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chore: add example to explanation cond_decide is not simp (#3615)

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This just adds a concrete example to the `cond_decide` lemma to explain
why it is not a simp rule.
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Joe Hendrix 2024-03-06 08:58:12 -08:00 • committed by GitHub
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src/Init/Data/Bool.lean
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@ -431,12 +431,17 @@ theorem cond_eq_if : (bif b then x else y) = (if b then x else y) := cond_eq_ite
@[simp] theorem cond_self (c : Bool) (t : α) : cond c t t = t := by cases c <;> rfl
/-
This is a simp rule in Mathlib, but results in non-confluence that is
difficult to fix as decide distributes over propositions.
This is a simp rule in Mathlib, but results in non-confluence that is difficult
to fix as decide distributes over propositions. As an example, observe that
`cond (decide (p ∧ q)) t f` could simplify to either:
A possible fix would be to completely simplify away `cond`, but that
is not taken since it could result in major rewriting of code that is
otherwise purely about `Bool`.
* `if p ∧ q then t else f` via `Bool.cond_decide` or
* `cond (decide p && decide q) t f` via `Bool.decide_and`.
A possible approach to improve normalization between `cond` and `ite` would be
to completely simplify away `cond` by making `cond_eq_ite` a `simp` rule, but
that has not been taken since it could surprise users to migrate pure `Bool`
operations like `cond` to a mix of `Prop` and `Bool`.
-/
theorem cond_decide {α} (p : Prop) [Decidable p] (t e : α) :
cond (decide p) t e = if p then t else e := by