blog-static/code/agda-issomething/example.agda

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open import Agda.Primitive using (Level; lsuc)
open import Relation.Binary.PropositionalEquality using (_≡_)
variable
a : Level
A : Set a
module FirstAttempt where
record Semigroup (A : Set a) : Set a where
field
_∙_ : A A A
isAssociative : (a₁ a₂ a₃ : A) a₁ (a₂ a₃) (a₁ a₂) a₃
record Monoid (A : Set a) : Set a where
field semigroup : Semigroup A
open Semigroup semigroup public
field
zero : A
isIdentityLeft : (a : A) zero a a
isIdentityRight : (a : A) a zero a
record ContrivedExample (A : Set a) : Set a where
field
-- first property
monoid : Monoid A
-- second property; Semigroup is a stand-in.
semigroup : Semigroup A
operationsEqual : Monoid._∙_ monoid Semigroup._∙_ semigroup
module SecondAttempt where
record IsSemigroup {A : Set a} (_∙_ : A A A) : Set a where
field isAssociative : (a₁ a₂ a₃ : A) a₁ (a₂ a₃) (a₁ a₂) a₃
record IsMonoid {A : Set a} (zero : A) (_∙_ : A A A) : Set a where
field
isSemigroup : IsSemigroup _∙_
isIdentityLeft : (a : A) zero a a
isIdentityRight : (a : A) a zero a
open IsSemigroup isSemigroup public
record IsContrivedExample {A : Set a} (_∙_ : A A A) : Set a where
field
-- first property
monoid : IsMonoid _∙_
-- second property; Semigroup is a stand-in.
semigroup : IsSemigroup _∙_
record Semigroup (A : Set a) : Set a where
field
_∙_ : A A A
isSemigroup : IsSemigroup _∙_
record Monoid (A : Set a) : Set a where
field
zero : A
_∙_ : A A A
isMonoid : IsMonoid zero _∙_
module ThirdAttempt {A : Set a} (_∙_ : A A A) where
record IsSemigroup : Set a where
field isAssociative : (a₁ a₂ a₃ : A) a₁ (a₂ a₃) (a₁ a₂) a₃
record IsMonoid (zero : A) : Set a where
field
isSemigroup : IsSemigroup
isIdentityLeft : (a : A) zero a a
isIdentityRight : (a : A) a zero a
open IsSemigroup isSemigroup public
record IsContrivedExample : Set a where
field
-- first property
monoid : IsMonoid _∙_
-- second property; Semigroup is a stand-in.
semigroup : IsSemigroup _∙_