashmap_hash_map_insert_fwd_back U64 hm key value let (st1, _) ← opaque_defs.hashmap_utils_serialize_fwd hm0 st0 Result.ret (st1, ()) @@ -596,6 +588,3 @@ def insert_on_disk_fwd def main_fwd : Result Unit := Result.ret () -/- Unit test for [hashmap_main::main] -/ -#assert (main_fwd == .ret ()) - diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean b/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean index 3531e6e0..d98f431a 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean @@ -7,9 +7,9 @@ structure OpaqueDefs where /- [hashmap_main::hashmap_utils::deserialize] -/ hashmap_utils_deserialize_fwd - : State -> Result (State × (hashmap_hash_map_t UInt64)) + : State -> Result (State × (hashmap_hash_map_t U64)) /- [hashmap_main::hashmap_utils::serialize] -/ hashmap_utils_serialize_fwd - : hashmap_hash_map_t UInt64 -> State -> Result (State × Unit) + : hashmap_hash_map_t U64 -> State -> Result (State × Unit) diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean index 989dd2a9..0509fbbd 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean @@ -4,14 +4,14 @@ import Base.Primitives /- [hashmap_main::hashmap::List] -/ inductive hashmap_list_t (T : Type) := -| Cons : USize -> T -> hashmap_list_t T -> hashmap_list_t T +| Cons : Usize -> T -> hashmap_list_t T -> hashmap_list_t T | Nil : hashmap_list_t T /- [hashmap_main::hashmap::HashMap] -/ structure hashmap_hash_map_t (T : Type) where - hashmap_hash_map_num_entries : USize - hashmap_hash_map_max_load_factor : (USize × USize) - hashmap_hash_map_max_load : USize + hashmap_hash_map_num_entries : Usize + hashmap_hash_map_max_load_factor : (Usize × Usize) + hashmap_hash_map_max_load : Usize hashmap_hash_map_slots : Vec (hashmap_list_t T) /- The state type used in the state-error monad -/ diff --git a/tests/lean/misc-constants/Base/Primitives.lean b/tests/lean/misc-constants/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-constants/Base/Primitives.lean +++ b/tests/lean/misc-constants/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-constants/Constants.lean b/tests/lean/misc-constants/Constants.lean index 937a15e5..8306ed85 100644 --- a/tests/lean/misc-constants/Constants.lean +++ b/tests/lean/misc-constants/Constants.lean @@ -2,143 +2,130 @@ -- [constants] import Base.Primitives -structure OpaqueDefs where - - /- [constants::X0] -/ - def x0_body : Result UInt32 := Result.ret (UInt32.ofNatCore 0 (by intlit)) - def x0_c : UInt32 := eval_global x0_body (by simp) - - /- [core::num::u32::{9}::MAX] -/ - def core_num_u32_max_body : Result UInt32 := - Result.ret (UInt32.ofNatCore 4294967295 (by intlit)) - def core_num_u32_max_c : UInt32 := - eval_global core_num_u32_max_body (by simp) - - /- [constants::X1] -/ - def x1_body : Result UInt32 := Result.ret core_num_u32_max_c - def x1_c : UInt32 := eval_global x1_body (by simp) - - /- [constants::X2] -/ - def x2_body : Result UInt32 := Result.ret (UInt32.ofNatCore 3 (by intlit)) - def x2_c : UInt32 := eval_global x2_body (by simp) - - /- [constants::incr] -/ - def incr_fwd (n : UInt32) : Result UInt32 := - UInt32.checked_add n (UInt32.ofNatCore 1 (by intlit)) - - /- [constants::X3] -/ - def x3_body : Result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit)) - def x3_c : UInt32 := eval_global x3_body (by simp) - - /- [constants::mk_pair0] -/ - def mk_pair0_fwd (x : UInt32) (y : UInt32) : Result (UInt32 × UInt32) := - Result.ret (x, y) - - /- [constants::Pair] -/ - structure pair_t (T1 T2 : Type) where - pair_x : T1 - pair_y : T2 - - /- [constants::mk_pair1] -/ - def mk_pair1_fwd (x : UInt32) (y : UInt32) : Result (pair_t UInt32 UInt32) := - Result.ret { pair_x := x, pair_y := y } - - /- [constants::P0] -/ - def p0_body : Result (UInt32 × UInt32) := - mk_pair0_fwd (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 1 (by intlit)) - def p0_c : (UInt32 × UInt32) := eval_global p0_body (by simp) - - /- [constants::P1] -/ - def p1_body : Result (pair_t UInt32 UInt32) := - mk_pair1_fwd (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 1 (by intlit)) - def p1_c : pair_t UInt32 UInt32 := eval_global p1_body (by simp) - - /- [constants::P2] -/ - def p2_body : Result (UInt32 × UInt32) := - Result.ret - ((UInt32.ofNatCore 0 (by intlit)), - (UInt32.ofNatCore 1 (by intlit))) - def p2_c : (UInt32 × UInt32) := eval_global p2_body (by simp) - - /- [constants::P3] -/ - def p3_body : Result (pair_t UInt32 UInt32) := - Result.ret - { - pair_x := (UInt32.ofNatCore 0 (by intlit)), - pair_y := (UInt32.ofNatCore 1 (by intlit)) - } - def p3_c : pair_t UInt32 UInt32 := eval_global p3_body (by simp) - - /- [constants::Wrap] -/ - structure wrap_t (T : Type) where - wrap_val : T - - /- [constants::Wrap::{0}::new] -/ - def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) := - Result.ret { wrap_val := val } - - /- [constants::Y] -/ - def y_body : Result (wrap_t Int32) := - wrap_new_fwd Int32 (Int32.ofNatCore 2 (by intlit)) - def y_c : wrap_t Int32 := eval_global y_body (by simp) - - /- [constants::unwrap_y] -/ - def unwrap_y_fwd : Result Int32 := - Result.ret y_c.wrap_val - - /- [constants::YVAL] -/ - def yval_body : Result Int32 := unwrap_y_fwd - def yval_c : Int32 := eval_global yval_body (by simp) - - /- [constants::get_z1::Z1] -/ - def get_z1_z1_body : Result Int32 := - Result.ret (Int32.ofNatCore 3 (by intlit)) - def get_z1_z1_c : Int32 := eval_global get_z1_z1_body (by simp) - - /- [constants::get_z1] -/ - def get_z1_fwd : Result Int32 := - Result.ret get_z1_z1_c - - /- [constants::add] -/ - def add_fwd (a : Int32) (b : Int32) : Result Int32 := - Int32.checked_add a b - - /- [constants::Q1] -/ - def q1_body : Result Int32 := Result.ret (Int32.ofNatCore 5 (by intlit)) - def q1_c : Int32 := eval_global q1_body (by simp) - - /- [constants::Q2] -/ - def q2_body : Result Int32 := Result.ret q1_c - def q2_c : Int32 := eval_global q2_body (by simp) - - /- [constants::Q3] -/ - def q3_body : Result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit)) - def q3_c : Int32 := eval_global q3_body (by simp) - - /- [constants::get_z2] -/ - def get_z2_fwd : Result Int32 := - do - let i ← get_z1_fwd - let i0 ← add_fwd i q3_c - add_fwd q1_c i0 - - /- [constants::S1] -/ - def s1_body : Result UInt32 := Result.ret (UInt32.ofNatCore 6 (by intlit)) - def s1_c : UInt32 := eval_global s1_body (by simp) - - /- [constants::S2] -/ - def s2_body : Result UInt32 := incr_fwd s1_c - def s2_c : UInt32 := eval_global s2_body (by simp) - - /- [constants::S3] -/ - def s3_body : Result (pair_t UInt32 UInt32) := Result.ret p3_c - def s3_c : pair_t UInt32 UInt32 := eval_global s3_body (by simp) - - /- [constants::S4] -/ - def s4_body : Result (pair_t UInt32 UInt32) := - mk_pair1_fwd (UInt32.ofNatCore 7 (by intlit)) - (UInt32.ofNatCore 8 (by intlit)) - def s4_c : pair_t UInt32 UInt32 := eval_global s4_body (by simp) - +/- [constants::X0] -/ +def x0_body : Result U32 := Result.ret (U32.ofInt 0 (by intlit)) +def x0_c : U32 := eval_global x0_body (by simp) + +/- [core::num::u32::{9}::MAX] -/ +def core_num_u32_max_body : Result U32 := + Result.ret (U32.ofInt 4294967295 (by intlit)) +def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp) + +/- [constants::X1] -/ +def x1_body : Result U32 := Result.ret core_num_u32_max_c +def x1_c : U32 := eval_global x1_body (by simp) + +/- [constants::X2] -/ +def x2_body : Result U32 := Result.ret (U32.ofInt 3 (by intlit)) +def x2_c : U32 := eval_global x2_body (by simp) + +/- [constants::incr] -/ +def incr_fwd (n : U32) : Result U32 := + n + (U32.ofInt 1 (by intlit)) + +/- [constants::X3] -/ +def x3_body : Result U32 := incr_fwd (U32.ofInt 32 (by intlit)) +def x3_c : U32 := eval_global x3_body (by simp) + +/- [constants::mk_pair0] -/ +def mk_pair0_fwd (x : U32) (y : U32) : Result (U32 × U32) := + Result.ret (x, y) + +/- [constants::Pair] -/ +structure pair_t (T1 T2 : Type) where + pair_x : T1 + pair_y : T2 + +/- [constants::mk_pair1] -/ +def mk_pair1_fwd (x : U32) (y : U32) : Result (pair_t U32 U32) := + Result.ret { pair_x := x, pair_y := y } + +/- [constants::P0] -/ +def p0_body : Result (U32 × U32) := + mk_pair0_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit)) +def p0_c : (U32 × U32) := eval_global p0_body (by simp) + +/- [constants::P1] -/ +def p1_body : Result (pair_t U32 U32) := + mk_pair1_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit)) +def p1_c : pair_t U32 U32 := eval_global p1_body (by simp) + +/- [constants::P2] -/ +def p2_body : Result (U32 × U32) := + Result.ret ((U32.ofInt 0 (by intlit)), (U32.ofInt 1 (by intlit))) +def p2_c : (U32 × U32) := eval_global p2_body (by simp) + +/- [constants::P3] -/ +def p3_body : Result (pair_t U32 U32) := + Result.ret + { pair_x := (U32.ofInt 0 (by intlit)), pair_y := (U32.ofInt 1 (by intlit)) } +def p3_c : pair_t U32 U32 := eval_global p3_body (by simp) + +/- [constants::Wrap] -/ +structure wrap_t (T : Type) where + wrap_val : T + +/- [constants::Wrap::{0}::new] -/ +def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) := + Result.ret { wrap_val := val } + +/- [constants::Y] -/ +def y_body : Result (wrap_t I32) := wrap_new_fwd I32 (I32.ofInt 2 (by intlit)) +def y_c : wrap_t I32 := eval_global y_body (by simp) + +/- [constants::unwrap_y] -/ +def unwrap_y_fwd : Result I32 := + Result.ret y_c.wrap_val + +/- [constants::YVAL] -/ +def yval_body : Result I32 := unwrap_y_fwd +def yval_c : I32 := eval_global yval_body (by simp) + +/- [constants::get_z1::Z1] -/ +def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3 (by intlit)) +def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp) + +/- [constants::get_z1] -/ +def get_z1_fwd : Result I32 := + Result.ret get_z1_z1_c + +/- [constants::add] -/ +def add_fwd (a : I32) (b : I32) : Result I32 := + a + b + +/- [constants::Q1] -/ +def q1_body : Result I32 := Result.ret (I32.ofInt 5 (by intlit)) +def q1_c : I32 := eval_global q1_body (by simp) + +/- [constants::Q2] -/ +def q2_body : Result I32 := Result.ret q1_c +def q2_c : I32 := eval_global q2_body (by simp) + +/- [constants::Q3] -/ +def q3_body : Result I32 := add_fwd q2_c (I32.ofInt 3 (by intlit)) +def q3_c : I32 := eval_global q3_body (by simp) + +/- [constants::get_z2] -/ +def get_z2_fwd : Result I32 := + do + let i ← get_z1_fwd + let i0 ← add_fwd i q3_c + add_fwd q1_c i0 + +/- [constants::S1] -/ +def s1_body : Result U32 := Result.ret (U32.ofInt 6 (by intlit)) +def s1_c : U32 := eval_global s1_body (by simp) + +/- [constants::S2] -/ +def s2_body : Result U32 := incr_fwd s1_c +def s2_c : U32 := eval_global s2_body (by simp) + +/- [constants::S3] -/ +def s3_body : Result (pair_t U32 U32) := Result.ret p3_c +def s3_c : pair_t U32 U32 := eval_global s3_body (by simp) + +/- [constants::S4] -/ +def s4_body : Result (pair_t U32 U32) := + mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit)) +def s4_c : pair_t U32 U32 := eval_global s4_body (by simp) + diff --git a/tests/lean/misc-external/Base/Primitives.lean b/tests/lean/misc-external/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-external/Base/Primitives.lean +++ b/tests/lean/misc-external/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-external/External/ExternalFuns.lean b/tests/lean/misc-external/External/ExternalFuns.lean new file mode 100644 index 00000000..6bd4f4a9 --- /dev/null +++ b/tests/lean/misc-external/External/ExternalFuns.lean @@ -0,0 +1,5 @@ +import Base.Primitives +import External.Types +import External.Opaque + +def opaque_defs : OpaqueDefs := sorry diff --git a/tests/lean/misc-external/External/Funs.lean b/tests/lean/misc-external/External/Funs.lean index 4e1f36a1..eeb83989 100644 --- a/tests/lean/misc-external/External/Funs.lean +++ b/tests/lean/misc-external/External/Funs.lean @@ -2,9 +2,7 @@ -- [external]: function definitions import Base.Primitives import External.Types -import External.Opaque - -section variable (opaque_defs: OpaqueDefs) +import External.ExternalFuns /- [external::swap] -/ def swap_fwd @@ -28,9 +26,7 @@ def swap_back /- [external::test_new_non_zero_u32] -/ def test_new_non_zero_u32_fwd - (x : UInt32) (st : State) : - Result (State × core_num_nonzero_non_zero_u32_t) - := + (x : U32) (st : State) : Result (State × core_num_nonzero_non_zero_u32_t) := do let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t @@ -39,13 +35,10 @@ def test_new_non_zero_u32_fwd /- [external::test_vec] -/ def test_vec_fwd : Result Unit := do - let v := vec_new UInt32 - let _ ← vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit)) + let v := vec_new U32 + let _ ← vec_push_back U32 v (U32.ofInt 0 (by intlit)) Result.ret () -/- Unit test for [external::test_vec] -/ -#assert (test_vec_fwd == .ret ()) - /- [external::custom_swap] -/ def custom_swap_fwd (T : Type) (x : T) (y : T) (st : State) : Result (State × T) := @@ -68,26 +61,24 @@ def custom_swap_back /- [external::test_custom_swap] -/ def test_custom_swap_fwd - (x : UInt32) (y : UInt32) (st : State) : Result (State × Unit) := + (x : U32) (y : U32) (st : State) : Result (State × Unit) := do - let (st0, _) ← custom_swap_fwd UInt32 x y st + let (st0, _) ← custom_swap_fwd U32 x y st Result.ret (st0, ()) /- [external::test_custom_swap] -/ def test_custom_swap_back - (x : UInt32) (y : UInt32) (st : State) (st0 : State) : - Result (State × (UInt32 × UInt32)) + (x : U32) (y : U32) (st : State) (st0 : State) : + Result (State × (U32 × U32)) := - custom_swap_back UInt32 x y st (UInt32.ofNatCore 1 (by intlit)) st0 + custom_swap_back U32 x y st (U32.ofInt 1 (by intlit)) st0 /- [external::test_swap_non_zero] -/ -def test_swap_non_zero_fwd - (x : UInt32) (st : State) : Result (State × UInt32) := +def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) := do - let (st0, _) ← swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st - let (st1, (x0, _)) ← - swap_back UInt32 x (UInt32.ofNatCore 0 (by intlit)) st st0 - if h: x0 = (UInt32.ofNatCore 0 (by intlit)) + let (st0, _) ← swap_fwd U32 x (U32.ofInt 0 (by intlit)) st + let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0 (by intlit)) st st0 + if h: x0 = (U32.ofInt 0 (by intlit)) then Result.fail Error.panic else Result.ret (st1, x0) diff --git a/tests/lean/misc-external/External/Opaque.lean b/tests/lean/misc-external/External/Opaque.lean index d3582de3..d641912b 100644 --- a/tests/lean/misc-external/External/Opaque.lean +++ b/tests/lean/misc-external/External/Opaque.lean @@ -19,8 +19,7 @@ structure OpaqueDefs where /- [core::num::nonzero::NonZeroU32::{14}::new] -/ core_num_nonzero_non_zero_u32_new_fwd : - UInt32 -> State -> Result (State × (Option - core_num_nonzero_non_zero_u32_t)) + U32 -> State -> Result (State × (Option core_num_nonzero_non_zero_u32_t)) /- [core::option::Option::{0}::unwrap] -/ core_option_option_unwrap_fwd diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-loops/Base/Primitives.lean +++ b/tests/lean/misc-loops/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean index 5ddb65ca..89a7ce34 100644 --- a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean +++ b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean @@ -4,7 +4,7 @@ import Loops.Types /- [loops::sum]: termination measure -/ @[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) +def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) syntax "sum_loop_decreases" term+ : tactic @@ -13,8 +13,7 @@ macro_rules /- [loops::sum_with_mut_borrows]: termination measure -/ @[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := +def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) := (max, mi, ms) syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic @@ -24,8 +23,7 @@ macro_rules /- [loops::sum_with_shared_borrows]: termination measure -/ @[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := +def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic @@ -34,7 +32,7 @@ macro_rules | `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry) /- [loops::clear]: termination measure -/ -@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i) +@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i) syntax "clear_loop_decreases" term+ : tactic @@ -43,7 +41,7 @@ macro_rules /- [loops::list_mem]: termination measure -/ @[simp] -def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) +def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls) syntax "list_mem_loop_decreases" term+ : tactic @@ -52,8 +50,7 @@ macro_rules /- [loops::list_nth_mut_loop]: termination measure -/ @[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) syntax "list_nth_mut_loop_loop_decreases" term+ : tactic @@ -63,8 +60,7 @@ macro_rules /- [loops::list_nth_shared_loop]: termination measure -/ @[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) syntax "list_nth_shared_loop_loop_decreases" term+ : tactic @@ -74,7 +70,7 @@ macro_rules /- [loops::get_elem_mut]: termination measure -/ @[simp] -def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) syntax "get_elem_mut_loop_decreases" term+ : tactic @@ -83,7 +79,7 @@ macro_rules /- [loops::get_elem_shared]: termination measure -/ @[simp] -def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) syntax "get_elem_shared_loop_decreases" term+ : tactic @@ -92,7 +88,7 @@ macro_rules /- [loops::list_nth_mut_loop_with_id]: termination measure -/ @[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -103,7 +99,7 @@ macro_rules /- [loops::list_nth_shared_loop_with_id]: termination measure -/ @[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -115,7 +111,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair]: termination measure -/ @[simp] def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic @@ -126,7 +122,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair]: termination measure -/ @[simp] def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic @@ -138,7 +134,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic @@ -150,7 +146,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic @@ -162,7 +158,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic @@ -174,7 +170,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic @@ -186,7 +182,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic @@ -198,7 +194,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean index d1e72d65..2e28a6c0 100644 --- a/tests/lean/misc-loops/Loops/Clauses/Template.lean +++ b/tests/lean/misc-loops/Loops/Clauses/Template.lean @@ -4,8 +4,7 @@ import Base.Primitives import Loops.Types /- [loops::sum]: termination measure -/ -@[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) +@[simp] def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) /- [loops::sum]: decreases_by tactic -/ syntax "sum_loop_decreases" term+ : tactic @@ -14,8 +13,7 @@ macro_rules /- [loops::sum_with_mut_borrows]: termination measure -/ @[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := +def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) := (max, mi, ms) /- [loops::sum_with_mut_borrows]: decreases_by tactic -/ @@ -25,8 +23,7 @@ macro_rules /- [loops::sum_with_shared_borrows]: termination measure -/ @[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := +def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) /- [loops::sum_with_shared_borrows]: decreases_by tactic -/ @@ -35,7 +32,7 @@ macro_rules | `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry) /- [loops::clear]: termination measure -/ -@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i) +@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i) /- [loops::clear]: decreases_by tactic -/ syntax "clear_loop_decreases" term+ : tactic @@ -43,8 +40,7 @@ macro_rules | `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry) /- [loops::list_mem]: termination measure -/ -@[simp] -def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) +@[simp] def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls) /- [loops::list_mem]: decreases_by tactic -/ syntax "list_mem_loop_decreases" term+ : tactic @@ -53,8 +49,7 @@ macro_rules /- [loops::list_nth_mut_loop]: termination measure -/ @[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) /- [loops::list_nth_mut_loop]: decreases_by tactic -/ @@ -64,8 +59,8 @@ macro_rules /- [loops::list_nth_shared_loop]: termination measure -/ @[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) + := (ls, i) /- [loops::list_nth_shared_loop]: decreases_by tactic -/ @@ -75,7 +70,7 @@ macro_rules /- [loops::get_elem_mut]: termination measure -/ @[simp] -def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) /- [loops::get_elem_mut]: decreases_by tactic -/ syntax "get_elem_mut_loop_decreases" term+ : tactic @@ -84,7 +79,7 @@ macro_rules /- [loops::get_elem_shared]: termination measure -/ @[simp] -def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) /- [loops::get_elem_shared]: decreases_by tactic -/ syntax "get_elem_shared_loop_decreases" term+ : tactic @@ -93,7 +88,7 @@ macro_rules /- [loops::list_nth_mut_loop_with_id]: termination measure -/ @[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -104,7 +99,7 @@ macro_rules /- [loops::list_nth_shared_loop_with_id]: termination measure -/ @[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -116,7 +111,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair]: termination measure -/ @[simp] def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/ @@ -127,7 +122,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair]: termination measure -/ @[simp] def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/ @@ -139,7 +134,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/ @@ -151,7 +146,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/ @@ -163,7 +158,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/ @@ -175,7 +170,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/ @@ -187,7 +182,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/ @@ -199,7 +194,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/ diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean index f79a27a9..fd8d62d7 100644 --- a/tests/lean/misc-loops/Loops/Funs.lean +++ b/tests/lean/misc-loops/Loops/Funs.lean @@ -5,79 +5,78 @@ import Loops.Types import Loops.Clauses.Clauses /- [loops::sum] -/ -def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := +def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) := if h: i < max then do - let s0 ← UInt32.checked_add s i - let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) + let s0 ← s + i + let i0 ← i + (U32.ofInt 1 (by intlit)) sum_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) + else s * (U32.ofInt 2 (by intlit)) termination_by sum_loop_fwd max i s => sum_loop_terminates max i s decreasing_by sum_loop_decreases max i s /- [loops::sum] -/ -def sum_fwd (max : UInt32) : Result UInt32 := - sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_fwd (max : U32) : Result U32 := + sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit)) /- [loops::sum_with_mut_borrows] -/ def sum_with_mut_borrows_loop_fwd - (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) := + (max : U32) (mi : U32) (ms : U32) : (Result U32) := if h: mi < max then do - let ms0 ← UInt32.checked_add ms mi - let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit)) + let ms0 ← ms + mi + let mi0 ← mi + (U32.ofInt 1 (by intlit)) sum_with_mut_borrows_loop_fwd max mi0 ms0 - else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit)) + else ms * (U32.ofInt 2 (by intlit)) termination_by sum_with_mut_borrows_loop_fwd max mi ms => sum_with_mut_borrows_loop_terminates max mi ms decreasing_by sum_with_mut_borrows_loop_decreases max mi ms /- [loops::sum_with_mut_borrows] -/ -def sum_with_mut_borrows_fwd (max : UInt32) : Result UInt32 := - sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_with_mut_borrows_fwd (max : U32) : Result U32 := + sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit)) + (U32.ofInt 0 (by intlit)) /- [loops::sum_with_shared_borrows] -/ def sum_with_shared_borrows_loop_fwd - (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + (max : U32) (i : U32) (s : U32) : (Result U32) := if h: i < max then do - let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) - let s0 ← UInt32.checked_add s i0 + let i0 ← i + (U32.ofInt 1 (by intlit)) + let s0 ← s + i0 sum_with_shared_borrows_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) + else s * (U32.ofInt 2 (by intlit)) termination_by sum_with_shared_borrows_loop_fwd max i s => sum_with_shared_borrows_loop_terminates max i s decreasing_by sum_with_shared_borrows_loop_decreases max i s /- [loops::sum_with_shared_borrows] -/ -def sum_with_shared_borrows_fwd (max : UInt32) : Result UInt32 := - sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_with_shared_borrows_fwd (max : U32) : Result U32 := + sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit)) + (U32.ofInt 0 (by intlit)) /- [loops::clear] -/ -def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) := - let i0 := vec_len UInt32 v +def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) := + let i0 := vec_len U32 v if h: i < i0 then do - let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) - let v0 ← vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit)) + let i1 ← i + (Usize.ofInt 1 (by intlit)) + let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit)) clear_loop_fwd_back v0 i1 else Result.ret v termination_by clear_loop_fwd_back v i => clear_loop_terminates v i decreasing_by clear_loop_decreases v i /- [loops::clear] -/ -def clear_fwd_back (v : Vec UInt32) : Result (Vec UInt32) := - clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit)) +def clear_fwd_back (v : Vec U32) : Result (Vec U32) := + clear_loop_fwd_back v (Usize.ofInt 0 (by intlit)) /- [loops::list_mem] -/ -def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) := +def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -88,19 +87,19 @@ termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls decreasing_by list_mem_loop_decreases x ls /- [loops::list_mem] -/ -def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : Result Bool := +def list_mem_fwd (x : U32) (ls : list_t U32) : Result Bool := list_mem_loop_fwd x ls /- [loops::list_nth_mut_loop] -/ def list_nth_mut_loop_loop_fwd - (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + (T : Type) (ls : list_t T) (i : U32) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_loop_fwd T tl i0 | list_t.Nil => Result.fail Error.panic termination_by list_nth_mut_loop_loop_fwd ls i => @@ -108,19 +107,19 @@ termination_by list_nth_mut_loop_loop_fwd ls i => decreasing_by list_nth_mut_loop_loop_decreases ls i /- [loops::list_nth_mut_loop] -/ -def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : Result T := +def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T := list_nth_mut_loop_loop_fwd T ls i /- [loops::list_nth_mut_loop] -/ def list_nth_mut_loop_loop_back - (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (Result (list_t T)) := + (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0 Result.ret (list_t.Cons x tl0) | list_t.Nil => Result.fail Error.panic @@ -130,19 +129,19 @@ decreasing_by list_nth_mut_loop_loop_decreases ls i /- [loops::list_nth_mut_loop] -/ def list_nth_mut_loop_back - (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_mut_loop_loop_back T ls i ret0 /- [loops::list_nth_shared_loop] -/ def list_nth_shared_loop_loop_fwd - (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + (T : Type) (ls : list_t T) (i : U32) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_loop_fwd T tl i0 | list_t.Nil => Result.fail Error.panic termination_by list_nth_shared_loop_loop_fwd ls i => @@ -150,12 +149,11 @@ termination_by list_nth_shared_loop_loop_fwd ls i => decreasing_by list_nth_shared_loop_loop_decreases ls i /- [loops::list_nth_shared_loop] -/ -def list_nth_shared_loop_fwd - (T : Type) (ls : list_t T) (i : UInt32) : Result T := +def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T := list_nth_shared_loop_loop_fwd T ls i /- [loops::get_elem_mut] -/ -def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (Result USize) := +def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -166,15 +164,15 @@ termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls decreasing_by get_elem_mut_loop_decreases x ls /- [loops::get_elem_mut] -/ -def get_elem_mut_fwd (slots : Vec (list_t USize)) (x : USize) : Result USize := +def get_elem_mut_fwd (slots : Vec (list_t Usize)) (x : Usize) : Result Usize := do let l ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit)) get_elem_mut_loop_fwd x l /- [loops::get_elem_mut] -/ def get_elem_mut_loop_back - (x : USize) (ls : list_t USize) (ret0 : USize) : (Result (list_t USize)) := + (x : Usize) (ls : list_t Usize) (ret0 : Usize) : (Result (list_t Usize)) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -190,18 +188,18 @@ decreasing_by get_elem_mut_loop_decreases x ls /- [loops::get_elem_mut] -/ def get_elem_mut_back - (slots : Vec (list_t USize)) (x : USize) (ret0 : USize) : - Result (Vec (list_t USize)) + (slots : Vec (list_t Usize)) (x : Usize) (ret0 : Usize) : + Result (Vec (list_t Usize)) := do let l ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit)) let l0 ← get_elem_mut_loop_back x l ret0 - vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0 + vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0 /- [loops::get_elem_shared] -/ def get_elem_shared_loop_fwd - (x : USize) (ls : list_t USize) : (Result USize) := + (x : Usize) (ls : list_t Usize) : (Result Usize) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -214,10 +212,9 @@ decreasing_by get_elem_shared_loop_decreases x ls /- [loops::get_elem_shared] -/ def get_elem_shared_fwd - (slots : Vec (list_t USize)) (x : USize) : Result USize := + (slots : Vec (list_t Usize)) (x : Usize) : Result Usize := do - let l ← - vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + let l ← vec_index_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit)) get_elem_shared_loop_fwd x l /- [loops::id_mut] -/ @@ -235,14 +232,14 @@ def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) := /- [loops::list_nth_mut_loop_with_id] -/ def list_nth_mut_loop_with_id_loop_fwd - (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + (T : Type) (i : U32) (ls : list_t T) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_with_id_loop_fwd T i0 tl | list_t.Nil => Result.fail Error.panic termination_by list_nth_mut_loop_with_id_loop_fwd i ls => @@ -251,21 +248,21 @@ decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls /- [loops::list_nth_mut_loop_with_id] -/ def list_nth_mut_loop_with_id_fwd - (T : Type) (ls : list_t T) (i : UInt32) : Result T := + (T : Type) (ls : list_t T) (i : U32) : Result T := do let ls0 ← id_mut_fwd T ls list_nth_mut_loop_with_id_loop_fwd T i ls0 /- [loops::list_nth_mut_loop_with_id] -/ def list_nth_mut_loop_with_id_loop_back - (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) := + (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0 Result.ret (list_t.Cons x tl0) | list_t.Nil => Result.fail Error.panic @@ -275,7 +272,7 @@ decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls /- [loops::list_nth_mut_loop_with_id] -/ def list_nth_mut_loop_with_id_back - (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := do let ls0 ← id_mut_fwd T ls let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0 @@ -283,14 +280,14 @@ def list_nth_mut_loop_with_id_back /- [loops::list_nth_shared_loop_with_id] -/ def list_nth_shared_loop_with_id_loop_fwd - (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + (T : Type) (i : U32) (ls : list_t T) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_with_id_loop_fwd T i0 tl | list_t.Nil => Result.fail Error.panic termination_by list_nth_shared_loop_with_id_loop_fwd i ls => @@ -299,25 +296,23 @@ decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls /- [loops::list_nth_shared_loop_with_id] -/ def list_nth_shared_loop_with_id_fwd - (T : Type) (ls : list_t T) (i : UInt32) : Result T := + (T : Type) (ls : list_t T) (i : U32) : Result T := do let ls0 ← id_shared_fwd T ls list_nth_shared_loop_with_id_loop_fwd T i ls0 /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -327,25 +322,23 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_loop_back'a - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) | list_t.Nil => Result.fail Error.panic @@ -356,25 +349,25 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_back'a - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0 /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_loop_back'b - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) | list_t.Nil => Result.fail Error.panic @@ -385,25 +378,23 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_loop_pair] -/ def list_nth_mut_loop_pair_back'b - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0 /- [loops::list_nth_shared_loop_pair] -/ def list_nth_shared_loop_pair_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -413,25 +404,21 @@ decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_loop_pair] -/ def list_nth_shared_loop_pair_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_loop_pair_merge] -/ def list_nth_mut_loop_pair_merge_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -441,27 +428,25 @@ decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_loop_pair_merge] -/ def list_nth_mut_loop_pair_merge_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_loop_pair_merge] -/ def list_nth_mut_loop_pair_merge_loop_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) : (Result ((list_t T) × (list_t T))) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then let (t, t0) := ret0 Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let (tl00, tl10) ← list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10) @@ -473,25 +458,23 @@ decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_loop_pair_merge] -/ def list_nth_mut_loop_pair_merge_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) : Result ((list_t T) × (list_t T)) := list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 /- [loops::list_nth_shared_loop_pair_merge] -/ def list_nth_shared_loop_pair_merge_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -501,25 +484,21 @@ decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_loop_pair_merge] -/ def list_nth_shared_loop_pair_merge_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair] -/ def list_nth_mut_shared_loop_pair_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -529,25 +508,23 @@ decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair] -/ def list_nth_mut_shared_loop_pair_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair] -/ def list_nth_mut_shared_loop_pair_loop_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) @@ -559,25 +536,23 @@ decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair] -/ def list_nth_mut_shared_loop_pair_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0 /- [loops::list_nth_mut_shared_loop_pair_merge] -/ def list_nth_mut_shared_loop_pair_merge_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -587,25 +562,23 @@ decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair_merge] -/ def list_nth_mut_shared_loop_pair_merge_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair_merge] -/ def list_nth_mut_shared_loop_pair_merge_loop_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) @@ -617,25 +590,23 @@ decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_mut_shared_loop_pair_merge] -/ def list_nth_mut_shared_loop_pair_merge_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0 /- [loops::list_nth_shared_mut_loop_pair] -/ def list_nth_shared_mut_loop_pair_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -645,25 +616,23 @@ decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair] -/ def list_nth_shared_mut_loop_pair_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair] -/ def list_nth_shared_mut_loop_pair_loop_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) @@ -675,25 +644,23 @@ decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair] -/ def list_nth_shared_mut_loop_pair_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0 /- [loops::list_nth_shared_mut_loop_pair_merge] -/ def list_nth_shared_mut_loop_pair_merge_loop_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - (Result (T × T)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -703,25 +670,23 @@ decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair_merge] -/ def list_nth_shared_mut_loop_pair_merge_fwd - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : - Result (T × T) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) := list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair_merge] -/ def list_nth_shared_mut_loop_pair_merge_loop_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) @@ -733,7 +698,7 @@ decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair_merge] -/ def list_nth_shared_mut_loop_pair_merge_back - (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 diff --git a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean b/tests/lean/misc-no_nested_borrows/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean +++ b/tests/lean/misc-no_nested_borrows/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean index e2697385..a73848de 100644 --- a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean +++ b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean @@ -2,556 +2,534 @@ -- [no_nested_borrows] import Base.Primitives -structure OpaqueDefs where - - /- [no_nested_borrows::Pair] -/ - structure pair_t (T1 T2 : Type) where - pair_x : T1 - pair_y : T2 - - /- [no_nested_borrows::List] -/ - inductive list_t (T : Type) := - | Cons : T -> list_t T -> list_t T - | Nil : list_t T - - /- [no_nested_borrows::One] -/ - inductive one_t (T1 : Type) := - | One : T1 -> one_t T1 - - /- [no_nested_borrows::EmptyEnum] -/ - inductive empty_enum_t := - | Empty : empty_enum_t - - /- [no_nested_borrows::Enum] -/ - inductive enum_t := - | Variant1 : enum_t - | Variant2 : enum_t - - /- [no_nested_borrows::EmptyStruct] -/ - structure empty_struct_t where - - /- [no_nested_borrows::Sum] -/ - inductive sum_t (T1 T2 : Type) := - | Left : T1 -> sum_t T1 T2 - | Right : T2 -> sum_t T1 T2 - - /- [no_nested_borrows::neg_test] -/ - def neg_test_fwd (x : Int32) : Result Int32 := - Int32.checked_neg x - - /- [no_nested_borrows::add_test] -/ - def add_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_add x y - - /- [no_nested_borrows::subs_test] -/ - def subs_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_sub x y - - /- [no_nested_borrows::div_test] -/ - def div_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_div x y - - /- [no_nested_borrows::div_test1] -/ - def div_test1_fwd (x : UInt32) : Result UInt32 := - UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit)) - - /- [no_nested_borrows::rem_test] -/ - def rem_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_rem x y - - /- [no_nested_borrows::cast_test] -/ - def cast_test_fwd (x : UInt32) : Result Int32 := - scalar_cast Int32 x - - /- [no_nested_borrows::test2] -/ - def test2_fwd : Result Unit := - do - let _ ← UInt32.checked_add (UInt32.ofNatCore 23 (by intlit)) - (UInt32.ofNatCore 44 (by intlit)) - Result.ret () - - /- Unit test for [no_nested_borrows::test2] -/ - #assert (test2_fwd == .ret ()) - - /- [no_nested_borrows::get_max] -/ - def get_max_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - if h: x >= y - then Result.ret x - else Result.ret y - - /- [no_nested_borrows::test3] -/ - def test3_fwd : Result Unit := - do - let x ← - get_max_fwd (UInt32.ofNatCore 4 (by intlit)) - (UInt32.ofNatCore 3 (by intlit)) - let y ← - get_max_fwd (UInt32.ofNatCore 10 (by intlit)) - (UInt32.ofNatCore 11 (by intlit)) - let z ← UInt32.checked_add x y - if h: not (z = (UInt32.ofNatCore 15 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test3] -/ - #assert (test3_fwd == .ret ()) - - /- [no_nested_borrows::test_neg1] -/ - def test_neg1_fwd : Result Unit := - do - let y ← Int32.checked_neg (Int32.ofNatCore 3 (by intlit)) - if h: not (y = (Int32.ofNatCore -3 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_neg1] -/ - #assert (test_neg1_fwd == .ret ()) - - /- [no_nested_borrows::refs_test1] -/ - def refs_test1_fwd : Result Unit := - if h: not ((Int32.ofNatCore 1 (by intlit)) = - (Int32.ofNatCore 1 (by intlit))) +/- [no_nested_borrows::Pair] -/ +structure pair_t (T1 T2 : Type) where + pair_x : T1 + pair_y : T2 + +/- [no_nested_borrows::List] -/ +inductive list_t (T : Type) := +| Cons : T -> list_t T -> list_t T +| Nil : list_t T + +/- [no_nested_borrows::One] -/ +inductive one_t (T1 : Type) := +| One : T1 -> one_t T1 + +/- [no_nested_borrows::EmptyEnum] -/ +inductive empty_enum_t := +| Empty : empty_enum_t + +/- [no_nested_borrows::Enum] -/ +inductive enum_t := +| Variant1 : enum_t +| Variant2 : enum_t + +/- [no_nested_borrows::EmptyStruct] -/ +structure empty_struct_t where + +/- [no_nested_borrows::Sum] -/ +inductive sum_t (T1 T2 : Type) := +| Left : T1 -> sum_t T1 T2 +| Right : T2 -> sum_t T1 T2 + +/- [no_nested_borrows::neg_test] -/ +def neg_test_fwd (x : I32) : Result I32 := + - x + +/- [no_nested_borrows::add_test] -/ +def add_test_fwd (x : U32) (y : U32) : Result U32 := + x + y + +/- [no_nested_borrows::subs_test] -/ +def subs_test_fwd (x : U32) (y : U32) : Result U32 := + x - y + +/- [no_nested_borrows::div_test] -/ +def div_test_fwd (x : U32) (y : U32) : Result U32 := + x / y + +/- [no_nested_borrows::div_test1] -/ +def div_test1_fwd (x : U32) : Result U32 := + x / (U32.ofInt 2 (by intlit)) + +/- [no_nested_borrows::rem_test] -/ +def rem_test_fwd (x : U32) (y : U32) : Result U32 := + x % y + +/- [no_nested_borrows::cast_test] -/ +def cast_test_fwd (x : U32) : Result I32 := + Scalar.cast .I32 x + +/- [no_nested_borrows::test2] -/ +def test2_fwd : Result Unit := + do + let _ ← (U32.ofInt 23 (by intlit)) + (U32.ofInt 44 (by intlit)) + Result.ret () + +/- Unit test for [no_nested_borrows::test2] -/ +#assert (test2_fwd == .ret ()) + +/- [no_nested_borrows::get_max] -/ +def get_max_fwd (x : U32) (y : U32) : Result U32 := + if h: x >= y + then Result.ret x + else Result.ret y + +/- [no_nested_borrows::test3] -/ +def test3_fwd : Result Unit := + do + let x ← get_max_fwd (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit)) + let y ← get_max_fwd (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit)) + let z ← x + y + if h: not (z = (U32.ofInt 15 (by intlit))) then Result.fail Error.panic else Result.ret () - - /- Unit test for [no_nested_borrows::refs_test1] -/ - #assert (refs_test1_fwd == .ret ()) - - /- [no_nested_borrows::refs_test2] -/ - def refs_test2_fwd : Result Unit := - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) + +/- Unit test for [no_nested_borrows::test3] -/ +#assert (test3_fwd == .ret ()) + +/- [no_nested_borrows::test_neg1] -/ +def test_neg1_fwd : Result Unit := + do + let y ← - (I32.ofInt 3 (by intlit)) + if h: not (y = (I32.ofInt (-(3:Int)) (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [no_nested_borrows::test_neg1] -/ +#assert (test_neg1_fwd == .ret ()) + +/- [no_nested_borrows::refs_test1] -/ +def refs_test1_fwd : Result Unit := + if h: not ((I32.ofInt 1 (by intlit)) = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [no_nested_borrows::refs_test1] -/ +#assert (refs_test1_fwd == .ret ()) + +/- [no_nested_borrows::refs_test2] -/ +def refs_test2_fwd : Result Unit := + if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit))) + then Result.fail Error.panic + else + if h: not ((I32.ofInt 0 (by intlit)) = (I32.ofInt 0 (by intlit))) then Result.fail Error.panic else - if h: not ((Int32.ofNatCore 0 (by intlit)) = - (Int32.ofNatCore 0 (by intlit))) + if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit))) then Result.fail Error.panic else - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) + if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit))) then Result.fail Error.panic - else - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::refs_test2] -/ - #assert (refs_test2_fwd == .ret ()) - - /- [no_nested_borrows::test_list1] -/ - def test_list1_fwd : Result Unit := - Result.ret () - - /- Unit test for [no_nested_borrows::test_list1] -/ - #assert (test_list1_fwd == .ret ()) - - /- [no_nested_borrows::test_box1] -/ - def test_box1_fwd : Result Unit := - let b := (Int32.ofNatCore 1 (by intlit)) - let x := b - if h: not (x = (Int32.ofNatCore 1 (by intlit))) + else Result.ret () + +/- Unit test for [no_nested_borrows::refs_test2] -/ +#assert (refs_test2_fwd == .ret ()) + +/- [no_nested_borrows::test_list1] -/ +def test_list1_fwd : Result Unit := + Result.ret () + +/- Unit test for [no_nested_borrows::test_list1] -/ +#assert (test_list1_fwd == .ret ()) + +/- [no_nested_borrows::test_box1] -/ +def test_box1_fwd : Result Unit := + let b := (I32.ofInt 1 (by intlit)) + let x := b + if h: not (x = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [no_nested_borrows::test_box1] -/ +#assert (test_box1_fwd == .ret ()) + +/- [no_nested_borrows::copy_int] -/ +def copy_int_fwd (x : I32) : Result I32 := + Result.ret x + +/- [no_nested_borrows::test_unreachable] -/ +def test_unreachable_fwd (b : Bool) : Result Unit := + if h: b + then Result.fail Error.panic + else Result.ret () + +/- [no_nested_borrows::test_panic] -/ +def test_panic_fwd (b : Bool) : Result Unit := + if h: b + then Result.fail Error.panic + else Result.ret () + +/- [no_nested_borrows::test_copy_int] -/ +def test_copy_int_fwd : Result Unit := + do + let y ← copy_int_fwd (I32.ofInt 0 (by intlit)) + if h: not ((I32.ofInt 0 (by intlit)) = y) then Result.fail Error.panic else Result.ret () - - /- Unit test for [no_nested_borrows::test_box1] -/ - #assert (test_box1_fwd == .ret ()) - - /- [no_nested_borrows::copy_int] -/ - def copy_int_fwd (x : Int32) : Result Int32 := - Result.ret x - - /- [no_nested_borrows::test_unreachable] -/ - def test_unreachable_fwd (b : Bool) : Result Unit := - if h: b + +/- Unit test for [no_nested_borrows::test_copy_int] -/ +#assert (test_copy_int_fwd == .ret ()) + +/- [no_nested_borrows::is_cons] -/ +def is_cons_fwd (T : Type) (l : list_t T) : Result Bool := + match h: l with + | list_t.Cons t l0 => Result.ret true + | list_t.Nil => Result.ret false + +/- [no_nested_borrows::test_is_cons] -/ +def test_is_cons_fwd : Result Unit := + do + let l := list_t.Nil + let b ← is_cons_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l) + if h: not b then Result.fail Error.panic else Result.ret () - - /- [no_nested_borrows::test_panic] -/ - def test_panic_fwd (b : Bool) : Result Unit := - if h: b + +/- Unit test for [no_nested_borrows::test_is_cons] -/ +#assert (test_is_cons_fwd == .ret ()) + +/- [no_nested_borrows::split_list] -/ +def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) := + match h: l with + | list_t.Cons hd tl => Result.ret (hd, tl) + | list_t.Nil => Result.fail Error.panic + +/- [no_nested_borrows::test_split_list] -/ +def test_split_list_fwd : Result Unit := + do + let l := list_t.Nil + let p ← split_list_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l) + let (hd, _) := p + if h: not (hd = (I32.ofInt 0 (by intlit))) then Result.fail Error.panic else Result.ret () - - /- [no_nested_borrows::test_copy_int] -/ - def test_copy_int_fwd : Result Unit := - do - let y ← copy_int_fwd (Int32.ofNatCore 0 (by intlit)) - if h: not ((Int32.ofNatCore 0 (by intlit)) = y) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_copy_int] -/ - #assert (test_copy_int_fwd == .ret ()) - - /- [no_nested_borrows::is_cons] -/ - def is_cons_fwd (T : Type) (l : list_t T) : Result Bool := - match h: l with - | list_t.Cons t l0 => Result.ret true - | list_t.Nil => Result.ret false - - /- [no_nested_borrows::test_is_cons] -/ - def test_is_cons_fwd : Result Unit := - do - let l := list_t.Nil - let b ← - is_cons_fwd Int32 (list_t.Cons (Int32.ofNatCore 0 (by intlit)) l) - if h: not b - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_is_cons] -/ - #assert (test_is_cons_fwd == .ret ()) - - /- [no_nested_borrows::split_list] -/ - def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) := - match h: l with - | list_t.Cons hd tl => Result.ret (hd, tl) - | list_t.Nil => Result.fail Error.panic - - /- [no_nested_borrows::test_split_list] -/ - def test_split_list_fwd : Result Unit := - do - let l := list_t.Nil - let p ← - split_list_fwd Int32 (list_t.Cons (Int32.ofNatCore 0 (by intlit)) l) - let (hd, _) := p - if h: not (hd = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_split_list] -/ - #assert (test_split_list_fwd == .ret ()) - - /- [no_nested_borrows::choose] -/ - def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := - if h: b - then Result.ret x - else Result.ret y - - /- [no_nested_borrows::choose] -/ - def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := - if h: b - then Result.ret (ret0, y) - else Result.ret (x, ret0) - - /- [no_nested_borrows::choose_test] -/ - def choose_test_fwd : Result Unit := - do - let z ← - choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) - let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) - if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let (x, y) ← - choose_back Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) z0 - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - if h: not (y = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::choose_test] -/ - #assert (choose_test_fwd == .ret ()) - - /- [no_nested_borrows::test_char] -/ - def test_char_fwd : Result Char := - Result.ret 'a' - - /- [no_nested_borrows::NodeElem] -/ - mutual inductive node_elem_t (T : Type) := - | Cons : tree_t T -> node_elem_t T -> node_elem_t T - | Nil : node_elem_t T - - /- [no_nested_borrows::Tree] -/ - inductive tree_t (T : Type) := - | Leaf : T -> tree_t T - | Node : T -> node_elem_t T -> tree_t T -> tree_t T - - /- [no_nested_borrows::list_length] -/ - def list_length_fwd (T : Type) (l : list_t T) : Result UInt32 := - match h: l with - | list_t.Cons t l1 => + +/- Unit test for [no_nested_borrows::test_split_list] -/ +#assert (test_split_list_fwd == .ret ()) + +/- [no_nested_borrows::choose] -/ +def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := + if h: b + then Result.ret x + else Result.ret y + +/- [no_nested_borrows::choose] -/ +def choose_back + (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := + if h: b + then Result.ret (ret0, y) + else Result.ret (x, ret0) + +/- [no_nested_borrows::choose_test] -/ +def choose_test_fwd : Result Unit := + do + let z ← + choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit)) + let z0 ← z + (I32.ofInt 1 (by intlit)) + if h: not (z0 = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else do - let i ← list_length_fwd T l1 - UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i - | list_t.Nil => Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::list_nth_shared] -/ - def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_fwd T tl i0 - | list_t.Nil => Result.fail Error.panic - - /- [no_nested_borrows::list_nth_mut] -/ - def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_fwd T tl i0 - | list_t.Nil => Result.fail Error.panic - - /- [no_nested_borrows::list_nth_mut] -/ - def list_nth_mut_back - (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := - match h: l with - | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.Cons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_back T tl i0 ret0 - Result.ret (list_t.Cons x tl0) - | list_t.Nil => Result.fail Error.panic - - /- [no_nested_borrows::list_rev_aux] -/ - def list_rev_aux_fwd - (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) := - match h: li with - | list_t.Cons hd tl => list_rev_aux_fwd T tl (list_t.Cons hd lo) - | list_t.Nil => Result.ret lo - - /- [no_nested_borrows::list_rev] -/ - def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) := - let li := mem_replace_fwd (list_t T) l list_t.Nil - list_rev_aux_fwd T li list_t.Nil - - /- [no_nested_borrows::test_list_functions] -/ - def test_list_functions_fwd : Result Unit := - do - let l := list_t.Nil - let l0 := list_t.Cons (Int32.ofNatCore 2 (by intlit)) l - let l1 := list_t.Cons (Int32.ofNatCore 1 (by intlit)) l0 - let i ← - list_length_fwd Int32 (list_t.Cons (Int32.ofNatCore 0 (by intlit)) l1) - if h: not (i = (UInt32.ofNatCore 3 (by intlit))) - then Result.fail Error.panic - else - do - let i0 ← - list_nth_shared_fwd Int32 (list_t.Cons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 0 (by intlit)) - if h: not (i0 = (Int32.ofNatCore 0 (by intlit))) + let (x, y) ← + choose_back I32 true (I32.ofInt 0 (by intlit)) + (I32.ofInt 0 (by intlit)) z0 + if h: not (x = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + if h: not (y = (I32.ofInt 0 (by intlit))) then Result.fail Error.panic - else - do - let i1 ← - list_nth_shared_fwd Int32 (list_t.Cons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 1 (by intlit)) - if h: not (i1 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let i2 ← - list_nth_shared_fwd Int32 (list_t.Cons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 2 (by intlit)) - if h: not (i2 = (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else - do - let ls ← - list_nth_mut_back Int32 (list_t.Cons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 1 (by intlit)) - (Int32.ofNatCore 3 (by intlit)) - let i3 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 0 (by intlit)) - if h: not (i3 = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else - do - let i4 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 1 (by intlit)) - if h: not (i4 = (Int32.ofNatCore 3 (by intlit))) - then Result.fail Error.panic - else - do - let i5 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 2 (by intlit)) - if h: not (i5 = (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_list_functions] -/ - #assert (test_list_functions_fwd == .ret ()) - - /- [no_nested_borrows::id_mut_pair1] -/ - def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := - Result.ret (x, y) - - /- [no_nested_borrows::id_mut_pair1] -/ - def id_mut_pair1_back - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := ret0 - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair2] -/ - def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := p - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair2] -/ - def id_mut_pair2_back - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := ret0 - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := - Result.ret (x, y) - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_back'a - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_back'b - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := p - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_back'a - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_back'b - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 := - Result.ret ret0 - - /- [no_nested_borrows::StructWithTuple] -/ - structure struct_with_tuple_t (T1 T2 : Type) where - struct_with_tuple_p : (T1 × T2) - - /- [no_nested_borrows::new_tuple1] -/ - def new_tuple1_fwd : Result (struct_with_tuple_t UInt32 UInt32) := - Result.ret - { - struct_with_tuple_p := - ((UInt32.ofNatCore 1 (by intlit)), (UInt32.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::new_tuple2] -/ - def new_tuple2_fwd : Result (struct_with_tuple_t Int16 Int16) := - Result.ret - { - struct_with_tuple_p := - ((Int16.ofNatCore 1 (by intlit)), (Int16.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::new_tuple3] -/ - def new_tuple3_fwd : Result (struct_with_tuple_t UInt64 Int64) := - Result.ret - { - struct_with_tuple_p := - ((UInt64.ofNatCore 1 (by intlit)), (Int64.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::StructWithPair] -/ - structure struct_with_pair_t (T1 T2 : Type) where - struct_with_pair_p : pair_t T1 T2 - - /- [no_nested_borrows::new_pair1] -/ - def new_pair1_fwd : Result (struct_with_pair_t UInt32 UInt32) := - Result.ret - { - struct_with_pair_p := - { - pair_x := (UInt32.ofNatCore 1 (by intlit)), - pair_y := (UInt32.ofNatCore 2 (by intlit)) - } - } - - /- [no_nested_borrows::test_constants] -/ - def test_constants_fwd : Result Unit := + else Result.ret () + +/- Unit test for [no_nested_borrows::choose_test] -/ +#assert (choose_test_fwd == .ret ()) + +/- [no_nested_borrows::test_char] -/ +def test_char_fwd : Result Char := + Result.ret 'a' + +/- [no_nested_borrows::NodeElem] -/ +mutual inductive node_elem_t (T : Type) := +| Cons : tree_t T -> node_elem_t T -> node_elem_t T +| Nil : node_elem_t T + +/- [no_nested_borrows::Tree] -/ +inductive tree_t (T : Type) := +| Leaf : T -> tree_t T +| Node : T -> node_elem_t T -> tree_t T -> tree_t T +end + +/- [no_nested_borrows::list_length] -/ +def list_length_fwd (T : Type) (l : list_t T) : Result U32 := + match h: l with + | list_t.Cons t l1 => do - let swt ← new_tuple1_fwd - let (i, _) := swt.struct_with_tuple_p - if h: not (i = (UInt32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swt0 ← new_tuple2_fwd - let (i0, _) := swt0.struct_with_tuple_p - if h: not (i0 = (Int16.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swt1 ← new_tuple3_fwd - let (i1, _) := swt1.struct_with_tuple_p - if h: not (i1 = (UInt64.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swp ← new_pair1_fwd - if h: not (swp.struct_with_pair_p.pair_x = - (UInt32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_constants] -/ - #assert (test_constants_fwd == .ret ()) - - /- [no_nested_borrows::test_weird_borrows1] -/ - def test_weird_borrows1_fwd : Result Unit := - Result.ret () - - /- Unit test for [no_nested_borrows::test_weird_borrows1] -/ - #assert (test_weird_borrows1_fwd == .ret ()) - - /- [no_nested_borrows::test_mem_replace] -/ - def test_mem_replace_fwd_back (px : UInt32) : Result UInt32 := - let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit)) - if h: not (y = (UInt32.ofNatCore 0 (by intlit))) + let i ← list_length_fwd T l1 + (U32.ofInt 1 (by intlit)) + i + | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit)) + +/- [no_nested_borrows::list_nth_shared] -/ +def list_nth_shared_fwd (T : Type) (l : list_t T) (i : U32) : Result T := + match h: l with + | list_t.Cons x tl => + if h: i = (U32.ofInt 0 (by intlit)) + then Result.ret x + else + do + let i0 ← i - (U32.ofInt 1 (by intlit)) + list_nth_shared_fwd T tl i0 + | list_t.Nil => Result.fail Error.panic + +/- [no_nested_borrows::list_nth_mut] -/ +def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T := + match h: l with + | list_t.Cons x tl => + if h: i = (U32.ofInt 0 (by intlit)) + then Result.ret x + else do + let i0 ← i - (U32.ofInt 1 (by intlit)) + list_nth_mut_fwd T tl i0 + | list_t.Nil => Result.fail Error.panic + +/- [no_nested_borrows::list_nth_mut] -/ +def list_nth_mut_back + (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := + match h: l with + | list_t.Cons x tl => + if h: i = (U32.ofInt 0 (by intlit)) + then Result.ret (list_t.Cons ret0 tl) + else + do + let i0 ← i - (U32.ofInt 1 (by intlit)) + let tl0 ← list_nth_mut_back T tl i0 ret0 + Result.ret (list_t.Cons x tl0) + | list_t.Nil => Result.fail Error.panic + +/- [no_nested_borrows::list_rev_aux] -/ +def list_rev_aux_fwd + (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) := + match h: li with + | list_t.Cons hd tl => list_rev_aux_fwd T tl (list_t.Cons hd lo) + | list_t.Nil => Result.ret lo + +/- [no_nested_borrows::list_rev] -/ +def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) := + let li := mem_replace_fwd (list_t T) l list_t.Nil + list_rev_aux_fwd T li list_t.Nil + +/- [no_nested_borrows::test_list_functions] -/ +def test_list_functions_fwd : Result Unit := + do + let l := list_t.Nil + let l0 := list_t.Cons (I32.ofInt 2 (by intlit)) l + let l1 := list_t.Cons (I32.ofInt 1 (by intlit)) l0 + let i ← list_length_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1) + if h: not (i = (U32.ofInt 3 (by intlit))) + then Result.fail Error.panic + else + do + let i0 ← + list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1) + (U32.ofInt 0 (by intlit)) + if h: not (i0 = (I32.ofInt 0 (by intlit))) + then Result.fail Error.panic + else + do + let i1 ← + list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) + l1) (U32.ofInt 1 (by intlit)) + if h: not (i1 = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + do + let i2 ← + list_nth_shared_fwd I32 (list_t.Cons + (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 2 (by intlit)) + if h: not (i2 = (I32.ofInt 2 (by intlit))) + then Result.fail Error.panic + else + do + let ls ← + list_nth_mut_back I32 (list_t.Cons + (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 1 (by intlit)) + (I32.ofInt 3 (by intlit)) + let i3 ← + list_nth_shared_fwd I32 ls (U32.ofInt 0 (by intlit)) + if h: not (i3 = (I32.ofInt 0 (by intlit))) + then Result.fail Error.panic + else + do + let i4 ← + list_nth_shared_fwd I32 ls (U32.ofInt 1 (by intlit)) + if h: not (i4 = (I32.ofInt 3 (by intlit))) + then Result.fail Error.panic + else + do + let i5 ← + list_nth_shared_fwd I32 ls + (U32.ofInt 2 (by intlit)) + if h: not (i5 = (I32.ofInt 2 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [no_nested_borrows::test_list_functions] -/ +#assert (test_list_functions_fwd == .ret ()) + +/- [no_nested_borrows::id_mut_pair1] -/ +def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := + Result.ret (x, y) + +/- [no_nested_borrows::id_mut_pair1] -/ +def id_mut_pair1_back + (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) := + let (t, t0) := ret0 + Result.ret (t, t0) + +/- [no_nested_borrows::id_mut_pair2] -/ +def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := + let (t, t0) := p + Result.ret (t, t0) + +/- [no_nested_borrows::id_mut_pair2] -/ +def id_mut_pair2_back + (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) := + let (t, t0) := ret0 + Result.ret (t, t0) + +/- [no_nested_borrows::id_mut_pair3] -/ +def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := + Result.ret (x, y) + +/- [no_nested_borrows::id_mut_pair3] -/ +def id_mut_pair3_back'a + (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 := + Result.ret ret0 + +/- [no_nested_borrows::id_mut_pair3] -/ +def id_mut_pair3_back'b + (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 := + Result.ret ret0 + +/- [no_nested_borrows::id_mut_pair4] -/ +def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := + let (t, t0) := p + Result.ret (t, t0) + +/- [no_nested_borrows::id_mut_pair4] -/ +def id_mut_pair4_back'a + (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 := + Result.ret ret0 + +/- [no_nested_borrows::id_mut_pair4] -/ +def id_mut_pair4_back'b + (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 := + Result.ret ret0 + +/- [no_nested_borrows::StructWithTuple] -/ +structure struct_with_tuple_t (T1 T2 : Type) where + struct_with_tuple_p : (T1 × T2) + +/- [no_nested_borrows::new_tuple1] -/ +def new_tuple1_fwd : Result (struct_with_tuple_t U32 U32) := + Result.ret + { + struct_with_tuple_p := + ((U32.ofInt 1 (by intlit)), (U32.ofInt 2 (by intlit))) + } + +/- [no_nested_borrows::new_tuple2] -/ +def new_tuple2_fwd : Result (struct_with_tuple_t I16 I16) := + Result.ret + { + struct_with_tuple_p := + ((I16.ofInt 1 (by intlit)), (I16.ofInt 2 (by intlit))) + } + +/- [no_nested_borrows::new_tuple3] -/ +def new_tuple3_fwd : Result (struct_with_tuple_t U64 I64) := + Result.ret + { + struct_with_tuple_p := + ((U64.ofInt 1 (by intlit)), (I64.ofInt 2 (by intlit))) + } + +/- [no_nested_borrows::StructWithPair] -/ +structure struct_with_pair_t (T1 T2 : Type) where + struct_with_pair_p : pair_t T1 T2 + +/- [no_nested_borrows::new_pair1] -/ +def new_pair1_fwd : Result (struct_with_pair_t U32 U32) := + Result.ret + { + struct_with_pair_p := + { + pair_x := (U32.ofInt 1 (by intlit)), + pair_y := (U32.ofInt 2 (by intlit)) + } + } + +/- [no_nested_borrows::test_constants] -/ +def test_constants_fwd : Result Unit := + do + let swt ← new_tuple1_fwd + let (i, _) := swt.struct_with_tuple_p + if h: not (i = (U32.ofInt 1 (by intlit))) then Result.fail Error.panic - else Result.ret (UInt32.ofNatCore 2 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_bool1] -/ - def test_shared_borrow_bool1_fwd (b : Bool) : Result UInt32 := - if h: b - then Result.ret (UInt32.ofNatCore 0 (by intlit)) - else Result.ret (UInt32.ofNatCore 1 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_bool2] -/ - def test_shared_borrow_bool2_fwd : Result UInt32 := - Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_enum1] -/ - def test_shared_borrow_enum1_fwd (l : list_t UInt32) : Result UInt32 := - match h: l with - | list_t.Cons i l0 => Result.ret (UInt32.ofNatCore 1 (by intlit)) - | list_t.Nil => Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_enum2] -/ - def test_shared_borrow_enum2_fwd : Result UInt32 := - Result.ret (UInt32.ofNatCore 0 (by intlit)) - + else + do + let swt0 ← new_tuple2_fwd + let (i0, _) := swt0.struct_with_tuple_p + if h: not (i0 = (I16.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + do + let swt1 ← new_tuple3_fwd + let (i1, _) := swt1.struct_with_tuple_p + if h: not (i1 = (U64.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + do + let swp ← new_pair1_fwd + if h: not (swp.struct_with_pair_p.pair_x = + (U32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [no_nested_borrows::test_constants] -/ +#assert (test_constants_fwd == .ret ()) + +/- [no_nested_borrows::test_weird_borrows1] -/ +def test_weird_borrows1_fwd : Result Unit := + Result.ret () + +/- Unit test for [no_nested_borrows::test_weird_borrows1] -/ +#assert (test_weird_borrows1_fwd == .ret ()) + +/- [no_nested_borrows::test_mem_replace] -/ +def test_mem_replace_fwd_back (px : U32) : Result U32 := + let y := mem_replace_fwd U32 px (U32.ofInt 1 (by intlit)) + if h: not (y = (U32.ofInt 0 (by intlit))) + then Result.fail Error.panic + else Result.ret (U32.ofInt 2 (by intlit)) + +/- [no_nested_borrows::test_shared_borrow_bool1] -/ +def test_shared_borrow_bool1_fwd (b : Bool) : Result U32 := + if h: b + then Result.ret (U32.ofInt 0 (by intlit)) + else Result.ret (U32.ofInt 1 (by intlit)) + +/- [no_nested_borrows::test_shared_borrow_bool2] -/ +def test_shared_borrow_bool2_fwd : Result U32 := + Result.ret (U32.ofInt 0 (by intlit)) + +/- [no_nested_borrows::test_shared_borrow_enum1] -/ +def test_shared_borrow_enum1_fwd (l : list_t U32) : Result U32 := + match h: l with + | list_t.Cons i l0 => Result.ret (U32.ofInt 1 (by intlit)) + | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit)) + +/- [no_nested_borrows::test_shared_borrow_enum2] -/ +def test_shared_borrow_enum2_fwd : Result U32 := + Result.ret (U32.ofInt 0 (by intlit)) + diff --git a/tests/lean/misc-paper/Base/Primitives.lean b/tests/lean/misc-paper/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-paper/Base/Primitives.lean +++ b/tests/lean/misc-paper/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-paper/Paper.lean b/tests/lean/misc-paper/Paper.lean index 05fde52c..0b16fb8e 100644 --- a/tests/lean/misc-paper/Paper.lean +++ b/tests/lean/misc-paper/Paper.lean @@ -2,126 +2,122 @@ -- [paper] import Base.Primitives -structure OpaqueDefs where - - /- [paper::ref_incr] -/ - def ref_incr_fwd_back (x : Int32) : Result Int32 := - Int32.checked_add x (Int32.ofNatCore 1 (by intlit)) - - /- [paper::test_incr] -/ - def test_incr_fwd : Result Unit := - do - let x ← ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit)) - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_incr] -/ - #assert (test_incr_fwd == .ret ()) - - /- [paper::choose] -/ - def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := - if h: b - then Result.ret x - else Result.ret y - - /- [paper::choose] -/ - def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := - if h: b - then Result.ret (ret0, y) - else Result.ret (x, ret0) - - /- [paper::test_choose] -/ - def test_choose_fwd : Result Unit := - do - let z ← - choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) - let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) - if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let (x, y) ← - choose_back Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) z0 - if h: not (x = (Int32.ofNatCore 1 (by intlit))) +/- [paper::ref_incr] -/ +def ref_incr_fwd_back (x : I32) : Result I32 := + x + (I32.ofInt 1 (by intlit)) + +/- [paper::test_incr] -/ +def test_incr_fwd : Result Unit := + do + let x ← ref_incr_fwd_back (I32.ofInt 0 (by intlit)) + if h: not (x = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [paper::test_incr] -/ +#assert (test_incr_fwd == .ret ()) + +/- [paper::choose] -/ +def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := + if h: b + then Result.ret x + else Result.ret y + +/- [paper::choose] -/ +def choose_back + (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := + if h: b + then Result.ret (ret0, y) + else Result.ret (x, ret0) + +/- [paper::test_choose] -/ +def test_choose_fwd : Result Unit := + do + let z ← + choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit)) + let z0 ← z + (I32.ofInt 1 (by intlit)) + if h: not (z0 = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + do + let (x, y) ← + choose_back I32 true (I32.ofInt 0 (by intlit)) + (I32.ofInt 0 (by intlit)) z0 + if h: not (x = (I32.ofInt 1 (by intlit))) + then Result.fail Error.panic + else + if h: not (y = (I32.ofInt 0 (by intlit))) then Result.fail Error.panic - else - if h: not (y = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_choose] -/ - #assert (test_choose_fwd == .ret ()) - - /- [paper::List] -/ - inductive list_t (T : Type) := - | Cons : T -> list_t T -> list_t T - | Nil : list_t T - - /- [paper::list_nth_mut] -/ - def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_fwd T tl i0 - | list_t.Nil => Result.fail Error.panic - - /- [paper::list_nth_mut] -/ - def list_nth_mut_back - (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := - match h: l with - | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.Cons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_back T tl i0 ret0 - Result.ret (list_t.Cons x tl0) - | list_t.Nil => Result.fail Error.panic - - /- [paper::sum] -/ - def sum_fwd (l : list_t Int32) : Result Int32 := - match h: l with - | list_t.Cons x tl => do - let i ← sum_fwd tl - Int32.checked_add x i - | list_t.Nil => Result.ret (Int32.ofNatCore 0 (by intlit)) - - /- [paper::test_nth] -/ - def test_nth_fwd : Result Unit := - do - let l := list_t.Nil - let l0 := list_t.Cons (Int32.ofNatCore 3 (by intlit)) l - let l1 := list_t.Cons (Int32.ofNatCore 2 (by intlit)) l0 - let x ← - list_nth_mut_fwd Int32 (list_t.Cons (Int32.ofNatCore 1 (by intlit)) l1) - (UInt32.ofNatCore 2 (by intlit)) - let x0 ← Int32.checked_add x (Int32.ofNatCore 1 (by intlit)) - let l2 ← - list_nth_mut_back Int32 (list_t.Cons (Int32.ofNatCore 1 (by intlit)) - l1) (UInt32.ofNatCore 2 (by intlit)) x0 - let i ← sum_fwd l2 - if h: not (i = (Int32.ofNatCore 7 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_nth] -/ - #assert (test_nth_fwd == .ret ()) - - /- [paper::call_choose] -/ - def call_choose_fwd (p : (UInt32 × UInt32)) : Result UInt32 := - do - let (px, py) := p - let pz ← choose_fwd UInt32 true px py - let pz0 ← UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit)) - let (px0, _) ← choose_back UInt32 true px py pz0 - Result.ret px0 - + else Result.ret () + +/- Unit test for [paper::test_choose] -/ +#assert (test_choose_fwd == .ret ()) + +/- [paper::List] -/ +inductive list_t (T : Type) := +| Cons : T -> list_t T -> list_t T +| Nil : list_t T + +/- [paper::list_nth_mut] -/ +def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T := + match h: l with + | list_t.Cons x tl => + if h: i = (U32.ofInt 0 (by intlit)) + then Result.ret x + else do + let i0 ← i - (U32.ofInt 1 (by intlit)) + list_nth_mut_fwd T tl i0 + | list_t.Nil => Result.fail Error.panic + +/- [paper::list_nth_mut] -/ +def list_nth_mut_back + (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := + match h: l with + | list_t.Cons x tl => + if h: i = (U32.ofInt 0 (by intlit)) + then Result.ret (list_t.Cons ret0 tl) + else + do + let i0 ← i - (U32.ofInt 1 (by intlit)) + let tl0 ← list_nth_mut_back T tl i0 ret0 + Result.ret (list_t.Cons x tl0) + | list_t.Nil => Result.fail Error.panic + +/- [paper::sum] -/ +def sum_fwd (l : list_t I32) : Result I32 := + match h: l with + | list_t.Cons x tl => do + let i ← sum_fwd tl + x + i + | list_t.Nil => Result.ret (I32.ofInt 0 (by intlit)) + +/- [paper::test_nth] -/ +def test_nth_fwd : Result Unit := + do + let l := list_t.Nil + let l0 := list_t.Cons (I32.ofInt 3 (by intlit)) l + let l1 := list_t.Cons (I32.ofInt 2 (by intlit)) l0 + let x ← + list_nth_mut_fwd I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1) + (U32.ofInt 2 (by intlit)) + let x0 ← x + (I32.ofInt 1 (by intlit)) + let l2 ← + list_nth_mut_back I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1) + (U32.ofInt 2 (by intlit)) x0 + let i ← sum_fwd l2 + if h: not (i = (I32.ofInt 7 (by intlit))) + then Result.fail Error.panic + else Result.ret () + +/- Unit test for [paper::test_nth] -/ +#assert (test_nth_fwd == .ret ()) + +/- [paper::call_choose] -/ +def call_choose_fwd (p : (U32 × U32)) : Result U32 := + do + let (px, py) := p + let pz ← choose_fwd U32 true px py + let pz0 ← pz + (U32.ofInt 1 (by intlit)) + let (px0, _) ← choose_back U32 true px py pz0 + Result.ret px0 + diff --git a/tests/lean/misc-polonius_list/Base/Primitives.lean b/tests/lean/misc-polonius_list/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-polonius_list/Base/Primitives.lean +++ b/tests/lean/misc-polonius_list/Base/Primitives.lean @@ -3,6 +3,28 @@ import Lean.Meta.Tactic.Simp import Init.Data.List.Basic import Mathlib.Tactic.RunCmd +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + ------------- -- PRELUDE -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., --- USize. They are generally defined in an idiomatic style, except that there is --- not a single type class to rule them all (more on that below). The absence of --- type class is intentional, and allows the Lean compiler to efficiently map --- them to machine integers during compilation. +-- We redefine our machine integers types. --- USize is designed properly: you cannot reduce `getNumBits` using the --- simplifier, meaning that proofs do not depend on the compile-time value of --- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really --- support, at least officially, 16-bit microcontrollers, so this seems like a --- fine design decision for now.) +-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits` +-- using the simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at +-- least officially, 16-bit microcontrollers, so this seems like a fine design decision +-- for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- Machine integer constants, done via `ofNatCore`, which requires a proof that -- the `Nat` fits within the desired integer type. We provide a custom tactic. -syntax "intlit" : tactic - -macro_rules - | `(tactic| intlit) => `(tactic| - match USize.size, usize_size_eq with - | _, Or.inl rfl => decide - | _, Or.inr rfl => decide) - --- This is how the macro is expected to be used -#eval USize.ofNatCore 0 (by intlit) - --- Also works for other integer types (at the expense of a needless disjunction) -#eval UInt32.ofNatCore 0 (by intlit) - --- The machine integer operations (e.g. sub) are always total, which is not what --- we want. We therefore define "checked" variants, below. Note that we add a --- tiny bit of complexity for the USize variant: we first check whether the --- result is < 2^32; if it is, we can compute the definition, rather than --- returning a term that is computationally stuck (the comparison to USize.size --- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +open System.Platform.getNumBits + +-- TODO: is there a way of only importing System.Platform.getNumBits? +-- +@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val + +-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention. +-- We keep the F* convention for now. +@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1)) +@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1 +@[simp] def I8.min : Int := - (HPow.hPow 2 7) +@[simp] def I8.max : Int := HPow.hPow 2 7 - 1 +@[simp] def I16.min : Int := - (HPow.hPow 2 15) +@[simp] def I16.max : Int := HPow.hPow 2 15 - 1 +@[simp] def I32.min : Int := -(HPow.hPow 2 31) +@[simp] def I32.max : Int := HPow.hPow 2 31 - 1 +@[simp] def I64.min : Int := -(HPow.hPow 2 63) +@[simp] def I64.max : Int := HPow.hPow 2 63 - 1 +@[simp] def I128.min : Int := -(HPow.hPow 2 127) +@[simp] def I128.max : Int := HPow.hPow 2 127 - 1 +@[simp] def Usize.min : Int := 0 +@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1 +@[simp] def U8.min : Int := 0 +@[simp] def U8.max : Int := HPow.hPow 2 8 - 1 +@[simp] def U16.min : Int := 0 +@[simp] def U16.max : Int := HPow.hPow 2 16 - 1 +@[simp] def U32.min : Int := 0 +@[simp] def U32.max : Int := HPow.hPow 2 32 - 1 +@[simp] def U64.min : Int := 0 +@[simp] def U64.max : Int := HPow.hPow 2 64 - 1 +@[simp] def U128.min : Int := 0 +@[simp] def U128.max : Int := HPow.hPow 2 128 - 1 + +#assert (I8.min == -128) +#assert (I8.max == 127) +#assert (I16.min == -32768) +#assert (I16.max == 32767) +#assert (I32.min == -2147483648) +#assert (I32.max == 2147483647) +#assert (I64.min == -9223372036854775808) +#assert (I64.max == 9223372036854775807) +#assert (I128.min == -170141183460469231731687303715884105728) +#assert (I128.max == 170141183460469231731687303715884105727) +#assert (U8.min == 0) +#assert (U8.max == 255) +#assert (U16.min == 0) +#assert (U16.max == 65535) +#assert (U32.min == 0) +#assert (U32.max == 4294967295) +#assert (U64.min == 0) +#assert (U64.max == 18446744073709551615) +#assert (U128.min == 0) +#assert (U128.max == 340282366920938463463374607431768211455) + +inductive ScalarTy := +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +def Scalar.min (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.min + | .I8 => I8.min + | .I16 => I16.min + | .I32 => I32.min + | .I64 => I64.min + | .I128 => I128.min + | .Usize => Usize.min + | .U8 => U8.min + | .U16 => U16.min + | .U32 => U32.min + | .U64 => U64.min + | .U128 => U128.min + +def Scalar.max (ty : ScalarTy) : Int := + match ty with + | .Isize => Isize.max + | .I8 => I8.max + | .I16 => I16.max + | .I32 => I32.max + | .I64 => I64.max + | .I128 => I128.max + | .Usize => Usize.max + | .U8 => U8.max + | .U16 => U16.max + | .U32 => U32.max + | .U64 => U64.max + | .U128 => U128.max + +-- "Conservative" bounds +-- We use those because we can't compare to the isize bounds (which can't +-- reduce at compile-time). Whenever we perform an arithmetic operation like +-- addition we need to check that the result is in bounds: we first compare +-- to the conservative bounds, which reduce, then compare to the real bounds. -- This is useful for the various #asserts that we want to reduce at -- type-checking time. +def Scalar.cMin (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.min + | _ => Scalar.min ty + +def Scalar.cMax (ty : ScalarTy) : Int := + match ty with + | .Isize => I32.max + | .Usize => U32.max + | _ => Scalar.max ty + +theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry +theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty <= x && x <= Scalar.cMax ty -> + (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true + := by sorry + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty := + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + Scalar.ofIntCore x hmin hmax -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): Result USize := - -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? - if n >= m then - let n' := USize.toNat n - let m' := USize.toNat n - let r := USize.ofNatCore (n' - m') (by - have h: n' - m' <= n' := by - apply Nat.sub_le_of_le_add - case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left - apply Nat.lt_of_le_of_lt h - apply n.val.isLt - ) - return r - else - fail integerOverflow - -@[simp] -theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := - match USize.size, usize_size_eq with - | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) - | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) - -def USize.checked_add (n: USize) (m: USize): Result USize := - if h: n.val + m.val < USize.size then - .ret ⟨ n.val + m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_rem (n: USize) (m: USize): Result USize := - if h: m > 0 then - .ret ⟨ n.val % m.val, by - have h1: ↑m.val < USize.size := m.val.isLt - have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h - apply Nat.lt_trans h2 h1 - ⟩ - else - .fail integerOverflow +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + -- TODO: write this with only one if then else + if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then + if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then + let hmin: Scalar.min ty <= x := by sorry + let hmax: x <= Scalar.max ty := by sorry + return Scalar.ofIntCore x hmin hmax + else fail integerOverflow + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero + +-- Checking that the % operation in Lean computes the same as the remainder operation in Rust +#assert 1 % 2 = (1:Int) +#assert (-1) % 2 = -1 +#assert 1 % (-2) = 1 +#assert (-1) % (-2) = -1 + +def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero + +def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val + y.val) + +def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val - y.val) + +def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := + Scalar.tryMk ty (x.val * y.val) + +-- TODO: instances of +, -, * etc. for scalars + +-- Cast an integer from a [src_ty] to a [tgt_ty] +-- TODO: check the semantics of casts in Rust +def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := + Scalar.tryMk tgt_ty x.val + +-- The scalar types +-- We declare the definitions as reducible so that Lean can unfold them (useful +-- for type class resolution for instance). +@[reducible] def Isize := Scalar .Isize +@[reducible] def I8 := Scalar .I8 +@[reducible] def I16 := Scalar .I16 +@[reducible] def I32 := Scalar .I32 +@[reducible] def I64 := Scalar .I64 +@[reducible] def I128 := Scalar .I128 +@[reducible] def Usize := Scalar .Usize +@[reducible] def U8 := Scalar .U8 +@[reducible] def U16 := Scalar .U16 +@[reducible] def U32 := Scalar .U32 +@[reducible] def U64 := Scalar .U64 +@[reducible] def U128 := Scalar .U128 + +-- TODO: below: not sure this is the best way. +-- Should we rather overload operations like +, -, etc.? +-- Also, it is possible to automate the generation of those definitions +-- with macros (but would it be a good idea? It would be less easy to +-- read the file, which is not supposed to change a lot) + +-- Negation + +/-- +Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce +one here. + +The notation typeclass for heterogeneous addition. +This enables the notation `- a : β` where `a : α`. +-/ +class HNeg (α : Type u) (β : outParam (Type v)) where + /-- `- a` computes the negation of `a`. + The meaning of this notation is type-dependent. -/ + hNeg : α → β + +prefix:75 "-" => HNeg.hNeg + +instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x +instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x +instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x +instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x +instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x +instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x + +-- Addition +instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hAdd x y := Scalar.add x y + +-- Substraction +instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hSub x y := Scalar.sub x y + +-- Multiplication +instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMul x y := Scalar.mul x y + +-- Division +instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hDiv x y := Scalar.div x y + +-- Remainder +instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where + hMod x y := Scalar.rem x y + +-- ofIntCore +-- TODO: typeclass? +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 + +-- ofInt +-- TODO: typeclass? +def Isize.ofInt := @Scalar.ofInt .Isize +def I8.ofInt := @Scalar.ofInt .I8 +def I16.ofInt := @Scalar.ofInt .I16 +def I32.ofInt := @Scalar.ofInt .I32 +def I64.ofInt := @Scalar.ofInt .I64 +def I128.ofInt := @Scalar.ofInt .I128 +def Usize.ofInt := @Scalar.ofInt .Usize +def U8.ofInt := @Scalar.ofInt .U8 +def U16.ofInt := @Scalar.ofInt .U16 +def U32.ofInt := @Scalar.ofInt .U32 +def U64.ofInt := @Scalar.ofInt .U64 +def U128.ofInt := @Scalar.ofInt .U128 + +-- Comparisons +instance {ty} : LT (Scalar ty) where + lt a b := LT.lt a.val b.val + +instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val + +instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt .. +instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe .. + +theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j + | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl + +theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val := + h ▸ rfl + +theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) := + fun h' => absurd (val_eq_of_eq h') h + +instance (ty : ScalarTy) : DecidableEq (Scalar ty) := + fun i j => + match decEq i.val j.val with + | isTrue h => isTrue (Scalar.eq_of_val_eq h) + | isFalse h => isFalse (Scalar.ne_of_val_ne h) + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic -def USize.checked_mul (n: USize) (m: USize): Result USize := - if h: n.val * m.val < USize.size then - .ret ⟨ n.val * m.val, h ⟩ - else - .fail integerOverflow - -def USize.checked_div (n: USize) (m: USize): Result USize := - if m > 0 then - .ret ⟨ n.val / m.val, by - have h1: ↑n.val < USize.size := n.val.isLt - have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val - apply Nat.lt_of_le_of_lt h2 h1 - ⟩ - else - .fail integerOverflow - --- Test behavior... -#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 - -#eval USize.checked_sub 20 10 --- NOTE: compare with concrete behavior here, which I do not think we want -#eval USize.sub 0 1 -#eval UInt8.add 255 255 - --- We now define a type class that subsumes the various machine integer types, so --- as to write a concise definition for scalar_cast, rather than exhaustively --- enumerating all of the possible pairs. We remark that Rust has sane semantics --- and fails if a cast operation would involve a truncation or modulo. - -class MachineInteger (t: Type) where - size: Nat - val: t -> Fin size - ofNatCore: (n:Nat) -> LT.lt n size -> t - -set_option hygiene false in -run_cmd - for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do - Lean.Elab.Command.elabCommand (← `( - namespace $typeName - instance: MachineInteger $typeName where - size := size - val := val - ofNatCore := ofNatCore - end $typeName - )) - --- Aeneas only instantiates the destination type (`src` is implicit). We rely on --- Lean to infer `src`. - -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := - if h: MachineInteger.val x < MachineInteger.size dst then - .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) - else - .fail integerOverflow +macro_rules + | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide) + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- VECTORS -- ------------- --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -def vec_len (α : Type u) (v : Vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : Usize := let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) + Usize.ofIntCore (List.length v) (by sorry) l def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ + if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then + return ⟨ List.concat v.val x, by sorry ⟩ else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } + let h: i < List.length v.val := by sorry .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := if i.val < List.length v.val then + let i : Nat := + match i.val with + | .ofNat n => n + | .negSucc n => by sorry -- TODO: we can't get here + let isLt: i < USize.size := by sorry + let i : Fin USize.size := { val := i, isLt := isLt } .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +578,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- ASSERT COMMAND -- --------------------- - -open Lean Elab Command Term Meta - -syntax (name := assert) "#assert" term: command - -@[command_elab assert] -unsafe -def assertImpl : CommandElab := fun (_stx: Syntax) => do - runTermElabM (fun _ => do - let r ← evalTerm Bool (mkConst ``Bool) _stx[1] - if not r then - logInfo "Assertion failed for: " - logInfo _stx[1] - logError "Expression reduced to false" - pure ()) - -#eval 2 == 2 -#assert (2 == 2) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-polonius_list/PoloniusList.lean b/tests/lean/misc-polonius_list/PoloniusList.lean index a3bbfd0a..79696996 100644 --- a/tests/lean/misc-polonius_list/PoloniusList.lean +++ b/tests/lean/misc-polonius_list/PoloniusList.lean @@ -2,35 +2,30 @@ -- [polonius_list] import Base.Primitives -structure OpaqueDefs where - - /- [polonius_list::List] -/ - inductive list_t (T : Type) := - | Cons : T -> list_t T -> list_t T - | Nil : list_t T - - /- [polonius_list::get_list_at_x] -/ - def get_list_at_x_fwd - (ls : list_t UInt32) (x : UInt32) : Result (list_t UInt32) := - match h: ls with - | list_t.Cons hd tl => - if h: hd = x - then Result.ret (list_t.Cons hd tl) - else get_list_at_x_fwd tl x - | list_t.Nil => Result.ret list_t.Nil - - /- [polonius_list::get_list_at_x] -/ - def get_list_at_x_back - (ls : list_t UInt32) (x : UInt32) (ret0 : list_t UInt32) : - Result (list_t UInt32) - := - match h: ls with - | list_t.Cons hd tl => - if h: hd = x - then Result.ret ret0 - else - do - let tl0 ← get_list_at_x_back tl x ret0 - Result.ret (list_t.Cons hd tl0) - | list_t.Nil => Result.ret ret0 - +/- [polonius_list::List] -/ +inductive list_t (T : Type) := +| Cons : T -> list_t T -> list_t T +| Nil : list_t T + +/- [polonius_list::get_list_at_x] -/ +def get_list_at_x_fwd (ls : list_t U32) (x : U32) : Result (list_t U32) := + match h: ls with + | list_t.Cons hd tl => + if h: hd = x + then Result.ret (list_t.Cons hd tl) + else get_list_at_x_fwd tl x + | list_t.Nil => Result.ret list_t.Nil + +/- [polonius_list::get_list_at_x] -/ +def get_list_at_x_back + (ls : list_t U32) (x : U32) (ret0 : list_t U32) : Result (list_t U32) := + match h: ls with + | list_t.Cons hd tl => + if h: hd = x + then Result.ret ret0 + else + do + let tl0 ← get_list_at_x_back tl x ret0 + Result.ret (list_t.Cons hd tl0) + | list_t.Nil => Result.ret ret0 + -- cgit v1.2.3