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module Core_via_fold_right (Req : Preface_specs.Foldable.WITH_FOLD_RIGHT) =
struct
include Req
let fold_map' neutral combine f x =
let reducer x acc = combine (f x) acc in
fold_right reducer x neutral
;;
end
module Core_via_fold_map (Req : Preface_specs.Foldable.WITH_FOLD_MAP) = struct
include Req
let fold_right f x acc =
(fold_map' (fun x -> x) (fun f g x -> f (g x)) f) x acc
;;
end
module Operation (C : Preface_specs.Foldable.CORE) = struct
type 'a t = 'a C.t
let fold_map (type m) (module M : Preface_specs.Monoid.CORE with type t = m) f
x =
C.fold_map' M.neutral M.combine f x
;;
let reduce (type m) (module M : Preface_specs.Monoid.CORE with type t = m) x =
fold_map (module M) (fun x -> x) x
;;
let fold_left f acc x =
let f' x k z = k (f z x) in
let fold = C.fold_right f' x (fun x -> x) in
fold acc
;;
let for_all p x = C.fold_map' true ( && ) p x
let exists p x = C.fold_map' false ( || ) p x
let length x = fold_left (fun acc _ -> succ acc) 0 x
end
module Via
(C : Preface_specs.Foldable.CORE)
(O : Preface_specs.Foldable.OPERATION with type 'a t = 'a C.t) =
struct
include C
include (O : Preface_specs.Foldable.OPERATION with type 'a t := 'a t)
end
module Via_fold_right (Req : Preface_specs.Foldable.WITH_FOLD_RIGHT) = struct
module C = Core_via_fold_right (Req)
module O = Operation (C)
include Via (C) (O)
end
module Via_fold_map (Req : Preface_specs.Foldable.WITH_FOLD_MAP) = struct
module C = Core_via_fold_map (Req)
module O = Operation (C)
include Via (C) (O)
end
module Composition (F : Preface_specs.FOLDABLE) (G : Preface_specs.FOLDABLE) =
Via_fold_map (struct
type 'a t = 'a G.t F.t
let fold_map' neutral combine f x =
F.fold_map' neutral combine (G.fold_map' neutral combine f) x
;;
end)
module Sum (F : Preface_specs.FOLDABLE) (G : Preface_specs.FOLDABLE) = struct
type 'a sum =
| L of 'a F.t
| R of 'a G.t
include Via_fold_map (struct
type 'a t = 'a sum
let fold_map' neutral combine f = function
| L x -> F.fold_map' neutral combine f x
| R x -> G.fold_map' neutral combine f x
;;
end)
end
module Product (F : Preface_specs.FOLDABLE) (G : Preface_specs.FOLDABLE) =
Via_fold_map (struct
type 'a t = 'a F.t * 'a G.t
let fold_map' neutral combine f (x, y) =
combine (F.fold_map' neutral combine f x) (G.fold_map' neutral combine f y)
;;
end)