Fantasy Land Cheat Sheet

Algebra Dependencies Function Laws
Setoid equals reflexivity, symmetry, transitivity
Ord Setoid lte totality, antisymmetry, transitivity
Semigroupoid compose associativity
Category Semigroupoid id left identity, right identity
Semigroup concat associativity
Monoid Semigroup empty left identity, right identity
Functor map identity, composition
Contravariant contramap identity, composition
Apply Functor ap composition
Applicative Apply of identity, homomorphism, interchange
Alt Functor alt associativity, distributivity
Plus Alt zero left identity, right identity, annihilation
Alternative Applicative, Plus distributivity, annihilation
Foldable reduce
Traversable Functor, Foldable traverse naturality, identity, composition
Chain Apply chain associativity
ChainRec Chain chainRec equivalence
Monad Applicative, Chain left identity, right identity
Extend Functor extend
Comonad Extend extract left identity, right identity
Bifunctor Functor bimap identity, composition
Profunctor Functor promap identity, composition
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See also: FP synonyms