├── .gitignore ├── .merlin ├── LICENSE ├── README.md ├── _oasis ├── _tags ├── free_demo.ml └── src ├── free.ml ├── free_applicative.ml ├── free_functor.ml ├── free_monad.ml └── free_utils.ml /.gitignore: -------------------------------------------------------------------------------- 1 | *.annot 2 | *.cmo 3 | *.cma 4 | *.cmi 5 | *.a 6 | *.o 7 | *.cmx 8 | *.cmxs 9 | *.cmxa 10 | 11 | _build/ 12 | AUTHORS.txt 13 | INSTALL.txt 14 | Makefile 15 | README.txt 16 | configure 17 | *.byte 18 | myocamlbuild.ml 19 | setup.data 20 | setup.log 21 | setup.ml 22 | src/META 23 | src/free.mldylib 24 | src/free.mllib 25 | _tags 26 | 27 | free_api.odocl 28 | -------------------------------------------------------------------------------- /.merlin: -------------------------------------------------------------------------------- 1 | S src 2 | 3 | B _build 4 | B _build/src 5 | 6 | PKG lwt 7 | PKG lwt.unix 8 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU LESSER GENERAL PUBLIC LICENSE 2 | Version 2.1, February 1999 3 | 4 | Copyright (C) 1991, 1999 Free Software Foundation, Inc. 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | (This is the first released version of the Lesser GPL. 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Here is a sample; alter the names: 496 | 497 | Yoyodyne, Inc., hereby disclaims all copyright interest in the 498 | library `Frob' (a library for tweaking knobs) written by James Random 499 | Hacker. 500 | 501 | {signature of Ty Coon}, 1 April 1990 502 | Ty Coon, President of Vice 503 | 504 | That's all there is to it! -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ocaml-free 2 | ========== 3 | 4 | A 'free monad' library for OCaml 5 | -------------------------------------------------------------------------------- /_oasis: -------------------------------------------------------------------------------- 1 | OASISFormat: 0.4 2 | Name: free 3 | Version: 999 4 | Synopsis: A 'free monad' implementation 5 | Authors: Nicolas Trangez 6 | License: LGPL-2.1 with OCaml linking exception 7 | Homepage: http://github.com/NicolasT/ocaml-free 8 | 9 | BuildTools: ocamlbuild 10 | Plugins: META (0.4), StdFiles (0.4), DevFiles (0.4) 11 | AlphaFeatures: ocamlbuild_more_args 12 | 13 | Library free 14 | Path: src 15 | FindlibName: free 16 | Modules: Free 17 | InternalModules: Free_monad, 18 | Free_utils, 19 | Free_functor, 20 | Free_applicative 21 | 22 | Executable "free-demo" 23 | Path: . 24 | Install: false 25 | MainIs: free_demo.ml 26 | BuildDepends: free, 27 | lwt, 28 | lwt.unix 29 | 30 | Document "free_api" 31 | Type: ocamlbuild (0.4) 32 | BuildTools: ocamldoc 33 | 34 | Title: API Reference for Free 35 | XOcamlbuildPath: . 36 | XOcamlbuildExtraArgs: "-docflags '-colorize-code -short-functors -charset utf-8'" 37 | XOcamlbuildLibraries: free 38 | 39 | SourceRepository head 40 | Type: git 41 | Location: git://github.com/NicolasT/ocaml-free.git 42 | Branch: master 43 | Browser: http://github.com/NicolasT/ocaml-free 44 | 45 | -------------------------------------------------------------------------------- /_tags: -------------------------------------------------------------------------------- 1 | true: warn_A 2 | true: warn_error_A 3 | 4 | # OASIS_START 5 | # OASIS_STOP 6 | -------------------------------------------------------------------------------- /free_demo.ml: -------------------------------------------------------------------------------- 1 | (* API for demo programs *) 2 | module Demo = struct 3 | (* Our functor *) 4 | module F = struct 5 | (* This type defines all possible actions *) 6 | type 'a t = Print of (string * (unit -> 'a)) 7 | | Random of (int -> 'a) 8 | | Abort of string 9 | 10 | (* Need a Functor instance *) 11 | let map f = function 12 | | Print (s, next) -> Print (s, fun () -> f (next ())) 13 | | Random next -> Random (fun rnd -> f (next rnd)) 14 | | Abort s -> Abort s 15 | end 16 | 17 | (* Magic! *) 18 | module M = Free.Monad.Make(F) 19 | include M 20 | 21 | module M' = Free.Monad.Utils(M) 22 | include M' 23 | 24 | (* Accessors for the actions. These could be generated mechanically. *) 25 | let print s = lift (F.Print (s, Free.Utils.id)) 26 | let random = lift (F.Random Free.Utils.id) 27 | let abort s = lift (F.Abort s) 28 | end 29 | 30 | (* A demo program *) 31 | let demo_program = 32 | let open Demo in 33 | let (>>=) = Demo.bind in 34 | 35 | print "abc" >>= fun () -> 36 | print "def" >>= fun () -> 37 | random >>= fun rnd -> 38 | print "g" >>= fun () -> print "h" >>= fun () -> print "i" >>= fun () -> 39 | if rnd > 42 40 | then abort "Randoms can't exceed 42!" 41 | else print (Printf.sprintf "Random was %d" rnd) >>= fun () -> 42 | replicateM_ 5 (print "a") 43 | 44 | 45 | let optimize : 'a Demo.t -> 'a Demo.t = 46 | let (>>=) = Demo.bind in 47 | 48 | let rec loop = function 49 | | Demo.Free a -> begin match a with 50 | | Demo.F.Print (s, n) -> 51 | begin match loop (n ()) with 52 | (* 2 or more consecutive 'print' actions become a single 'print' 53 | * of the concatenated string 54 | *) 55 | | Demo.Free (Demo.F.Print (s', n')) -> 56 | Demo.print (s ^ s') >>= n' 57 | | Demo.Free (Demo.F.Random _ | Demo.F.Abort _) -> 58 | Demo.print s >>= fun () -> loop (n ()) 59 | | Demo.Pure v -> Demo.Pure v 60 | end 61 | | Demo.F.Random n -> Demo.Free (Demo.F.Random (fun rnd -> loop (n rnd))) 62 | | Demo.F.Abort s -> Demo.Free (Demo.F.Abort s) 63 | end 64 | | Demo.Pure a -> Demo.Pure a 65 | in 66 | loop 67 | 68 | (* An interpreter for demo programs. This one uses Pervasives IO *) 69 | let run_demo = 70 | Demo.iter (function 71 | | Demo.F.Print (s, n) -> 72 | Printf.printf "Pervasives says: %s\n" s; 73 | n () 74 | | Demo.F.Random n -> 75 | n 42 76 | | Demo.F.Abort s -> 77 | failwith (Printf.sprintf "Abort: %s" s)) 78 | 79 | (* An interpreter for demo programs. This uses an underlying monad (Lwt). *) 80 | let run_demo_lwt = 81 | (* Lwt needs some fiddling for it to conform to our Monad interface *) 82 | let module DI = Demo.IterM(struct 83 | include Lwt 84 | 85 | let pure = Lwt.return 86 | 87 | let ap f a = 88 | let (>>=) = Lwt.bind in 89 | f >>= fun f' -> 90 | a >>= fun a' -> 91 | return (f' a') 92 | end) in 93 | 94 | DI.iterM (function 95 | | Demo.F.Print (s, n) -> 96 | Lwt.bind 97 | (Lwt_io.printlf "Lwt says: %s" s) 98 | n 99 | | Demo.F.Random n -> 100 | n 43 101 | | Demo.F.Abort s -> 102 | Lwt.fail (Failure (Printf.sprintf "Abort: %s" s))) 103 | 104 | let main () = 105 | run_demo demo_program; 106 | flush_all (); 107 | Lwt_main.run (run_demo_lwt (optimize demo_program)) 108 | ;; 109 | 110 | main () 111 | -------------------------------------------------------------------------------- /src/free.ml: -------------------------------------------------------------------------------- 1 | module type Functor = Free_functor.Functor 2 | module type Applicative = Free_applicative.Applicative 3 | module type Monad = Free_monad.Monad 4 | 5 | module Monad = Free_monad 6 | 7 | module Utils = Free_utils 8 | -------------------------------------------------------------------------------- /src/free_applicative.ml: -------------------------------------------------------------------------------- 1 | module type Applicative = sig 2 | include Free_functor.Functor 3 | 4 | val pure : 'a -> 'a t 5 | val ap : ('a -> 'b) t -> 'a t -> 'b t 6 | end 7 | 8 | module Infix(A : Applicative) : sig 9 | val (<$>) : ('a -> 'b) -> 'a A.t -> 'b A.t 10 | val (<*>) : ('a -> 'b) A.t -> 'a A.t -> 'b A.t 11 | end = struct 12 | module F = Free_functor.Infix(A) 13 | include F 14 | 15 | let (<*>) = A.ap 16 | end 17 | 18 | module Utils(A : Applicative) : sig 19 | module Infix : sig 20 | val (<$>) : ('a -> 'b) -> 'a A.t -> 'b A.t 21 | val (<$) : 'a -> 'b A.t -> 'a A.t 22 | 23 | val (<*>) : ('a -> 'b) A.t -> 'a A.t -> 'b A.t 24 | val (<**>) : 'a A.t -> ('a -> 'b) A.t -> 'b A.t 25 | 26 | val ( *>) : 'a A.t -> 'b A.t -> 'b A.t 27 | val (<*) : 'a A.t -> 'b A.t -> 'a A.t 28 | end 29 | 30 | val map : ('a -> 'b) -> 'a A.t -> 'b A.t 31 | 32 | val pure : 'a -> 'a A.t 33 | val ap : ('a -> 'b) A.t -> 'a A.t -> 'b A.t 34 | 35 | val liftA : ('a -> 'b) -> 'a A.t -> 'b A.t 36 | val liftA2 : ('a -> 'b -> 'c) -> 'a A.t -> 'b A.t -> 'c A.t 37 | val liftA3 : ('a -> 'b -> 'c -> 'd) -> 'a A.t -> 'b A.t -> 'c A.t -> 'd A.t 38 | end = struct 39 | include A 40 | 41 | module F = Free_functor.Utils(A) 42 | 43 | module Infix = struct 44 | include F.Infix 45 | module AI = Infix(A) 46 | include AI 47 | 48 | let (<**>) a f = f <*> a 49 | 50 | let ( *>) a b = (fun _ b -> b) <$> a <*> b 51 | let (<*) a b = (fun a _ -> a) <$> a <*> b 52 | end 53 | 54 | open Infix 55 | 56 | let liftA = A.map 57 | let liftA2 f a b = liftA f a <*> b 58 | let liftA3 f a b c = liftA2 f a b <*> c 59 | end 60 | -------------------------------------------------------------------------------- /src/free_functor.ml: -------------------------------------------------------------------------------- 1 | module type Functor = sig 2 | type 'a t 3 | 4 | val map : ('a -> 'b) -> 'a t -> 'b t 5 | end 6 | 7 | module Infix(F : Functor) : sig 8 | val (<$>) : ('a -> 'b) -> 'a F.t -> 'b F.t 9 | end = struct 10 | let (<$>) = F.map 11 | end 12 | 13 | module Utils(F : Functor) : sig 14 | module Infix : sig 15 | val (<$>) : ('a -> 'b) -> 'a F.t -> 'b F.t 16 | val (<$) : 'a -> 'b F.t -> 'a F.t 17 | end 18 | 19 | val map : ('a -> 'b) -> 'a F.t -> 'b F.t 20 | end = struct 21 | include F 22 | 23 | module Infix = struct 24 | module M = Infix(F) 25 | include M 26 | 27 | let (<$) a f = F.map (fun _ -> a) f 28 | end 29 | 30 | let map = F.map 31 | end 32 | -------------------------------------------------------------------------------- /src/free_monad.ml: -------------------------------------------------------------------------------- 1 | module type Monad = sig 2 | include Free_applicative.Applicative 3 | 4 | val bind : 'a t -> ('a -> 'b t) -> 'b t 5 | end 6 | 7 | module Make(F : Free_functor.Functor) : sig 8 | type 'a t = Pure of 'a 9 | | Free of ('a t) F.t 10 | 11 | include Monad with type 'a t := 'a t 12 | 13 | val lift : 'a F.t -> 'a t 14 | val iter : ('a F.t -> 'a) -> 'a t -> 'a 15 | 16 | module IterM(M : Monad) : sig 17 | val iterM : ('a M.t F.t -> 'a M.t) -> 'a t -> 'a M.t 18 | end 19 | end = struct 20 | type 'a t = Pure of 'a 21 | | Free of ('a t) F.t 22 | 23 | let map f = 24 | let rec loop = function 25 | | Pure a -> Pure (f a) 26 | | Free fa -> Free (F.map loop fa) 27 | in 28 | loop 29 | 30 | let pure a = Pure a 31 | let ap = 32 | let rec loop a b = match a with 33 | | Pure a' -> begin match b with 34 | | Pure b' -> Pure (a' b') 35 | | Free b' -> Free (F.map (map a') b') 36 | end 37 | | Free a' -> Free (F.map (fun a'' -> loop a'' b) a') 38 | in 39 | loop 40 | 41 | let bind = 42 | let rec loop a b = match a with 43 | | Pure a' -> b a' 44 | | Free a' -> Free (F.map (fun a'' -> loop a'' b) a') 45 | in 46 | loop 47 | 48 | let lift f = Free (F.map pure f) 49 | 50 | let iter hnd = 51 | let rec loop = function 52 | | Pure a -> a 53 | | Free f -> hnd (F.map loop f) 54 | in 55 | loop 56 | 57 | module IterM(M : Monad) = struct 58 | let iterM hnd = 59 | let rec loop = function 60 | | Pure a -> M.pure a 61 | | Free f -> hnd (F.map loop f) 62 | in 63 | loop 64 | end 65 | end 66 | 67 | module Infix(M : Monad) : sig 68 | val (<$>) : ('a -> 'b) -> 'a M.t -> 'b M.t 69 | val (<*>) : ('a -> 'b) M.t -> 'a M.t -> 'b M.t 70 | val (>>=) : 'a M.t -> ('a -> 'b M.t) -> 'b M.t 71 | end = struct 72 | module A = Free_applicative.Infix(M) 73 | include A 74 | 75 | let (>>=) = M.bind 76 | end 77 | 78 | module Utils(M : Monad) : sig 79 | module Infix : sig 80 | val (<$>) : ('a -> 'b) -> 'a M.t -> 'b M.t 81 | val (<$) : 'a -> 'b M.t -> 'a M.t 82 | 83 | val (<*>) : ('a -> 'b) M.t -> 'a M.t -> 'b M.t 84 | val (<**>) : 'a M.t -> ('a -> 'b) M.t -> 'b M.t 85 | 86 | val ( *>) : 'a M.t -> 'b M.t -> 'b M.t 87 | val (<*) : 'a M.t -> 'b M.t -> 'a M.t 88 | 89 | val (<=<) : ('b -> 'c M.t) -> ('a -> 'b M.t) -> 'a -> 'c M.t 90 | val (=<<) : ('a -> 'b M.t) -> 'a M.t -> 'b M.t 91 | val (>=>) : ('a -> 'b M.t) -> ('b -> 'c M.t) -> 'a -> 'c M.t 92 | end 93 | 94 | val map : ('a -> 'b) -> 'a M.t -> 'b M.t 95 | 96 | val pure : 'a -> 'a M.t 97 | val ap : ('a -> 'b) M.t -> 'a M.t -> 'b M.t 98 | 99 | val liftA : ('a -> 'b) -> 'a M.t -> 'b M.t 100 | val liftA2 : ('a -> 'b -> 'c) -> 'a M.t -> 'b M.t -> 'c M.t 101 | val liftA3 : ('a -> 'b -> 'c -> 'd) -> 'a M.t -> 'b M.t -> 'c M.t -> 'd M.t 102 | 103 | val bind : 'a M.t -> ('a -> 'b M.t) -> 'b M.t 104 | 105 | val filterM : ('a -> bool M.t) -> 'a list -> 'a list M.t 106 | val foldM : ('a -> 'b -> 'a M.t) -> 'a -> 'b list -> 'a M.t 107 | val foldM_ : ('a -> 'b -> 'a M.t) -> 'a -> 'b list -> unit M.t 108 | val forM : 'a list -> ('a -> 'b M.t) -> 'b list M.t 109 | val forM_ : 'a list -> ('a -> 'b M.t) -> unit M.t 110 | val forever : 'a M.t -> 'b M.t 111 | val join : 'a M.t M.t -> 'a M.t 112 | val liftM : ('a -> 'b) -> 'a M.t -> 'b M.t 113 | val liftM2 : ('a -> 'b -> 'c) -> 'a M.t -> 'b M.t -> 'c M.t 114 | val liftM3 : ('a -> 'b -> 'c -> 'd) -> 'a M.t -> 'b M.t -> 'c M.t -> 'd M.t 115 | val liftM4 : ('a -> 'b -> 'c -> 'd -> 'e) -> 'a M.t -> 'b M.t -> 'c M.t -> 'd M.t -> 'e M.t 116 | val liftM5 : ('a -> 'b -> 'c -> 'd -> 'e -> 'f) -> 'a M.t -> 'b M.t -> 'c M.t -> 'd M.t -> 'e M.t -> 'f M.t 117 | val mapAndUnzipM : ('a -> ('b * 'c) M.t) -> 'a list -> ('b list * 'c list) M.t 118 | val mapM : ('a -> 'b M.t) -> 'a list -> 'b list M.t 119 | val mapM_ : ('a -> 'b M.t) -> 'a list -> unit M.t 120 | val replicateM : int -> 'a M.t -> 'a list M.t 121 | val replicateM_ : int -> 'a M.t -> unit M.t 122 | val sequence : 'a M.t list -> 'a list M.t 123 | val sequence_ : 'a M.t list -> unit M.t 124 | val unless : bool -> unit M.t -> unit M.t 125 | (* `void` could be defined on Functor, but seems rather useless *) 126 | val void : 'a M.t -> unit M.t 127 | val when_ : bool -> unit M.t -> unit M.t 128 | val zipWithM : ('a -> 'b -> 'c M.t) -> 'a list -> 'b list -> 'c list M.t 129 | val zipWithM_ : ('a -> 'b -> 'c M.t) -> 'a list -> 'b list -> unit M.t 130 | end = struct 131 | include M 132 | 133 | module A = Free_applicative.Utils(M) 134 | 135 | module Infix = struct 136 | include A.Infix 137 | module MI = Infix(M) 138 | include MI 139 | 140 | let (>=>) a b = fun x -> a x >>= b 141 | let (<=<) a b = b >=> a 142 | let (=<<) a b = b >>= a 143 | end 144 | 145 | include (A : sig 146 | val liftA : ('a -> 'b) -> 'a M.t -> 'b M.t 147 | val liftA2 : ('a -> 'b -> 'c) -> 'a M.t -> 'b M.t -> 'c M.t 148 | val liftA3 : ('a -> 'b -> 'c -> 'd) -> 'a M.t -> 'b M.t -> 'c M.t -> 'd M.t 149 | end) 150 | 151 | open Infix 152 | 153 | let filterM p = 154 | let rec loop = function 155 | | [] -> pure [] 156 | | (x :: xs) -> 157 | p x >>= fun k -> 158 | loop xs >>= fun r -> 159 | pure (if k then x :: r else r) 160 | in 161 | loop 162 | 163 | let foldM f = 164 | let rec loop a = function 165 | | [] -> pure a 166 | | (x :: xs) -> 167 | f a x >>= fun a' -> 168 | loop a' xs 169 | in 170 | loop 171 | 172 | let foldM_ f a l = foldM f a l >>= fun _ -> pure () 173 | 174 | let sequence ls = 175 | let helper t0 t1 = 176 | t0 >>= fun x -> 177 | t1 >>= fun xs -> 178 | pure (x :: xs) 179 | in 180 | List.fold_right helper ls (pure []) 181 | 182 | let sequence_ ls = List.fold_right (fun a b -> a >>= fun _ -> b) ls (pure ()) 183 | 184 | let mapM f l = sequence (List.map f l) 185 | let mapM_ f l = sequence_ (List.map f l) 186 | 187 | let forM l f = mapM f l 188 | let forM_ l f = mapM_ f l 189 | 190 | let forever = 191 | let rec loop f = f >>= fun _ -> loop f in 192 | loop 193 | 194 | let join a = a >>= Free_utils.id 195 | 196 | let liftM = liftA 197 | let liftM2 = liftA2 198 | let liftM3 = liftA3 199 | let liftM4 f a b c d = liftM3 f a b c <*> d 200 | let liftM5 f a b c d e = liftM4 f a b c d <*> e 201 | 202 | let void f = map (fun _ -> ()) f 203 | let when_ b f = if b then f else pure () 204 | let unless b f = if b then pure () else f 205 | 206 | let replicateM c f = sequence (Free_utils.replicate c f) 207 | let replicateM_ c f = sequence_ (Free_utils.replicate c f) 208 | 209 | let zipWithM f xs ys = sequence (Free_utils.zipWith f xs ys) 210 | let zipWithM_ f xs ys = sequence_ (Free_utils.zipWith f xs ys) 211 | 212 | let mapAndUnzipM f xs = sequence (List.map f xs) >>= fun r -> pure (List.split r) 213 | end 214 | -------------------------------------------------------------------------------- /src/free_utils.ml: -------------------------------------------------------------------------------- 1 | external id : 'a -> 'a = "%identity" 2 | external apply : ('a -> 'b) -> 'a -> 'b = "%apply" 3 | external revapply : 'a -> ('a -> 'b) -> 'b = "%revapply" 4 | 5 | let flip f = fun a b -> f b a 6 | 7 | let replicate c v = 8 | let rec loop acc = function 9 | | 0 -> acc 10 | | n -> loop (v :: acc) (n - 1) 11 | in 12 | loop [] c 13 | 14 | let zipWith f xs ys = 15 | let rec loop = function 16 | | ([], _) -> [] 17 | | (_, []) -> [] 18 | | ((x :: xs), (y :: ys)) -> f x y :: loop (xs, ys) 19 | in 20 | loop (xs, ys) 21 | --------------------------------------------------------------------------------