diff options
Diffstat (limited to 'backends')
| -rw-r--r-- | backends/lean/Primitives.lean | 90 |
1 files changed, 57 insertions, 33 deletions
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean index e5634bfe..034f41b2 100644 --- a/backends/lean/Primitives.lean +++ b/backends/lean/Primitives.lean @@ -112,17 +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. - --- 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.) +-- We redefine our machine integers types. + +-- 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 @@ -134,20 +130,6 @@ 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) - open System.Platform.getNumBits -- TODO: is there a way of only importing System.Platform.getNumBits? @@ -264,11 +246,19 @@ def Scalar.cMax (ty : ScalarTy) : Int := | .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 } @@ -445,6 +435,12 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) := def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val +-- Tactic to prove that integers are in bounds +syntax "intlit" : tactic + +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 @@ -497,14 +493,22 @@ def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) 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.max := v.property rewrite [ List.length_set v.val i.val x ] @@ -513,26 +517,46 @@ def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α 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.max := v.property rewrite [ List.length_set v.val i.val x ] |