summaryrefslogtreecommitdiff
path: root/tests/lean/betree
diff options
context:
space:
mode:
Diffstat (limited to 'tests/lean/betree')
-rw-r--r--tests/lean/betree/Base/Primitives.lean392
-rw-r--r--tests/lean/betree/BetreeMain/Clauses/Template.lean185
-rw-r--r--tests/lean/betree/BetreeMain/Funs.lean1222
-rw-r--r--tests/lean/betree/BetreeMain/Opaque.lean33
-rw-r--r--tests/lean/betree/BetreeMain/Types.lean61
-rw-r--r--tests/lean/betree/lakefile.lean18
6 files changed, 1911 insertions, 0 deletions
diff --git a/tests/lean/betree/Base/Primitives.lean b/tests/lean/betree/Base/Primitives.lean
new file mode 100644
index 00000000..5b64e908
--- /dev/null
+++ b/tests/lean/betree/Base/Primitives.lean
@@ -0,0 +1,392 @@
+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/Clauses/Template.lean b/tests/lean/betree/BetreeMain/Clauses/Template.lean
new file mode 100644
index 00000000..1d18174e
--- /dev/null
+++ b/tests/lean/betree/BetreeMain/Clauses/Template.lean
@@ -0,0 +1,185 @@
+-- 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
new file mode 100644
index 00000000..e40ca4ca
--- /dev/null
+++ b/tests/lean/betree/BetreeMain/Funs.lean
@@ -0,0 +1,1222 @@
+-- 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.BetreeUpsertFunStateAdd v => Result.ret v
+ | betree_upsert_fun_state_t.BetreeUpsertFunStateSub i =>
+ Result.ret (UInt64.ofNatCore 0 (by intlit))
+ | Option.some prev0 =>
+ match h: st with
+ | betree_upsert_fun_state_t.BetreeUpsertFunStateAdd 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.BetreeUpsertFunStateSub 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.BetreeListCons t tl =>
+ do
+ let i ← betree_list_len_fwd T tl
+ UInt64.checked_add (UInt64.ofNatCore 1 (by intlit)) i
+ | betree_list_t.BetreeListNil => 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.BetreeListNil, self)
+ else
+ match h: self with
+ | betree_list_t.BetreeListCons 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.BetreeListCons hd l, ls1)
+ | betree_list_t.BetreeListNil => 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.BetreeListNil
+ let l := tl
+ Result.ret (betree_list_t.BetreeListCons 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.BetreeListNil
+ match h: ls with
+ | betree_list_t.BetreeListCons x tl => Result.ret x
+ | betree_list_t.BetreeListNil => 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.BetreeListNil
+ match h: ls with
+ | betree_list_t.BetreeListCons x tl => Result.ret tl
+ | betree_list_t.BetreeListNil => 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.BetreeListCons hd l => Result.ret hd
+ | betree_list_t.BetreeListNil => 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.BetreeListCons hd l => let (i, _) := hd
+ Result.ret (i = key)
+ | betree_list_t.BetreeListNil => 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.BetreeListCons hd tl =>
+ let (i, t) := hd
+ if h: i >= pivot
+ then
+ Result.ret (betree_list_t.BetreeListNil, betree_list_t.BetreeListCons (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.BetreeListCons (i, t) l, ls1)
+ | betree_list_t.BetreeListNil =>
+ Result.ret (betree_list_t.BetreeListNil, betree_list_t.BetreeListNil)
+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.BetreeNodeLeaf
+ {
+ betree_leaf_id := id0,
+ betree_leaf_size := params.betree_params_split_size
+ }
+ let n0 := betree_node_t.BetreeNodeLeaf
+ {
+ betree_leaf_id := id1,
+ betree_leaf_size := params.betree_params_split_size
+ }
+ Result.ret (st1,
+ {
+ betree_internal_id := self.betree_leaf_id,
+ betree_internal_pivot := pivot,
+ betree_internal_left := n,
+ betree_internal_right := 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.BetreeListCons 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.BetreeListNil => 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.BetreeListCons x next_msgs =>
+ let (i, m) := x
+ if h: i >= key
+ then Result.ret (betree_list_t.BetreeListCons (i, m) next_msgs)
+ else betree_node_lookup_first_message_for_key_fwd key next_msgs
+ | betree_list_t.BetreeListNil => Result.ret betree_list_t.BetreeListNil
+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.BetreeListCons 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.BetreeListCons (i, m) next_msgs0)
+ | betree_list_t.BetreeListNil => 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.BetreeMessageInsert i => Result.fail Error.panic
+ | betree_message_t.BetreeMessageDelete => Result.fail Error.panic
+ | betree_message_t.BetreeMessageUpsert 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.BetreeMessageInsert 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.BetreeMessageInsert i => Result.fail Error.panic
+ | betree_message_t.BetreeMessageDelete => Result.fail Error.panic
+ | betree_message_t.BetreeMessageUpsert 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.BetreeMessageInsert 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.BetreeNodeInternal node =>
+ do
+ let (st0, msgs) ←
+ betree_load_internal_node_fwd node.betree_internal_id st
+ let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+ match h: pending with
+ | betree_list_t.BetreeListCons p l =>
+ let (k, msg) := p
+ if h: k != key
+ then
+ do
+ let (st1, opt) ←
+ betree_internal_lookup_in_children_fwd node key st0
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ (betree_list_t.BetreeListCons (k, msg) l)
+ Result.ret (st1, opt)
+ else
+ match h: msg with
+ | betree_message_t.BetreeMessageInsert v =>
+ do
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageInsert v) l)
+ Result.ret (st0, Option.some v)
+ | betree_message_t.BetreeMessageDelete =>
+ do
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageDelete) l)
+ Result.ret (st0, Option.none)
+ | betree_message_t.BetreeMessageUpsert ufs =>
+ do
+ let (st1, v) ←
+ betree_internal_lookup_in_children_fwd node key st0
+ let (st2, v0) ←
+ betree_node_apply_upserts_fwd (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageUpsert ufs) l) v key st1
+ let node0 ←
+ betree_internal_lookup_in_children_back node key st0
+ let pending0 ←
+ betree_node_apply_upserts_back (betree_list_t.BetreeListCons
+ (k, betree_message_t.BetreeMessageUpsert 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 node0.betree_internal_id msgs0
+ st2
+ Result.ret (st3, Option.some v0)
+ | betree_list_t.BetreeListNil =>
+ do
+ let (st1, opt) ←
+ betree_internal_lookup_in_children_fwd node key st0
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ betree_list_t.BetreeListNil
+ Result.ret (st1, opt)
+ | betree_node_t.BetreeNodeLeaf 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.BetreeNodeInternal node =>
+ do
+ let (st0, msgs) ←
+ betree_load_internal_node_fwd node.betree_internal_id st
+ let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+ match h: pending with
+ | betree_list_t.BetreeListCons 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.BetreeListCons (k, msg) l)
+ let node0 ← betree_internal_lookup_in_children_back node key st0
+ Result.ret (betree_node_t.BetreeNodeInternal node0)
+ else
+ match h: msg with
+ | betree_message_t.BetreeMessageInsert v =>
+ do
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageInsert v) l)
+ Result.ret (betree_node_t.BetreeNodeInternal node)
+ | betree_message_t.BetreeMessageDelete =>
+ do
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageDelete) l)
+ Result.ret (betree_node_t.BetreeNodeInternal node)
+ | betree_message_t.BetreeMessageUpsert ufs =>
+ do
+ let (st1, v) ←
+ betree_internal_lookup_in_children_fwd node key st0
+ let (st2, _) ←
+ betree_node_apply_upserts_fwd (betree_list_t.BetreeListCons (k,
+ betree_message_t.BetreeMessageUpsert ufs) l) v key st1
+ let node0 ←
+ betree_internal_lookup_in_children_back node key st0
+ let pending0 ←
+ betree_node_apply_upserts_back (betree_list_t.BetreeListCons
+ (k, betree_message_t.BetreeMessageUpsert ufs) l) v key st1
+ let msgs0 ←
+ betree_node_lookup_first_message_for_key_back key msgs pending0
+ let _ ←
+ betree_store_internal_node_fwd node0.betree_internal_id msgs0
+ st2
+ Result.ret (betree_node_t.BetreeNodeInternal node0)
+ | betree_list_t.BetreeListNil =>
+ do
+ let _ ←
+ betree_node_lookup_first_message_for_key_back key msgs
+ betree_list_t.BetreeListNil
+ let node0 ← betree_internal_lookup_in_children_back node key st0
+ Result.ret (betree_node_t.BetreeNodeInternal node0)
+ | betree_node_t.BetreeNodeLeaf 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.BetreeNodeLeaf 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)))
+ :=
+ if h: key < self.betree_internal_pivot
+ then betree_node_lookup_fwd self.betree_internal_left key st
+ else betree_node_lookup_fwd self.betree_internal_right 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)
+ :=
+ if h: key < self.betree_internal_pivot
+ then
+ do
+ let n ← betree_node_lookup_back self.betree_internal_left key st
+ Result.ret
+ {
+ betree_internal_id := self.betree_internal_id,
+ betree_internal_pivot := self.betree_internal_pivot,
+ betree_internal_left := n,
+ betree_internal_right := self.betree_internal_right
+ }
+ else
+ do
+ let n ← betree_node_lookup_back self.betree_internal_right key st
+ Result.ret
+ {
+ betree_internal_id := self.betree_internal_id,
+ betree_internal_pivot := self.betree_internal_pivot,
+ betree_internal_left := self.betree_internal_left,
+ betree_internal_right := n
+ }
+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.BetreeListCons hd tl =>
+ let (i, i0) := hd
+ if h: i >= key
+ then Result.ret (betree_list_t.BetreeListCons (i, i0) tl)
+ else betree_node_lookup_mut_in_bindings_fwd key tl
+ | betree_list_t.BetreeListNil => Result.ret betree_list_t.BetreeListNil
+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.BetreeListCons 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.BetreeListCons (i, i0) tl0)
+ | betree_list_t.BetreeListNil => 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.BetreeMessageInsert 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.BetreeMessageDelete =>
+ do
+ let bindings1 ←
+ betree_list_pop_front_back (UInt64 × UInt64) bindings0
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ | betree_message_t.BetreeMessageUpsert 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.BetreeMessageInsert 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.BetreeMessageDelete =>
+ betree_node_lookup_mut_in_bindings_back key bindings bindings0
+ | betree_message_t.BetreeMessageUpsert 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.BetreeListCons 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.BetreeListNil => 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.BetreeListCons 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.BetreeListCons (k, m) l)
+ betree_node_filter_messages_for_key_fwd_back key msgs0
+ else Result.ret (betree_list_t.BetreeListCons (k, m) l)
+ | betree_list_t.BetreeListNil => Result.ret betree_list_t.BetreeListNil
+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.BetreeListCons 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.BetreeListCons (k, m) next_msgs)
+ | betree_list_t.BetreeListNil => Result.ret betree_list_t.BetreeListNil
+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.BetreeListCons 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.BetreeListCons (k, m) next_msgs0)
+ else Result.ret ret0
+ | betree_list_t.BetreeListNil => 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.BetreeMessageInsert 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.BetreeMessageInsert i)
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ | betree_message_t.BetreeMessageDelete =>
+ 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.BetreeMessageDelete)
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ | betree_message_t.BetreeMessageUpsert s =>
+ do
+ let p ← betree_list_hd_fwd (UInt64 × betree_message_t) msgs0
+ let (_, m) := p
+ match h: m with
+ | betree_message_t.BetreeMessageInsert 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.BetreeMessageInsert v)
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ | betree_message_t.BetreeMessageDelete =>
+ 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.BetreeMessageInsert v)
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ | betree_message_t.BetreeMessageUpsert 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.BetreeMessageUpsert 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.BetreeListCons 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.BetreeListNil => 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.BetreeNodeInternal node =>
+ do
+ let (st0, content) ←
+ betree_load_internal_node_fwd node.betree_internal_id 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 node params node_id_cnt content0 st0
+ let (node0, _) ←
+ betree_internal_flush_back node params node_id_cnt content0 st0
+ let (st2, _) ←
+ betree_store_internal_node_fwd node0.betree_internal_id content1
+ st1
+ Result.ret (st2, ())
+ else
+ do
+ let (st1, _) ←
+ betree_store_internal_node_fwd node.betree_internal_id content0 st0
+ Result.ret (st1, ())
+ | betree_node_t.BetreeNodeLeaf 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.BetreeListNil 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.BetreeNodeInternal node =>
+ do
+ let (st0, content) ←
+ betree_load_internal_node_fwd node.betree_internal_id 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 node params node_id_cnt content0 st0
+ let (node0, node_id_cnt0) ←
+ betree_internal_flush_back node params node_id_cnt content0 st0
+ let _ ←
+ betree_store_internal_node_fwd node0.betree_internal_id content1
+ st1
+ Result.ret (betree_node_t.BetreeNodeInternal node0, node_id_cnt0)
+ else
+ do
+ let _ ←
+ betree_store_internal_node_fwd node.betree_internal_id content0 st0
+ Result.ret (betree_node_t.BetreeNodeInternal node, node_id_cnt)
+ | betree_node_t.BetreeNodeLeaf 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.BetreeListNil st1
+ let node_id_cnt0 ←
+ betree_leaf_split_back node content0 params node_id_cnt st0
+ Result.ret (betree_node_t.BetreeNodeInternal new_node, node_id_cnt0)
+ else
+ do
+ let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+ Result.ret (betree_node_t.BetreeNodeLeaf
+ { betree_leaf_id := node.betree_leaf_id, 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 p ←
+ betree_list_partition_at_pivot_fwd betree_message_t content
+ self.betree_internal_pivot
+ 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 self.betree_internal_left params
+ node_id_cnt msgs_left st
+ let (_, node_id_cnt0) ←
+ betree_node_apply_messages_back self.betree_internal_left 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 self.betree_internal_right params
+ node_id_cnt0 msgs_right st0
+ let _ ←
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt0 msgs_right st0
+ Result.ret (st1, betree_list_t.BetreeListNil)
+ else Result.ret (st0, msgs_right)
+ else
+ do
+ let (st0, _) ←
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt msgs_right st
+ let _ ←
+ betree_node_apply_messages_back self.betree_internal_right 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 p ←
+ betree_list_partition_at_pivot_fwd betree_message_t content
+ self.betree_internal_pivot
+ 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 self.betree_internal_left params
+ node_id_cnt msgs_left st
+ let (n, node_id_cnt0) ←
+ betree_node_apply_messages_back self.betree_internal_left 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 (n0, node_id_cnt1) ←
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt0 msgs_right st0
+ Result.ret
+ ({
+ betree_internal_id := self.betree_internal_id,
+ betree_internal_pivot := self.betree_internal_pivot,
+ betree_internal_left := n,
+ betree_internal_right := n0
+ }, node_id_cnt1)
+ else
+ Result.ret
+ ({
+ betree_internal_id := self.betree_internal_id,
+ betree_internal_pivot := self.betree_internal_pivot,
+ betree_internal_left := n,
+ betree_internal_right := self.betree_internal_right
+ }, node_id_cnt0)
+ else
+ do
+ let (n, node_id_cnt0) ←
+ betree_node_apply_messages_back self.betree_internal_right params
+ node_id_cnt msgs_right st
+ Result.ret
+ ({
+ betree_internal_id := self.betree_internal_id,
+ betree_internal_pivot := self.betree_internal_pivot,
+ betree_internal_left := self.betree_internal_left,
+ betree_internal_right := n
+ }, 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.BetreeListNil
+ let (st0, _) ←
+ betree_node_apply_messages_fwd self params node_id_cnt
+ (betree_list_t.BetreeListCons (key, new_msg) l) st
+ let _ ←
+ betree_node_apply_messages_back self params node_id_cnt
+ (betree_list_t.BetreeListCons (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.BetreeListNil
+ betree_node_apply_messages_back self params node_id_cnt
+ (betree_list_t.BetreeListCons (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.BetreeListNil 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.BetreeNodeLeaf
+ {
+ 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
+ {
+ betree_be_tree_params := self.betree_be_tree_params,
+ 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.BetreeMessageInsert
+ value) st
+ let _ ←
+ betree_be_tree_apply_back self key (betree_message_t.BetreeMessageInsert
+ 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.BetreeMessageInsert
+ 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.BetreeMessageDelete st
+ let _ ←
+ betree_be_tree_apply_back self key betree_message_t.BetreeMessageDelete
+ 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.BetreeMessageDelete 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.BetreeMessageUpsert
+ upd) st
+ let _ ←
+ betree_be_tree_apply_back self key (betree_message_t.BetreeMessageUpsert
+ 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.BetreeMessageUpsert 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
+ {
+ betree_be_tree_params := self.betree_be_tree_params,
+ betree_be_tree_node_id_cnt := self.betree_be_tree_node_id_cnt,
+ 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
new file mode 100644
index 00000000..b3db37c2
--- /dev/null
+++ b/tests/lean/betree/BetreeMain/Opaque.lean
@@ -0,0 +1,33 @@
+-- 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
new file mode 100644
index 00000000..2726e1f0
--- /dev/null
+++ b/tests/lean/betree/BetreeMain/Types.lean
@@ -0,0 +1,61 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: type definitions
+import Base.Primitives
+
+/- [betree_main::betree::List] -/
+inductive betree_list_t (T : Type) :=
+| BetreeListCons : T -> betree_list_t T -> betree_list_t T
+| BetreeListNil : betree_list_t T
+
+/- [betree_main::betree::UpsertFunState] -/
+inductive betree_upsert_fun_state_t :=
+| BetreeUpsertFunStateAdd : UInt64 -> betree_upsert_fun_state_t
+| BetreeUpsertFunStateSub : UInt64 -> betree_upsert_fun_state_t
+
+/- [betree_main::betree::Message] -/
+inductive betree_message_t :=
+| BetreeMessageInsert : UInt64 -> betree_message_t
+| BetreeMessageDelete : betree_message_t
+| BetreeMessageUpsert : 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 :=
+| BetreeNodeInternal : betree_internal_t -> betree_node_t
+| BetreeNodeLeaf : 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/lakefile.lean b/tests/lean/betree/lakefile.lean
new file mode 100644
index 00000000..aa702300
--- /dev/null
+++ b/tests/lean/betree/lakefile.lean
@@ -0,0 +1,18 @@
+import Lake
+open Lake DSL
+
+require mathlib from git
+ "https://github.com/leanprover-community/mathlib4.git"
+
+package «betree_main» {
+ -- add package configuration options here
+}
+
+lean_lib «Base» {
+ -- add library configuration options here
+}
+
+lean_lib «BetreeMain» {
+ -- add library configuration options here
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-23 20:05:27 +0000