a4d41beab1
We use `let_delayed` to elaborate `match_expr` join points, which elaborate the body of the `let` before its value. Thus, there is a difference between: - `let_delayed f (x : Expr) := <val>; <body>` - `let_delayed f := fun (x : Expr) => <val>; <body>` In the latter, when `<body>` is elaborated, the elaborator does not know that `f` takes an argument of type `Expr`, and that `f` is a function. Before this commit ensures the former representation is used.
63 lines
2.6 KiB
Text
63 lines
2.6 KiB
Text
/-
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Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Scott Morrison
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-/
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prelude
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import Lean.Elab.Tactic.Omega.Core
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import Lean.Elab.Tactic.FalseOrByContra
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import Lean.Meta.Tactic.Cases
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import Lean.Elab.Tactic.Config
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open Lean Meta Omega
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set_option maxHeartbeats 5000
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def pushNot (h P : Expr) : MetaM (Option Expr) := do
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let P ← whnfR P
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trace[omega] "pushing negation: {P}"
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match P with
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| .forallE _ t b _ =>
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if (← isProp t) && (← isProp b) then
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return some (mkApp4 (.const ``Decidable.and_not_of_not_imp []) t b
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(.app (.const ``Classical.propDecidable []) t) h)
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else
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return none
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| .app _ _ =>
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match_expr P with
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| LT.lt α _ x y => match_expr α with
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| Nat => return some (mkApp3 (.const ``Nat.le_of_not_lt []) x y h)
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| Int => return some (mkApp3 (.const ``Int.le_of_not_lt []) x y h)
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| Fin n => return some (mkApp4 (.const ``Fin.le_of_not_lt []) n x y h)
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| _ => return none
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| LE.le α _ x y => match_expr α with
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| Nat => return some (mkApp3 (.const ``Nat.lt_of_not_le []) x y h)
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| Int => return some (mkApp3 (.const ``Int.lt_of_not_le []) x y h)
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| Fin n => return some (mkApp4 (.const ``Fin.lt_of_not_le []) n x y h)
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| _ => return none
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| Eq α x y => match_expr α with
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| Nat => return some (mkApp3 (.const ``Nat.lt_or_gt_of_ne []) x y h)
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| Int => return some (mkApp3 (.const ``Int.lt_or_gt_of_ne []) x y h)
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| Fin n => return some (mkApp4 (.const ``Fin.lt_or_gt_of_ne []) n x y h)
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| _ => return none
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| Dvd.dvd α _ k x => match_expr α with
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| Nat => return some (mkApp3 (.const ``Nat.emod_pos_of_not_dvd []) k x h)
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| Int =>
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-- This introduces a disjunction that could be avoided by checking `k ≠ 0`.
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return some (mkApp3 (.const ``Int.emod_pos_of_not_dvd []) k x h)
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| _ => return none
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| Prod.Lex _ _ _ _ _ _ => return some (← mkAppM ``Prod.of_not_lex #[h])
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| Not P =>
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return some (mkApp3 (.const ``Decidable.of_not_not []) P
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(.app (.const ``Classical.propDecidable []) P) h)
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| And P Q =>
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return some (mkApp5 (.const ``Decidable.or_not_not_of_not_and []) P Q
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(.app (.const ``Classical.propDecidable []) P)
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(.app (.const ``Classical.propDecidable []) Q) h)
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| Or P Q =>
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return some (mkApp3 (.const ``and_not_not_of_not_or []) P Q h)
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| Iff P Q =>
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return some (mkApp5 (.const ``Decidable.and_not_or_not_and_of_not_iff []) P Q
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(.app (.const ``Classical.propDecidable []) P)
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(.app (.const ``Classical.propDecidable []) Q) h)
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| _ => return none
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| _ => return none
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