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open Preface_core.Fun
module Core_via_bind (Req : Preface_specs.Monad.WITH_BIND) :
Preface_specs.Monad.CORE with type 'a t = 'a Req.t = struct
include Req
let join m = bind id m
let map f m = bind (return <% f) m
let compose_left_to_right f g x = bind g (f x)
end
module Core_via_map_and_join (Req : Preface_specs.Monad.WITH_MAP_AND_JOIN) :
Preface_specs.Monad.CORE with type 'a t = 'a Req.t = struct
include Req
let bind f m = join (map f m)
let compose_left_to_right f g x = bind g (f x)
end
module Core_via_kleisli_composition
(Req : Preface_specs.Monad.WITH_KLEISLI_COMPOSITION) :
Preface_specs.Monad.CORE with type 'a t = 'a Req.t = struct
include Req
let bind f m = (compose_left_to_right (const m) f) ()
let join m = bind id m
let map f m = bind (return <% f) m
end
module Operation (Core : Preface_specs.Monad.CORE) :
Preface_specs.Monad.OPERATION with type 'a t = 'a Core.t = struct
include Functor.Operation (Core)
let void _ = Core.return ()
let compose_right_to_left f g x = Core.compose_left_to_right g f x
let lift = Core.map
let lift2 f ma mb =
Core.(bind (fun a -> bind (fun b -> return (f a b)) mb) ma)
;;
let lift3 f ma mb mc =
let open Core in
bind (fun a -> bind (fun b -> bind (fun c -> return (f a b c)) mc) mb) ma
;;
end
module Syntax (Core : Preface_specs.Monad.CORE) :
Preface_specs.Monad.SYNTAX with type 'a t = 'a Core.t = struct
type 'a t = 'a Core.t
let ( let* ) m f = Core.bind f m
let ( let+ ) m f = Core.map f m
end
module Infix
(Core : Preface_specs.Monad.CORE)
(Operation : Preface_specs.Monad.OPERATION with type 'a t = 'a Core.t) :
Preface_specs.Monad.INFIX with type 'a t = 'a Core.t = struct
include Functor.Infix (Core) (Operation)
let ( >|= ) x f = Core.map f x
let ( =|< ) = Core.map
let ( >>= ) x f = Core.bind f x
let ( =<< ) = Core.bind
let ( >=> ) = Core.compose_left_to_right
let ( <=< ) = Operation.compose_right_to_left
let ( >> ) ma mb = ma >>= (fun _ -> mb)
let ( << ) ma _ = ma
end
module Via
(Core : Preface_specs.Monad.CORE)
(Operation : Preface_specs.Monad.OPERATION with type 'a t = 'a Core.t)
(Infix : Preface_specs.Monad.INFIX with type 'a t = 'a Core.t)
(Syntax : Preface_specs.Monad.SYNTAX with type 'a t = 'a Core.t) :
Preface_specs.MONAD with type 'a t = 'a Core.t = struct
include Core
include Operation
include Syntax
include Infix
module Syntax = Syntax
module Infix = Infix
end
module Via_bind (Req : Preface_specs.Monad.WITH_BIND) :
Preface_specs.MONAD with type 'a t = 'a Req.t = struct
module Core = Core_via_bind (Req)
module Operation = Operation (Core)
module Syntax = Syntax (Core)
module Infix = Infix (Core) (Operation)
include Core
include Operation
include Syntax
include Infix
end
module Via_map_and_join (Req : Preface_specs.Monad.WITH_MAP_AND_JOIN) :
Preface_specs.MONAD with type 'a t = 'a Req.t = struct
module Core = Core_via_map_and_join (Req)
module Operation = Operation (Core)
module Syntax = Syntax (Core)
module Infix = Infix (Core) (Operation)
include Core
include Operation
include Syntax
include Infix
end
module Via_kleisli_composition
(Req : Preface_specs.Monad.WITH_KLEISLI_COMPOSITION) :
Preface_specs.MONAD with type 'a t = 'a Req.t = struct
module Core = Core_via_kleisli_composition (Req)
module Operation = Operation (Core)
module Syntax = Syntax (Core)
module Infix = Infix (Core) (Operation)
include Core
include Operation
include Syntax
include Infix
end
module From_monad_plus (Monad_plus : Preface_specs.MONAD_PLUS) :
Preface_specs.MONAD with type 'a t = 'a Monad_plus.t =
Monad_plus
module From_arrow_apply (A : Preface_specs.ARROW_APPLY) :
Preface_specs.MONAD with type 'a t = (unit, 'a) A.t = Via_bind (struct
type 'a t = (unit, 'a) A.t
let return x = A.arrow (const x)
let bind f x = A.(x >>> arrow (fun x -> (f x, ())) >>> apply)
end)
module Product (F : Preface_specs.MONAD) (G : Preface_specs.MONAD) :
Preface_specs.MONAD with type 'a t = 'a F.t * 'a G.t = Via_bind (struct
type 'a t = 'a F.t * 'a G.t
let return x = (F.return x, G.return x)
let bind f (m, n) = (F.bind (fst % f) m, G.bind (snd % f) n)
end)