fd2c42a8bf
sed -Ei 's/^(\s*)((private |protected )?(noncomputable )?(abbreviation|definition|meta_definition|theorem|lemma|proposition|corollary)\s+\S+\s*)((\s*\[(\S+(\s+[0-9]+)*|priority.*)\])+)\s*/\1attribute \6\n\1\2/' library/**/*.lean tests/**/*.lean sed -Ei 's/\s+$//' library/**/*.lean # remove trailing whitespace
57 lines
2.2 KiB
Text
57 lines
2.2 KiB
Text
attribute [reducible]
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definition nat_has_add2 : has_add nat :=
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has_add.mk (λ x y : nat, x + y)
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set_option pp.all true
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-- set_option trace.defeq_simplifier true
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open tactic
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example (a b : nat) (H : @add nat (id (id nat_has_add)) a b = @add nat nat_has_add2 a b) : true :=
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by do
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get_local `H >>= infer_type >>= defeq_simp >>= trace,
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constructor
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constant x1 : nat -- update the environment to force defeq_canonize cache to be reset
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example (a b : nat) (H : (λ x : nat, @add nat (id (id nat_has_add)) a b) = (λ x : nat, @add nat nat_has_add2 a x)) : true :=
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by do
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get_local `H >>= infer_type >>= defeq_simp >>= trace,
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constructor
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attribute [reducible]
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definition nat_has_add3 : nat → has_add nat :=
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λ n, has_add.mk (λ x y : nat, x + y)
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constant x2 : nat -- update the environment to force defeq_canonize cache to be reset
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example (a b : nat) (H : (λ x : nat, @add nat nat_has_add2 a x) = (λ x : nat, @add nat (nat_has_add3 x) a b)) : true :=
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by do
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get_local `H >>= infer_type >>= defeq_simp >>= trace,
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constructor
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constant x3 : nat
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-- Example where instance canonization does not work.
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-- Remark: we can "fix" it by re-running defeq_simp until there is no change.
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-- However, this is too expensive. Well, if users want they can define their own defeq_simp that implements this
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-- behavior.
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example (a b : nat) (H : (λ x : nat, @add nat (nat_has_add3 x) a b) = (λ x : nat, @add nat nat_has_add2 a x)) : true :=
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by do
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get_local `H >>= infer_type >>= defeq_simp >>= trace,
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trace "---------",
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-- The following should work
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get_local `H >>= infer_type >>= defeq_simp >>= defeq_simp >>= trace,
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constructor
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constant x4 : nat -- update the environment to force defeq_canonize cache to be reset
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-- Example where instance canonization does not work.
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-- This is a different issue. We can only make them work if we normalize (nat_has_add3 x) and (nat_has_add3 y).
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-- Again, the user can workaround it by manually normalizing these instances before invoking defeq_simp.
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example (a b : nat)
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(H : (λ x y : nat, @add nat (nat_has_add3 x) a b) =
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(λ x y : nat, @add nat (nat_has_add3 y) a x)) : true :=
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by do
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get_local `H >>= infer_type >>= defeq_simp >>= trace,
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constructor
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