Add a first draft of the IsSomething article

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 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