preface 1.1.0 · OCaml Package

Set of functors (in ML sense) whose role is to achieve the abstractions described in Preface_specs. Each abstraction described in the specifications has its image in Preface.Make and the functors take as arguments modules constrained by the signatures described in Preface_specs and produce modules whose complete interface is also described in Preface_specs.)

For a detailed description of the module breakdown logic, go to the homepage.

Multiple path

The achievement of an abstraction usually offers several paths:

using the minimal definition or implement as few combiners as possible. Some abstractions offer several minimal definitions, so it is up to you to choose the path that seems most relevant .
A construction on top of another abstraction (ie: Preface_specs.MONOID defined over a Preface_specs.SEMIGROUP)
A manual approach where each feature has to be provided (while offering intermediate functors to avoid boring tasks such as defining infix operators).
A simplification of an existing abstraction, such as turning a Preface_specs.ALTERNATIVE into a Preface_specs.MONOID by fixing the type of the Alternative.
Using a fixed algebra. For example, the sum, product or composition of Preface_specs.FUNCTOR.

Monoid hierarchy

module Semigroup : sig ... end

Building a Preface_specs.Semigroup

module Monoid : sig ... end

Building a Preface_specs.Monoid

Lattice hierarchy

module Meet_semilattice : sig ... end

Building a Preface_specs.Meet_semilattice

module Join_semilattice : sig ... end

Building a Preface_specs.Join_semilattice

module Bounded_meet_semilattice : sig ... end

Building a Preface_specs.Bounded_meet_semilattice

module Bounded_join_semilattice : sig ... end

Building a Preface_specs.Bounded_join_semilattice

module Bounded_lattice : sig ... end

Building a Preface_specs.Bounded_lettice

module Lattice : sig ... end

Building a Preface_specs.Lettice

Indexed Functor hierarchy

module Indexed_functor : sig ... end

Building a Preface_specs.Indexed_functor

module Indexed_alt : sig ... end

Building a Preface_specs.Indexed_alt

module Indexed_apply : sig ... end

Building a Preface_specs.INDEXED_APPLY

module Indexed_applicative : sig ... end

Building a Preface_specs.Indexed_applicative

module Indexed_alternative : sig ... end

Building a Preface_specs.Indexed_alternative

module Indexed_selective : sig ... end

Building a Preface_specs.Indexed_selective

module Indexed_bind : sig ... end

Building a Preface_specs.Indexed_bind

module Indexed_monad : sig ... end

Building a Preface_specs.Indexed_monad

module Indexed_monad_plus : sig ... end

Building a Preface_specs.Indexed_monad_plus

module Indexed_comonad : sig ... end

Building an Preface_specs.Indexed_comonad

module Indexed_foldable : sig ... end

Building an Preface_specs.INDEXED_FOLDABLE

Functor hierarchy

module Invariant : sig ... end

Building a Preface_specs.Invariant

module Functor : sig ... end

Building a Preface_specs.Functor

module Alt : sig ... end

Building a Preface_specs.Alt

module Apply : sig ... end

Building a Preface_specs.APPLY

module Applicative : sig ... end

Building a Preface_specs.Applicative

module Alternative : sig ... end

Building a Preface_specs.Alternative

module Selective : sig ... end

Building a Preface_specs.Selective

module Bind : sig ... end

Building a Preface_specs.Bind

module Monad : sig ... end

Building a Preface_specs.Monad

module Monad_plus : sig ... end

Building a Preface_specs.Monad_plus

module Comonad : sig ... end

Building a Preface_specs.Comonad

module Foldable : sig ... end

Building a Preface_specs.Foldable

module Traversable : sig ... end

Building a Preface_specs.Traversable

Contravariant hierarchy

module Contravariant : sig ... end

Building a Preface_specs.Contravariant

module Divisible : sig ... end

Building a Preface_specs.Divisible

module Decidable : sig ... end

Building a Preface_specs.Decidable

Bifunctor hierarchy

module Bifunctor : sig ... end

Building a Preface_specs.Bifunctor

Profunctor hierarchy

module Profunctor : sig ... end

Building a Preface_specs.Profunctor

module Strong : sig ... end

Building a Preface_specs.Strong

module Choice : sig ... end

Building a Preface_specs.Choice

module Closed : sig ... end

Building a Preface_specs.Closed

Arrow hierarchy

module Semigroupoid : sig ... end

Building a Preface_specs.Semigroupoid

module Category : sig ... end

Building a Preface_specs.Category

module Arrow : sig ... end

Building a Preface_specs.Arrow

module Arrow_zero : sig ... end

Building a Preface_specs.Arrow_zero

module Arrow_alt : sig ... end

Building a Preface_specs.Arrow_alt

module Arrow_plus : sig ... end

Building a Preface_specs.Arrow_plus

module Arrow_choice : sig ... end

Building a Preface_specs.Arrow_choice

module Arrow_apply : sig ... end

Building a Preface_specs.Arrow_apply

Transformers

Monad Transformers

module Reader : sig ... end

Building a Preface_specs.Reader, a Reader transformer.

module Writer : sig ... end

Building a Preface_specs.Writer, a Writer transformer.

module State : sig ... end

Building a Preface_specs.State, a State transformer.

Comonad Transformers

module Store : sig ... end

Building a Preface_specs.Store, a Store transformer.

module Env : sig ... end

Building a Preface_specs.Env, an Env transformer.

module Traced : sig ... end

Building a Preface_specs.Traced, a Traced transformer.

Free constructions

module Free_applicative : sig ... end

Building a Preface_specs.Free_applicative

module Free_selective : sig ... end

Building a Preface_specs.Free_selective

module Freer_selective : sig ... end

Building a Preface_specs.Freer_selective

module Free_monad : sig ... end

Building a Preface_specs.Free_monad

module Freer_monad : sig ... end

Building a Preface_specs.Freer_monad

Conversion and Expansion

Produces abstractions based on other abstractions (e.g. bifunctors from functors). Mainly for dealing with different arities.

module Join : sig ... end

Join produces a Functor from a Bifunctor using both arguments of a Bifunctor.

module Clown : sig ... end

Clown can produces Bifunctor or Profunctor using a Functor (or a Contravariant) on the first argument of the Bi/Profunctor as described in Clowns to the Left, Jokers to the Right (Functional Pearl)

module Joker : sig ... end

Joker can produces Bifunctor or Profunctor using a Functor on the second argument of the Bi/Profunctor as described in Clowns to the Left, Jokers to the Right (Functional Pearl)

module Kleisli : sig ... end

Kleisli uses the Kleisli category to describe arity 2 constructions for arity 1 constructions, usually using the form: type ('a, 'b) t = 'a -> F.t.

module Cokleisli : sig ... end

Cokleisli uses the Cokleisli category to describe arity 2 constructions for arity 1 constructions, usually using the form: type ('a, 'b) t = 'a F.t -> 'b.

package preface