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Diffstat (limited to '')
-rw-r--r-- | backends/lean/Base/Arith/Scalar.lean | 49 |
1 files changed, 49 insertions, 0 deletions
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean new file mode 100644 index 00000000..b792ff21 --- /dev/null +++ b/backends/lean/Base/Arith/Scalar.lean @@ -0,0 +1,49 @@ +import Base.Arith.Int +import Base.Primitives.Scalar + +/- Automation for scalars - TODO: not sure it is worth having two files (Int.lean and Scalar.lean) -/ +namespace Arith + +open Lean Lean.Elab Lean.Meta +open Primitives + +def scalarTacExtraPreprocess : Tactic.TacticM Unit := do + Tactic.withMainContext do + -- Inroduce the bounds for the isize/usize types + let add (e : Expr) : Tactic.TacticM Unit := do + let ty ← inferType e + let _ ← Utils.addDeclTac (← Utils.mkFreshAnonPropUserName) e ty (asLet := false) + add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []]) + add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []]) + add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []]) + -- Reveal the concrete bounds + Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax, + ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min, + ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max, + ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min, + ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max, + ``Usize.min + ] [] [] .wildcard + +elab "scalar_tac_preprocess" : tactic => + intTacPreprocess scalarTacExtraPreprocess + +-- A tactic to solve linear arithmetic goals in the presence of scalars +def scalarTac (splitGoalConjs : Bool) : Tactic.TacticM Unit := do + intTac splitGoalConjs scalarTacExtraPreprocess + +elab "scalar_tac" : tactic => + scalarTac false + +instance (ty : ScalarTy) : HasIntProp (Scalar ty) where + -- prop_ty is inferred + prop := λ x => And.intro x.hmin x.hmax + +example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by + intro_has_int_prop_instances + simp [*] + +example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by + scalar_tac + +end Arith |