feat: add support for other types in norm_num #8100
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| Original file line number | Diff line number | Diff line change |
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| /- | ||
| Copyright (c) 2022 Mario Carneiro. All rights reserved. | ||
| Released under Apache 2.0 license as described in the file LICENSE. | ||
| Authors: Mario Carneiro | ||
| -/ | ||
| import Mathlib.Tactic.NormNum.Core | ||
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| /-! | ||
| # `norm_num` extension for inductive constructors | ||
| -/ | ||
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| set_option autoImplicit true | ||
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| open Lean Meta Qq | ||
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| namespace Mathlib.Meta.NormNum | ||
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| theorem prod_ne_1 {a₁ b₁ : α} {a₂ b₂ : β} (h : a₁ ≠ b₁) : (a₁, a₂) ≠ (b₁, b₂) | rfl => h rfl | ||
| theorem prod_ne_2 {a₁ b₁ : α} {a₂ b₂ : β} (h : a₂ ≠ b₂) : (a₁, a₂) ≠ (b₁, b₂) | rfl => h rfl | ||
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| theorem cons_ne_1 {a₁ b₁ : α} {a₂ b₂ : List α} (h : a₁ ≠ b₁) : | ||
| (a₁ :: a₂) ≠ (b₁ :: b₂) | rfl => h rfl | ||
| theorem cons_ne_2 {a₁ b₁ : α} {a₂ b₂ : List α} (h : a₂ ≠ b₂) : | ||
| (a₁ :: a₂) ≠ (b₁ :: b₂) | rfl => h rfl | ||
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| inductive MatchList {α : Q(Type u)} (a : Q(List $α)) where | ||
| | nil (_ : $a =Q []) | ||
| | cons (a₁ : Q($α)) (a₂ : Q(List $α)) (_ : $a =Q $a₁ :: $a₂) | ||
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| def matchList {α : Q(Type u)} (a : Q(List $α)) : MetaM (MatchList a) := do | ||
| match ← whnfR a with | ||
| | .app (.const ``List.nil _) _ => return .nil ⟨⟩ | ||
| | .app (.app (.app (.const ``List.cons _) _) a₁) a₂ => return .cons a₁ a₂ ⟨⟩ | ||
| | _ => failure | ||
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| /-- The `norm_num` extension which identifies expressions of the form `(a, b)`, | ||
| such that `norm_num` successfully recognises both `a` and `b`. -/ | ||
| @[norm_num (_, _)] def evalProdMk : NormNumExt where eval {u α} e := do | ||
| trace[Meta.debug] "norm_num prod.mk {e}" | ||
| let .app (.app (.app (.app (.const ``Prod.mk [u₁, u₂]) | ||
| (α₁ : Q(Type u₁))) (α₂ : Q(Type u₂))) (a₁ : Q($α₁))) (a₂ : Q($α₂)) ← whnf e | failure | ||
| have : u =QL max u₁ u₂ := ⟨⟩ | ||
| have : $α =Q ($α₁ × $α₂) := ⟨⟩ | ||
| have : $e =Q ($a₁, $a₂) := ⟨⟩ | ||
| let ⟨b₁, p₁⟩ := (← derive a₁).toRawEq | ||
| let ⟨b₂, p₂⟩ := (← derive a₂).toRawEq | ||
| return .other q(($b₁, $b₂)) q(congr (congrArg _ $p₁) $p₂) | ||
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| /-- The `norm_num` extension which identifies expressions of the form `[]`. -/ | ||
| @[norm_num []] def evalListNil : NormNumExt where eval {u α} e := do | ||
| let e' : Q($α) ← whnf e | ||
| have : $e =Q $e' := ⟨⟩ | ||
| return .other e' q(@rfl _ $e') | ||
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| /-- The `norm_num` extension which identifies expressions of the form `(a, b)`, | ||
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| such that `norm_num` successfully recognises both `a` and `b`. -/ | ||
| @[norm_num (_ :: _)] def evalListCons : NormNumExt where eval {u α} e := do | ||
| let .app (.app (.app (.const ``List.cons _) | ||
| (β : Q(Type u))) (a₁ : Q($β))) (a₂ : Q(List $β)) ← whnf e | failure | ||
| have : $α =Q List $β := ⟨⟩ | ||
| have : $e =Q $a₁ :: $a₂ := ⟨⟩ | ||
| let ⟨b₁, p₁⟩ := (← derive a₁).toRawEq | ||
| let ⟨b₂, p₂⟩ := (← derive (u := u) a₂).toRawEq | ||
| return .other q(($b₁ :: $b₂)) q(congr (congrArg _ $p₁) $p₂) | ||
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| /-- Evaluates an equality up to inductive constructors, using `norm_num` on the leaves. -/ | ||
| partial def evalStructuralEq {α : Q(Type u)} (a b : Q($α)) : MetaM <| Q($a = $b) ⊕ Q($a ≠ $b) := do | ||
| let α ← whnf α | ||
| let .const f ls := α.getAppFn | failure | ||
| match f with | ||
| | ``Nat | ``Int | ``_root_.Rat => | ||
| match ← derive q($a = $b) with | ||
| | .isTrue p => return .inl p | ||
| | .isFalse p => return .inr p | ||
| | _ => failure | ||
| | ``Prod => | ||
| let [u₁, u₂] := ls | failure | ||
| have : u =QL max u₁ u₂ := ⟨⟩ | ||
| have α₁ : Q(Type u₁) := α.getRevArg! 1 | ||
| have α₂ : Q(Type u₂) := α.getRevArg! 0 | ||
| have : $α =Q ($α₁ × $α₂) := ⟨⟩ | ||
| let .app (.app fa (a₁ : Q($α₁))) (a₂ : Q($α₂)) ← whnfR a | failure | ||
| let .app (.app fb (b₁ : Q($α₁))) (b₂ : Q($α₂)) ← whnfR b | failure | ||
| have : $a =Q ($a₁, $a₂) := ⟨⟩ | ||
| have : $b =Q ($b₁, $b₂) := ⟨⟩ | ||
| unless fa.isAppOfArity ``Prod.mk 2 && fb.isAppOfArity ``Prod.mk 2 do failure | ||
| match ← evalStructuralEq a₁ b₁ with | ||
| | .inr p₁ => return .inr q(prod_ne_1 $p₁) | ||
| | .inl p₁ => match ← evalStructuralEq a₂ b₂ with | ||
| | .inr p₂ => return .inr q(prod_ne_2 $p₂) | ||
| | .inl p₂ => return .inl q(congr (congrArg _ $p₁) $p₂) | ||
| | ``List => | ||
| have β : Q(Type u) := α.getRevArg! 0 | ||
| let rec evalList (a b : Q(List $β)) : | ||
| MetaM <| Q($a ≠ $b) ⊕ MetaM (Q($a = $b) ⊕ Q($a ≠ $b)) := do | ||
| match ← matchList a, ← matchList b with | ||
| | .nil _, .nil _ => pure <| .inr <| pure <| .inl q(rfl) | ||
| | .cons .., .nil _ => pure <| .inl q(List.cons_ne_nil _ _) | ||
| | .nil _, .cons .. => pure <| .inl q((List.cons_ne_nil _ _).symm) | ||
| | .cons a₁ a₂ _, .cons b₁ b₂ _ => | ||
| match ← evalList a₂ b₂ with | ||
| | .inl no => return .inl q(cons_ne_2 $no) | ||
| | .inr p₂ => return .inr do | ||
| match ← evalStructuralEq a₁ b₁ with | ||
| | .inr p₁ => return .inr q(cons_ne_1 $p₁) | ||
| | .inl p₁ => match ← p₂ with | ||
| | .inr p₂ => return .inr q(cons_ne_2 $p₂) | ||
| | .inl p₂ => return .inl q(congr (congrArg _ $p₁) $p₂) | ||
| have : $α =Q List $β := ⟨⟩ | ||
| match ← evalList a b with | ||
| | .inl no => return .inr no | ||
| | .inr k => k | ||
| | _ => | ||
| matchConstInduct α.getAppFn (fun _ => failure) fun v us => do | ||
| let a ← whnfR a; let b ← whnfR b | ||
| let .const fa _ := a.getAppFn | failure | ||
| let .const fb _ := b.getAppFn | failure | ||
| let some (.ctorInfo info) := (← getEnv).find? fa | failure | ||
| unless fa == fb do | ||
| let some (.ctorInfo _) := (← getEnv).find? fb | failure | ||
| return .inr <| mkAppN (.const (.str v.name "noConfusion") (.zero :: us)) | ||
| (α.getAppArgs ++ #[(q(False) : Expr), a, b]) | ||
| let aArgs := a.getAppArgs; let bArgs := b.getAppArgs | ||
| let mut args : Array ((u' : Level) × (α' : Q(Type u')) × Q($α') × Q($α')) := #[] | ||
| for ai in aArgs[info.numParams:], bi in bArgs[info.numParams:] do | ||
| let ⟨_, α', ai⟩ ← inferTypeQ' ai | ||
| unless ← isDefEq α' (← inferType bi) do failure | ||
| args := args.push ⟨_, _, ai, bi⟩ | ||
| let mut eq : Expr ← mkEqRefl <| mkAppN a.getAppFn a.getAppArgs[:info.numParams] | ||
| for ⟨_, _, ai, bi⟩ in args, i in [0:args.size] do | ||
| match ← evalStructuralEq ai bi with | ||
| | .inl eq' => eq ← mkCongr eq eq' | ||
| | .inr ne => | ||
| return .inr <| ← withLocalDeclD `h q($a = $b) fun h => do | ||
| let e := mkAppN (.const (.str v.name "noConfusion") (.zero :: us)) | ||
| (α.getAppArgs ++ (#[q(False), a, b, h] : Array Expr)) | ||
| let .forallE _ dom _ _ ← whnf (← inferType e) | failure | ||
| forallTelescopeReducing dom fun xs _ => do | ||
| unless xs.size == args.size do failure | ||
| mkLambdaFVars #[h] <| mkApp e <| ← mkLambdaFVars xs (.app ne xs[i]!) | ||
| return .inl eq | ||
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This doc comment is a verbatim copy of the
Result.isRatcomment. Did you mean to have something different here?