ce73bbe277
When the `decide` tactic fails, it can try to give hints about the failure: - It tells you which `Decidable` instances it unfolded, by making use of the diagnostics feature. - If it encounters `Eq.rec`, it gives you a hint that one of these instances was likely defined using tactics. - If it encounters `Classical.choice`, it hints that you might have classical instances in scope. - During this, it tries to process `Decidable.rec`s and matchers to pin blame on a particular instance that failed to reduce. This idea comes from discussion with Heather Macbeth [on Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Decidable.20with.20structures/near/449409870).
50 lines
1.5 KiB
Text
50 lines
1.5 KiB
Text
structure Foo where num : Nat deriving DecidableEq
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namespace Foo
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instance : OfNat Foo n := ⟨⟨n⟩⟩
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/-! # Example 1 -/
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@[irreducible] def mul (a b : Foo) : Foo :=
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let d := Nat.gcd a.num 1
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⟨(a.num.div d) * (b.num.div d)⟩
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-- should fail fast; exact heartbeat count at time of writing is 31
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set_option maxHeartbeats 310
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/--
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error: tactic 'decide' failed for proposition
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((mul 4 1).mul 1).mul 1 = 4
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since its 'Decidable' instance
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instDecidableEqFoo (((mul 4 1).mul 1).mul 1) 4
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'decEqFoo✝', 'instDecidableEqFoo', 'instDecidableEqNat' and
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'Nat.decEq', reduction got stuck at the 'Decidable' instance
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match h : (((mul 4 1).mul 1).mul 1).num.beq 4 with
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| true => isTrue ⋯
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| false => isFalse ⋯
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-/
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#guard_msgs in
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example : ((Foo.mul 4 1).mul 1).mul 1 = 4 := by decide
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/-! # Example 2 -/
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@[irreducible] def add (a b : Foo) : Foo := ⟨a.num * b.num⟩
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-- should not succeed (and fail fast); exact heartbeat count at time of writing is 21
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/--
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error: tactic 'decide' failed for proposition
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((add 4 1).add 1).add 1 = 4
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since its 'Decidable' instance
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instDecidableEqFoo (((add 4 1).add 1).add 1) 4
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'decEqFoo✝', 'instDecidableEqFoo', 'instDecidableEqNat' and
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'Nat.decEq', reduction got stuck at the 'Decidable' instance
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match h : (((add 4 1).add 1).add 1).num.beq 4 with
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| true => isTrue ⋯
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| false => isFalse ⋯
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-/
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#guard_msgs in
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example : ((Foo.add 4 1).add 1).add 1 = 4 := by decide
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