33aaabaed7
This PR improves the generation of `.induct_unfolding` by rewriting `match` statements more reliably, using the new “congruence equations” introduced in #8284. Fixes #8195.
106 lines
2.9 KiB
Text
106 lines
2.9 KiB
Text
import Lean
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-- set_option trace.Meta.FunInd true
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axiom testSorry : α
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def test (l : List Nat) : Nat :=
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match l with
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| [] => 0
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| x :: l =>
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match x == 3 with
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| false => test l
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| true => test l
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/--
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info: test.induct_unfolding (motive : List Nat → Nat → Prop) (case1 : motive [] 0)
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(case2 : ∀ (x : Nat) (l : List Nat), (x == 3) = false → motive l (test l) → motive (x :: l) (test l))
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(case3 : ∀ (x : Nat) (l : List Nat), (x == 3) = true → motive l (test l) → motive (x :: l) (test l)) (l : List Nat) :
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motive l (test l)
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-/
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#guard_msgs in
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#check test.induct_unfolding
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opaque someFunction (x : Nat) (h : (x == 3) = false) : Nat
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opaque someOtherFunction (x : Nat) (h : (x == 3) = true) : Nat
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def deptest (l : List Nat) : Nat :=
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match l with
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| [] => 0
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| x :: l =>
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match h : x == 3 with
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| false => deptest l + someFunction x h
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| true => deptest l + someOtherFunction x h
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/--
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info: deptest.induct_unfolding (motive : List Nat → Nat → Prop) (case1 : motive [] 0)
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(case2 :
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∀ (x : Nat) (l : List Nat) (h : (x == 3) = false),
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motive l (deptest l) → motive (x :: l) (deptest l + someFunction x h))
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(case3 :
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∀ (x : Nat) (l : List Nat) (h : (x == 3) = true),
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motive l (deptest l) → motive (x :: l) (deptest l + someOtherFunction x h))
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(l : List Nat) : motive l (deptest l)
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-/
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#guard_msgs in
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#check deptest.induct_unfolding
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-- This one doesn't work, the result type varies in the branches
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-- But we fail gracefully
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def depTestOddType (l : List Nat) :
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match l with
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| [] => Unit
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| x :: _ =>
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if x == 3 then
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Unit
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else
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Nat
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:=
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match l with
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| [] => ()
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| x :: _ =>
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(match h : x == 3 with
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| false => someFunction x h
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| true => () : if x == 3 then Unit else Nat)
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/--
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info: depTestOddType.fun_cases_unfolding
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(motive :
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(l : List Nat) →
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(match l with
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| [] => Unit
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| x :: tail => if (x == 3) = true then Unit else Nat) →
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Prop)
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(case1 : motive [] ())
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(case2 :
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∀ (x : Nat) (l : List Nat),
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(x == 3) = false →
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motive (x :: l)
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(match h : x == 3 with
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| false => someFunction x h
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| true => ()))
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(case3 :
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∀ (x : Nat) (l : List Nat),
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(x == 3) = true →
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motive (x :: l)
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(match h : x == 3 with
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| false => someFunction x h
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| true => ()))
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(l : List Nat) : motive l (depTestOddType l)
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-/
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#guard_msgs in
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#check depTestOddType.fun_cases_unfolding
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-- set_option trace.Meta.FunInd true in
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set_option linter.unusedVariables false in
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def testMe (n : Nat) : Bool :=
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match _ : n - 2 with
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| 0 => true
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| m => false
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/--
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info: testMe.fun_cases_unfolding (motive : Nat → Bool → Prop) (case1 : ∀ (n : Nat), n - 2 = 0 → motive n true)
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(case2 : ∀ (n : Nat), (n - 2 = 0 → False) → motive n false) (n : Nat) : motive n (testMe n)
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-/
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#guard_msgs in
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#check testMe.fun_cases_unfolding
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