Created
August 27, 2017 22:56
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| -- | Binary operation | |
| class Magma a where | |
| op ∷ a → a → a | |
| -- | Associativity: `∀ a b. (a • b) • c = a • (b • c)` | |
| class Magma a ⇐ Associative a | |
| -- | Identity: `∀ a. a • identity = a && identity • a = a` | |
| class Magma a ⇐ Identity a where | |
| identity ∷ a | |
| -- | Inverse element: `∃ e. a • b = b • a = e` | |
| class Magma a ⇐ Inverse a where | |
| inverse ∷ a → a | |
| -- | Commutativity: `∀ a b. a • b = b • a` | |
| class Magma a ⇐ Commutative a | |
| -- | Idempotent: `∀ a. a • a = a` | |
| class Magma a ⇐ Idempotent a | |
| type Semigroup a = Associative a ⇒ Magma a ⇒ a | |
| type Monoid a = Identity a ⇒ Semigroup a | |
| type Band a = Idempotent a ⇒ Semigroup a | |
| type Semilattice a = Commutative a ⇒ Band a | |
| type Group a = Inverse a ⇒ Monoid a | |
| type AbelianGroup a = Commutative a ⇒ Group a |
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@garyb Is there an issue/PR on a github project where I can watch discussion of this idea?