# 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 |

See also: FP synonyms