a3ca15d2b2
building upon #3714, this (almost) implements the second half of #3302. The main effect is that we now get a better error message when `rfl` fails. For ```lean example : n+1+m = n + (1+m) := by rfl ``` instead of the wall of text ``` The rfl tactic failed. Possible reasons: - The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma). - The arguments of the relation are not equal. Try using the reflexivity lemma for your relation explicitly, e.g. `exact Eq.refl _` or `exact HEq.rfl` etc. n m : Nat ⊢ n + 1 + m = n + (1 + m) ``` we now get ``` error: tactic 'rfl' failed, the left-hand side n + 1 + m is not definitionally equal to the right-hand side n + (1 + m) n m : Nat ⊢ n + 1 + m = n + (1 + m) ``` Unfortunately, because of very subtle differences in semantics (which transparency setting is used when reducing the goal and whether the “implicit lambda” feature applies) I could not make this simply the only `rfl` implementation. So `rfl` remains a macro and is still expanded to `eq_refl` (difference transparency setting) and `exact Iff.rfl` and `exact HEq.rfl` (implicit lambda) to not break existing code. This can be revised later, so this still closes: #3302. A user might still be puzzled *why* to terms are not defeq. Explaining that better (“reduced to… and reduces to… etc.”) would also be great, but that’s not specific to `rfl`, so better left for some other time.
47 lines
1.7 KiB
Text
47 lines
1.7 KiB
Text
-- NB: well-founded recursion, so irreducible
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def sorted_from_var [x: LE α] [DecidableRel x.le] (a: Array α) (i: Nat): Bool :=
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if h: i + 1 < a.size then
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have : i < a.size := Nat.lt_of_succ_lt h
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a[i] ≤ a[i+1] && sorted_from_var a (i + 1)
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else
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true
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termination_by a.size - i
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def check_sorted [x: LE α] [DecidableRel x.le] (a: Array α): Bool :=
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sorted_from_var a 0
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/--
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error: tactic 'rfl' failed, the left-hand side
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check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]
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is not definitionally equal to the right-hand side
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true
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⊢ check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
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-/
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#guard_msgs in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true := by
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rfl -- fails because `rfl` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
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/--
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error: tactic 'decide' failed for proposition
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check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
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since its 'Decidable' instance
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instDecidableEqBool (check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]) true
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'instDecidableEqBool' and 'Bool.decEq', reduction got stuck at the 'Decidable' instance
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match check_sorted #[0, 3, 3, 5, 8, 10, 10, 10], true with
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| false, false => isTrue ⋯
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| false, true => isFalse ⋯
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| true, false => isFalse ⋯
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| true, true => isTrue ⋯
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-/
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#guard_msgs in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- fails because `decide` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
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unseal sorted_from_var in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- works
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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with_unfolding_all decide -- should work
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