Reorganize the Lean tests and extract the Polonius tests to Lean

1 files changed, 0 insertions, 392 deletions

diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean
deleted file mode 100644
index 5b64e908..00000000
--- a/tests/lean/misc/constants/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)