8293fd4e09
This makes changes to the definitions of Associativity, Commutativity,
Idempotence and Identity classes to be more aligned with Mathlib's
versions.
The changes are:
* Move classes are moved from `Lean` to root namespace.
* Drop `Is` prefix from names.
* Rename `IsNeutral` to `LawfulIdentity` and add Left and Right
subclasses.
* Change neutral/identity element to outParam.
* Introduce `HasIdentity` for operations not intended for proofs to
implement
The identity changes are to make this compatible with
[Mathlib](718042db9d/Mathlib/Init/Algebra/Classes.lean)
and to enable nicer fold operations in Std that can use type classes to
infer the identity/initial element on binary operations.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
17 lines
508 B
Text
17 lines
508 B
Text
opaque f : Bool → Bool → Bool
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axiom f_comm (a b : Bool) : f a b = f b a
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axiom f_assoc (a b c : Bool) : f (f a b) c = f a (f b c)
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open Std
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instance : Commutative f := ⟨f_comm⟩
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instance : Associative f := ⟨f_assoc⟩
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example (a b c : Bool) : f (f a b) c = f (f a c) b :=
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by ac_rfl -- good
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example (a b c : Bool) : (f (f a b) c = f (f a c) b) ∧ true :=
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And.intro (by ac_rfl) rfl -- good
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example (a b c : Bool) : (f (f a b) c = f (f a c) b) ∧ true := by
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apply And.intro
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. ac_rfl
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. rfl
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