316ff35afd
This PR changes the naming of the internal functions in deriving instances like BEq to use accessible names. This is necessary to reasonably easily prove things about these functions. For example after `deriving BEq` for a type `T`, the implementation of `instBEqT` is in `instBEqT.beq`.
48 lines
1.6 KiB
Text
48 lines
1.6 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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because 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 `instDecidableEqFoo`, `instDecidableEqNat`, `Nat.decEq`, and `instDecidableEqFoo.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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because 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 `instDecidableEqFoo`, `instDecidableEqNat`, `Nat.decEq`, and `instDecidableEqFoo.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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