Source file arrow_choice.ml
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open Preface_core.Shims
let = function Either.Left x | Either.Right x -> x
module Choose_over_left
(Category : Preface_specs.Category.CORE)
(Arrow : Preface_specs.Arrow.CORE with type ('a, 'b) t = ('a, 'b) Category.t)
(Left : Preface_specs.Arrow_choice.WITH_LEFT
with type ('a, 'b) t = ('a, 'b) Arrow.t) =
struct
let choose f g =
let ( >>> ) f g = Category.compose g f in
Left.left f
>>> Arrow.arrow Either.swap
>>> Left.left g
>>> Arrow.arrow Either.swap
;;
end
module Left_over_choose
(Category : Preface_specs.Category.CORE)
(Choose : Preface_specs.Arrow_choice.WITH_CHOOSE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
let left x = Choose.choose x Category.id
end
module Core_over_category_and_via_arrow_and_fst_and_left
(Category : Preface_specs.Category.CORE)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_FST_AND_LEFT
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module C = Arrow.Core_over_category_and_via_arrow_and_fst (Category) (Req)
include C
let left = Req.left
include Choose_over_left (Category) (C) (Req)
end
module Core_over_category_and_via_arrow_and_split_and_left
(Category : Preface_specs.Category.CORE)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_SPLIT_AND_LEFT
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module C = Arrow.Core_over_category_and_via_arrow_and_split (Category) (Req)
include C
let left = Req.left
include Choose_over_left (Category) (C) (Req)
end
module Core_over_category_and_via_arrow_and_fst_and_choose
(Category : Preface_specs.Category.CORE)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_FST_AND_CHOOSE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
include Arrow.Core_over_category_and_via_arrow_and_fst (Category) (Req)
let choose = Req.choose
include Left_over_choose (Category) (Req)
end
module Core_over_category_and_via_arrow_and_split_and_choose
(Category : Preface_specs.Category.CORE)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_SPLIT_AND_CHOOSE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
include Arrow.Core_over_category_and_via_arrow_and_split (Category) (Req)
let choose = Req.choose
include Left_over_choose (Category) (Req)
end
module Operation_over_category
(Category : Preface_specs.Category.OPERATION)
(Core : Preface_specs.Arrow_choice.CORE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
include Arrow.Operation_over_category (Category) (Core)
let right x = Core.choose Core.id x
let fan_in f g = Core.compose (Core.arrow extract) (Core.choose f g)
end
module Alias = Arrow.Alias
module Infix_over_category
(Category : Preface_specs.Category.INFIX)
(Core : Preface_specs.Arrow_choice.CORE
with type ('a, 'b) t = ('a, 'b) Category.t)
(Operation : Preface_specs.Arrow_choice.OPERATION
with type ('a, 'b) t = ('a, 'b) Core.t) =
struct
include Arrow.Infix_over_category (Category) (Core) (Operation)
let ( +++ ) = Core.choose
let ( ||| ) = Operation.fan_in
end
module Via
(Core : Preface_specs.Arrow_choice.CORE)
(Operation : Preface_specs.Arrow_choice.OPERATION)
(Alias : Preface_specs.Arrow_choice.ALIAS)
(Infix : Preface_specs.Arrow_choice.INFIX) =
struct
include Core
include Operation
include Alias
include Infix
module Infix = Infix
end
module Over_category_and_via_arrow_and_fst_and_left
(Category : Preface_specs.CATEGORY)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_FST_AND_LEFT
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module Core =
Core_over_category_and_via_arrow_and_fst_and_left (Category) (Req)
module Operation = Operation_over_category (Category) (Core)
module Alias = Alias (Operation)
module Infix = Infix_over_category (Category.Infix) (Core) (Operation)
include Core
include Operation
include Alias
include Infix
end
module Over_over_category_and_via_arrow_and_split_and_left
(Category : Preface_specs.CATEGORY)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_SPLIT_AND_LEFT
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module Core =
Core_over_category_and_via_arrow_and_split_and_left (Category) (Req)
module Operation = Operation_over_category (Category) (Core)
module Alias = Alias (Operation)
module Infix = Infix_over_category (Category.Infix) (Core) (Operation)
include Core
include Operation
include Alias
include Infix
end
module Over_category_and_via_arrow_and_fst_and_choose
(Category : Preface_specs.CATEGORY)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_FST_AND_CHOOSE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module Core =
Core_over_category_and_via_arrow_and_fst_and_choose (Category) (Req)
module Operation = Operation_over_category (Category) (Core)
module Alias = Alias (Operation)
module Infix = Infix_over_category (Category.Infix) (Core) (Operation)
include Core
include Operation
include Alias
include Infix
end
module Over_category_and_via_arrow_and_split_and_choose
(Category : Preface_specs.CATEGORY)
(Req : Preface_specs.Arrow_choice.WITH_ARROW_AND_SPLIT_AND_CHOOSE
with type ('a, 'b) t = ('a, 'b) Category.t) =
struct
module Core =
Core_over_category_and_via_arrow_and_split_and_choose (Category) (Req)
module Operation = Operation_over_category (Category) (Core)
module Alias = Alias (Operation)
module Infix = Infix_over_category (Category) (Core) (Operation)
include Core
include Operation
include Alias
include Infix
end
module Over_arrow_with_left
(Arrow : Preface_specs.ARROW)
(Left : Preface_specs.Arrow_choice.WITH_LEFT
with type ('a, 'b) t = ('a, 'b) Arrow.t) =
struct
module Core_aux =
Core_over_category_and_via_arrow_and_fst_and_left
(Arrow)
(struct
include Arrow
include Left
end)
module Operation_aux = Operation_over_category (Arrow) (Core_aux)
module Infix_aux = Infix_over_category (Arrow) (Core_aux) (Operation_aux)
include Core_aux
include Operation_aux
include Arrow
module Infix = struct
include Arrow.Infix
include Infix_aux
end
include Infix
end
module Over_arrow_with_choose
(Arrow : Preface_specs.ARROW)
(Choose : Preface_specs.Arrow_choice.WITH_CHOOSE
with type ('a, 'b) t = ('a, 'b) Arrow.t) =
struct
module Core_aux =
Core_over_category_and_via_arrow_and_fst_and_choose
(Arrow)
(struct
include Arrow
include Choose
end)
module Operation_aux = Operation_over_category (Arrow) (Core_aux)
module Infix_aux = Infix_over_category (Arrow) (Core_aux) (Operation_aux)
include Core_aux
include Operation_aux
include Arrow
module Infix = struct
include Arrow.Infix
include Infix_aux
end
include Infix
end
module Over_arrow_with_left_and_choose
(Arrow : Preface_specs.ARROW)
(Choose_left : Preface_specs.Arrow_choice.WITH_LEFT_AND_CHOOSE
with type ('a, 'b) t = ('a, 'b) Arrow.t) =
struct
module Core_aux = struct
include Arrow
include Choose_left
end
module Operation_aux = Operation_over_category (Arrow) (Core_aux)
module Infix_aux = Infix_over_category (Arrow) (Core_aux) (Operation_aux)
include Core_aux
include Operation_aux
include Arrow
module Infix = struct
include Arrow.Infix
include Infix_aux
end
include Infix
end
module From_monad (Monad : Preface_specs.Monad.CORE) = struct
module Arr = Arrow.From_monad (Monad)
include
Over_arrow_with_choose
(Arr)
(struct
type ('a, 'b) t = 'a -> 'b Monad.t
let choose f g =
let left = Arr.(f >>> arrow Either.left)
and right = Arr.(g >>> arrow Either.right) in
Preface_core.Shims.Either.case left right
;;
end)
end
module Product (F : Preface_specs.ARROW_CHOICE) (G : Preface_specs.ARROW_CHOICE) =
Over_arrow_with_left
(Arrow.Product (F) (G))
(struct
type ('a, 'b) t = ('a, 'b) F.t * ('a, 'b) G.t
let left (x, y) = (F.left x, G.left y)
end)