Module Arrow.From_strong_and_category

Parameters

module Category : Preface_specs.CATEGORY with type ('a, 'b) t = ( 'a, 'b ) Strong.t

Signature

Type

type ('a, 'b) t = ( 'a, 'b ) Category.t

The type held by the Arrow.

Functions

include Preface_specs.Category.WITH_ID with type ('a, 'b) t := ( 'a, 'b ) t
val id : ( 'a, 'a ) t

The identity morphism.

include Preface_specs.Semigroupoid.WITH_COMPOSE with type ('a, 'b) t := ( 'a, 'b ) t
val compose : ( 'b, 'c ) t -> ( 'a, 'b ) t -> ( 'a, 'c ) t

Morphism composition (from right to left).

val fst : ( 'a, 'b ) t -> ( 'a * 'd, 'b * 'd ) t

Send the first component of the input through the argument Arrow, and copy the rest unchanged to the output.

val arrow : ( 'a -> 'b ) -> ( 'a, 'b ) t

Lift a function to an Arrow.

val split : ( 'a, 'b ) t -> ( 'c, 'd ) t -> ( 'a * 'c, 'b * 'd ) t

Split the input between the two given Arrows and combine their output.

val compose_right_to_left : ( 'b, 'c ) t -> ( 'a, 'b ) t -> ( 'a, 'c ) t

An alias of CORE.compose.

val compose_left_to_right : ( 'a, 'b ) t -> ( 'b, 'c ) t -> ( 'a, 'c ) t

An alias of CORE.compose with flipped argument.

val return : unit -> ( 'a, 'a ) t

Represent the identity Arrow.

val snd : ( 'a, 'b ) t -> ( 'd * 'a, 'd * 'b ) t

Send the second component of the input through the given Arrow, and copy the rest unchanged to the output.

val fan_out : ( 'a, 'b ) t -> ( 'a, 'c ) t -> ( 'a, 'b * 'c ) t

Send the input to both argument arrows and combine their output.

val pre_compose_left_to_right : ( 'a -> 'b ) -> ( 'b, 'c ) t -> ( 'a, 'c ) t

Pre composition with a function (the function should be pure).

val post_compose_left_to_right : ( 'a, 'b ) t -> ( 'b -> 'c ) -> ( 'a, 'c ) t

Post composition with a function (the function should be pure).

val pre_compose_right_to_left : ( 'b, 'c ) t -> ( 'a -> 'b ) -> ( 'a, 'c ) t
val post_compose_right_to_left : ( 'b -> 'c ) -> ( 'a, 'b ) t -> ( 'a, 'c ) t

Infix operators

module Infix : Preface_specs.Arrow.INFIX with type ('a, 'b) t = ( 'a, 'b ) t
val (%) : ( 'b, 'c ) t -> ( 'a, 'b ) t -> ( 'a, 'c ) t

An alias of CORE.compose (to be iso with Preface_core).

val (<%) : ( 'b, 'c ) t -> ( 'a, 'b ) t -> ( 'a, 'c ) t

An alias of CORE.compose (to be iso with Preface_core).

val (%>) : ( 'a, 'b ) t -> ( 'b, 'c ) t -> ( 'a, 'c ) t

An alias of OPERATION.compose_left_to_right (to be iso with Preface_core).

val (<<<) : ( 'b, 'c ) t -> ( 'a, 'b ) t -> ( 'a, 'c ) t

An alias of CORE.compose (to be iso with Haskell's approach). Even <<< looks like <% (it is an alias for the same function), they differ in their priorities. OCaml documentation of operators priorities

val (>>>) : ( 'a, 'b ) t -> ( 'b, 'c ) t -> ( 'a, 'c ) t

An alias of CORE.compose_left_to_right (to be iso with Haskell's approach). Even >>> looks like %> (it is an alias for the same function), they differ in their priorities. OCaml documentation of operators priorities

val (***) : ( 'a, 'b ) t -> ( 'c, 'd ) t -> ( 'a * 'c, 'b * 'd ) t
val (&&&) : ( 'a, 'b ) t -> ( 'a, 'c ) t -> ( 'a, 'b * 'c ) t
val (^>>) : ( 'a -> 'b ) -> ( 'b, 'c ) t -> ( 'a, 'c ) t
val (>>^) : ( 'a, 'b ) t -> ( 'b -> 'c ) -> ( 'a, 'c ) t
val (<<^) : ( 'b, 'c ) t -> ( 'a -> 'b ) -> ( 'a, 'c ) t
val (^<<) : ( 'b -> 'c ) -> ( 'a, 'b ) t -> ( 'a, 'c ) t