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-rw-r--r--backends/lean/Base/Arith.lean64
1 files changed, 37 insertions, 27 deletions
diff --git a/backends/lean/Base/Arith.lean b/backends/lean/Base/Arith.lean
index a792deb2..bb776b55 100644
--- a/backends/lean/Base/Arith.lean
+++ b/backends/lean/Base/Arith.lean
@@ -5,6 +5,8 @@ import Lean.Meta.Tactic.Simp
import Init.Data.List.Basic
import Mathlib.Tactic.RunCmd
import Mathlib.Tactic.Linarith
+-- TODO: there is no Omega tactic for now - it seems it hasn't been ported yet
+--import Mathlib.Tactic.Omega
import Base.Primitives
/-
@@ -77,26 +79,19 @@ instance (ty : ScalarTy) : IsScalar (Scalar ty) where
example (ty : ScalarTy) : IsScalar (Scalar ty) := inferInstance
--- TODO: lookup doesn't work
-class HasProp {a : Type} (x : a) where
- prop_ty : Prop
- prop : prop_ty
-
-class HasProp' (a : Type) where
+-- Remark: I tried a version of the shape `HasProp {a : Type} (x : a)`
+-- but the lookup didn't work
+class HasProp (a : Type) where
prop_ty : a → Prop
prop : ∀ x:a, prop_ty x
-instance {ty : ScalarTy} (x : Scalar x) : HasProp x where
- -- prop_ty is inferred
- prop := And.intro x.hmin x.hmax
-
-instance (ty : ScalarTy) : HasProp' (Scalar ty) where
+instance (ty : ScalarTy) : HasProp (Scalar ty) where
-- prop_ty is inferred
prop := λ x => And.intro x.hmin x.hmax
-example {a : Type} (x : a) [HasProp x] : Prop :=
- let i : HasProp x := inferInstance
- i.prop_ty
+instance (a : Type) : HasProp (Vec a) where
+ prop_ty := λ v => v.val.length ≤ Scalar.max ScalarTy.Usize
+ prop := λ ⟨ _, l ⟩ => l
open Lean Lean.Elab Command Term Lean.Meta
@@ -117,8 +112,6 @@ def isScalarExpr (e : Expr) : MetaM Bool := do
| .some _ => pure true
| _ => pure false
-#check @HasProp'.prop
-
-- Return an instance of `HasProp` for `e` if it has some
def lookupHasProp (e : Expr) : MetaM (Option Expr) := do
logInfo f!"lookupHasProp"
@@ -127,7 +120,7 @@ def lookupHasProp (e : Expr) : MetaM (Option Expr) := do
Lean.observing? do
logInfo f!"lookupHasProp: observing"
let ty ← Lean.Meta.inferType e
- let hasProp ← mkAppM `Arith.HasProp' #[ty]
+ let hasProp ← mkAppM ``Arith.HasProp #[ty]
let hasPropInst ← trySynthInstance hasProp
match hasPropInst with
| LOption.some i =>
@@ -212,9 +205,9 @@ elab "display_has_prop_instances" : tactic => do
logInfo m!"+ HasProp instance: {e}"
example (x : U32) : True := by
- let i : HasProp' U32 := inferInstance
- have p := @HasProp'.prop _ i x
- simp only [HasProp'.prop_ty] at p
+ let i : HasProp U32 := inferInstance
+ have p := @HasProp.prop _ i x
+ simp only [HasProp.prop_ty] at p
display_has_prop_instances
simp
@@ -304,10 +297,7 @@ example : Nat := by
example (x : Bool) : Nat := by
cases x <;> custom_let x := 3 <;> apply x
-#check mkIdent
-#check Syntax
-
--- Lookup the instances of `HasProp' for all the sub-expressions in the context,
+-- Lookup the instances of `HasProp for all the sub-expressions in the context,
-- and introduce the corresponding assumptions
elab "intro_has_prop_instances" : tactic => do
logInfo m!"Introducing the HasProp instances"
@@ -317,10 +307,9 @@ elab "intro_has_prop_instances" : tactic => do
let name := `h
evalAddDecl name e type (asLet := false)
-- Simplify to unfold the `prop_ty` projector
- --let simpTheorems := ++ [``HasProp'.prop_ty]
let simpTheorems ← Tactic.simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
-- Add the equational theorem for `HashProp'.prop_ty`
- let simpTheorems ← simpTheorems.addDeclToUnfold ``HasProp'.prop_ty
+ let simpTheorems ← simpTheorems.addDeclToUnfold ``HasProp.prop_ty
let congrTheorems ← getSimpCongrTheorems
let ctx : Simp.Context := { simpTheorems := #[simpTheorems], congrTheorems }
-- Where to apply the simplifier
@@ -328,11 +317,32 @@ elab "intro_has_prop_instances" : tactic => do
-- Apply the simplifier
let _ ← Tactic.simpLocation ctx (discharge? := .none) loc
pure ()
- -- simpLocation
example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
intro_has_prop_instances
simp [*]
+example {a: Type} (v : Vec a) : v.val.length ≤ Scalar.max ScalarTy.Usize := by
+ intro_has_prop_instances
+ simp_all [Scalar.max, Scalar.min]
+
+-- A tactic to solve linear arithmetic goals
+syntax "int_tac" : tactic
+macro_rules
+ | `(tactic| int_tac) =>
+ `(tactic|
+ intro_has_prop_instances;
+ have := Scalar.cMin_bound ScalarTy.Usize;
+ have := Scalar.cMin_bound ScalarTy.Isize;
+ have := Scalar.cMax_bound ScalarTy.Usize;
+ have := Scalar.cMax_bound ScalarTy.Isize;
+ simp only [*, Scalar.max, Scalar.min, Scalar.cMin, Scalar.cMax] at *;
+ linarith)
+
+example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
+ int_tac
+
+example {a: Type} (v : Vec a) : v.val.length ≤ Scalar.max ScalarTy.Usize := by
+ int_tac
end Arith