val (>=>) : ('a -> 'b m) -> ('b -> 'c m) -> 'a -> 'c m
val do_when : bool -> unit m -> unit m
val do_unless : bool -> unit m -> unit m
- val forever : 'a m -> 'b m
+ val forever : (unit -> 'a m) -> 'b m
val sequence : 'a m list -> 'a list m
val sequence_ : 'a m list -> unit m
end
let (>=>) f g = fun a -> f a >>= g
let do_when test u = if test then u else unit ()
let do_unless test u = if test then unit () else u
- let rec forever u = u >> forever u
+ let forever uthunk =
+ let rec loop () = uthunk () >>= fun _ -> loop ()
+ in loop ()
let sequence ms =
let op u v = u >>= fun x -> v >>= fun xs -> unit (x :: xs) in
Util.fold_right op ms (unit [])
val (>=>) : ('a -> ('x,'b) m) -> ('b -> ('x,'c) m) -> 'a -> ('x,'c) m
val do_when : bool -> ('x,unit) m -> ('x,unit) m
val do_unless : bool -> ('x,unit) m -> ('x,unit) m
- val forever : ('x,'a) m -> ('x,'b) m
+ val forever : (unit -> ('x,'a) m) -> ('x,'b) m
val sequence : ('x,'a) m list -> ('x,'a list) m
val sequence_ : ('x,'a) m list -> ('x,unit) m
end
let (>=>) f g = fun a -> f a >>= g
let do_when test u = if test then u else unit ()
let do_unless test u = if test then unit () else u
- let rec forever u = u >> forever u
+ let forever uthunk =
+ let rec loop () = uthunk () >>= fun _ -> loop ()
+ in loop ()
let sequence ms =
let op u v = u >>= fun x -> v >>= fun xs -> unit (x :: xs) in
Util.fold_right op ms (unit [])
(* declare additional operations, while still hiding implementation of type m *)
type err = Err.err
type 'a error = Error of err | Success of 'a
- type 'a result = 'a
+ type 'a result = 'a error
type 'a result_exn = 'a
include Monad.S with type 'a result := 'a result and type 'a result_exn := 'a result_exn
(* include Monad.PLUS with type 'a m := 'a m *)
val catch : 'a m -> (err -> 'a m) -> 'a m
(* ErrorT transformer *)
module T : functor (Wrapped : Monad.S) -> sig
+ type 'a result = 'a error Wrapped.result
+ type 'a result_exn = 'a Wrapped.result_exn
+ include Monad.S with type 'a result := 'a result and type 'a result_exn := 'a result_exn
+ val elevate : 'a Wrapped.m -> 'a m
+ val throw : err -> 'a m
+ val catch : 'a m -> (err -> 'a m) -> 'a m
+ end
+ (* ErrorT transformer when wrapped monad has plus, zero *)
+ module TP : functor (Wrapped : Monad.P) -> sig
type 'a result = 'a Wrapped.result
type 'a result_exn = 'a Wrapped.result_exn
include Monad.S with type 'a result := 'a result and type 'a result_exn := 'a result_exn
val elevate : 'a Wrapped.m -> 'a m
val throw : err -> 'a m
val catch : 'a m -> (err -> 'a m) -> 'a m
+ include Monad.PLUS with type 'a m := 'a m
end
module T2 : functor (Wrapped : Monad.S2) -> sig
+ type ('x,'a) result = ('x,'a error) Wrapped.result
+ type ('x,'a) result_exn = ('x,'a) Wrapped.result_exn
+ include Monad.S2 with type ('x,'a) result := ('x,'a) result and type ('x,'a) result_exn := ('x,'a) result_exn
+ val elevate : ('x,'a) Wrapped.m -> ('x,'a) m
+ val throw : err -> ('x,'a) m
+ val catch : ('x,'a) m -> (err -> ('x,'a) m) -> ('x,'a) m
+ end
+ module TP2 : functor (Wrapped : Monad.P2) -> sig
type ('x,'a) result = ('x,'a) Wrapped.result
type ('x,'a) result_exn = ('x,'a) Wrapped.result_exn
include Monad.S2 with type ('x,'a) result := ('x,'a) result and type ('x,'a) result_exn := ('x,'a) result_exn
val elevate : ('x,'a) Wrapped.m -> ('x,'a) m
val throw : err -> ('x,'a) m
val catch : ('x,'a) m -> (err -> ('x,'a) m) -> ('x,'a) m
+ include Monad.PLUS2 with type ('x,'a) m := ('x,'a) m
end
end = struct
type err = Err.err
type 'a error = Error of err | Success of 'a
module Base = struct
type 'a m = 'a error
- type 'a result = 'a
+ type 'a result = 'a error
type 'a result_exn = 'a
let unit a = Success a
let bind u f = match u with
| Success a -> f a
| Error e -> Error e (* input and output may be of different 'a types *)
- (* TODO: should run refrain from failing? *)
- let run u = match u with
+ let run u = u
+ let run_exn u = match u with
| Success a -> a
| Error e -> raise (Err.Exc e)
- let run_exn = run
(*
let zero () = Error Err.zero
let plus u v = match (u, v) with
module Trans = struct
module Wrapped = Wrapped
type 'a m = 'a error Wrapped.m
- type 'a result = 'a Wrapped.result
+ type 'a result = 'a error Wrapped.result
type 'a result_exn = 'a Wrapped.result_exn
let elevate w = Wrapped.bind w (fun a -> Wrapped.unit (Success a))
let bind u f = Wrapped.bind u (fun t -> match t with
| Success a -> f a
| Error e -> Wrapped.unit (Error e))
- (* TODO: should run refrain from failing? *)
- let run u =
- let w = Wrapped.bind u (fun t -> match t with
- | Success a -> Wrapped.unit a
- (* | _ -> Wrapped.fail () *)
- | Error e -> raise (Err.Exc e))
- in Wrapped.run w
+ let run u = Wrapped.run u
let run_exn u =
let w = Wrapped.bind u (fun t -> match t with
| Success a -> Wrapped.unit a
- (* | _ -> Wrapped.fail () *)
| Error e -> raise (Err.Exc e))
in Wrapped.run_exn w
end
| Success _ -> Wrapped.unit t
| Error e -> handler e)
end
+ module TP(Wrapped : Monad.P) = struct
+ (* code repetition, ugh *)
+ module TransP = struct
+ include Monad.MakeT(struct
+ module Wrapped = Wrapped
+ type 'a m = 'a error Wrapped.m
+ type 'a result = 'a Wrapped.result
+ type 'a result_exn = 'a Wrapped.result_exn
+ let elevate w = Wrapped.bind w (fun a -> Wrapped.unit (Success a))
+ let bind u f = Wrapped.bind u (fun t -> match t with
+ | Success a -> f a
+ | Error e -> Wrapped.unit (Error e))
+ let run u =
+ let w = Wrapped.bind u (fun t -> match t with
+ | Success a -> Wrapped.unit a
+ | Error e -> Wrapped.zero ())
+ in Wrapped.run w
+ let run_exn u =
+ let w = Wrapped.bind u (fun t -> match t with
+ | Success a -> Wrapped.unit a
+ | Error e -> raise (Err.Exc e))
+ in Wrapped.run_exn w
+ end)
+ let throw e = Wrapped.unit (Error e)
+ let catch u handler = Wrapped.bind u (fun t -> match t with
+ | Success _ -> Wrapped.unit t
+ | Error e -> handler e)
+ let plus u v = Wrapped.plus u v
+ let zero () = elevate (Wrapped.zero ())
+ end
+ include TransP
+ include (Monad.MakeDistrib(TransP) : Monad.PLUS with type 'a m := 'a m)
+ end
module T2(Wrapped : Monad.S2) = struct
module Trans = struct
module Wrapped = Wrapped
type ('x,'a) m = ('x,'a error) Wrapped.m
- type ('x,'a) result = ('x,'a) Wrapped.result
+ type ('x,'a) result = ('x,'a error) Wrapped.result
type ('x,'a) result_exn = ('x,'a) Wrapped.result_exn
(* code repetition, ugh *)
let elevate w = Wrapped.bind w (fun a -> Wrapped.unit (Success a))
let bind u f = Wrapped.bind u (fun t -> match t with
| Success a -> f a
| Error e -> Wrapped.unit (Error e))
- let run u =
- let w = Wrapped.bind u (fun t -> match t with
- | Success a -> Wrapped.unit a
- | Error e -> raise (Err.Exc e))
- in Wrapped.run w
+ let run u = Wrapped.run u
let run_exn u =
let w = Wrapped.bind u (fun t -> match t with
| Success a -> Wrapped.unit a
| Success _ -> Wrapped.unit t
| Error e -> handler e)
end
+ module TP2(Wrapped : Monad.P2) = struct
+ (* code repetition, ugh *)
+ module TransP = struct
+ include Monad.MakeT2(struct
+ module Wrapped = Wrapped
+ type ('x,'a) m = ('x,'a error) Wrapped.m
+ type ('x,'a) result = ('x,'a) Wrapped.result
+ type ('x,'a) result_exn = ('x,'a) Wrapped.result_exn
+ let elevate w = Wrapped.bind w (fun a -> Wrapped.unit (Success a))
+ let bind u f = Wrapped.bind u (fun t -> match t with
+ | Success a -> f a
+ | Error e -> Wrapped.unit (Error e))
+ let run u =
+ let w = Wrapped.bind u (fun t -> match t with
+ | Success a -> Wrapped.unit a
+ | Error e -> Wrapped.zero ())
+ in Wrapped.run w
+ let run_exn u =
+ let w = Wrapped.bind u (fun t -> match t with
+ | Success a -> Wrapped.unit a
+ | Error e -> raise (Err.Exc e))
+ in Wrapped.run_exn w
+ end)
+ let throw e = Wrapped.unit (Error e)
+ let catch u handler = Wrapped.bind u (fun t -> match t with
+ | Success _ -> Wrapped.unit t
+ | Error e -> handler e)
+ let plus u v = Wrapped.plus u v
+ let zero () = elevate (Wrapped.zero ())
+ end
+ include TransP
+ include (Monad.MakeDistrib2(TransP) : Monad.PLUS2 with type ('x,'a) m := ('x,'a) m)
+ end
end
(* pre-define common instance of Error_monad *)
*)
end)
+(*
+# EL.(run( plus (throw "bye") (unit 20) >>= fun i -> unit(i+10)));;
+- : int EL.result = [Failure.Error "bye"; Failure.Success 30]
+# LE.(run( plus (elevate (Failure.throw "bye")) (unit 20) >>= fun i -> unit(i+10)));;
+- : int LE.result = Failure.Error "bye"
+# EL.(run_exn( plus (throw "bye") (unit 20) >>= fun i -> unit(i+10)));;
+Exception: Failure "bye".
+# LE.(run_exn( plus (elevate (Failure.throw "bye")) (unit 20) >>= fun i -> unit(i+10)));;
+Exception: Failure "bye".
+
+# ES.(run( elevate (S.puts succ) >> throw "bye" >> elevate S.get >>= fun i -> unit(i+10) )) 0;;
+- : int Failure.error * S.store = (Failure.Error "bye", 1)
+# SE.(run( puts succ >> elevate (Failure.throw "bye") >> get >>= fun i -> unit(i+10) )) 0;;
+- : (int * S.store) Failure.result = Failure.Error "bye"
+# ES.(run_exn( elevate (S.puts succ) >> throw "bye" >> elevate S.get >>= fun i -> unit(i+10) )) 0;;
+Exception: Failure "bye".
+# SE.(run_exn( puts succ >> elevate (Failure.throw "bye") >> get >>= fun i -> unit(i+10) )) 0;;
+Exception: Failure "bye".
+ *)
+
+
(* must be parameterized on (struct type env = ... end) *)
module Reader_monad(Env : sig type env end) : sig
(* declare additional operations, while still hiding implementation of type m *)
end
module TP2(Wrapped : Monad.P2) = struct
module TransP = struct
- (* code repetition, ugh *)
include T2(Wrapped)
+ (* code repetition, ugh *)
let plus u v = fun s -> Wrapped.plus (u s) (v s)
let zero () = elevate (Wrapped.zero ())
let asks selector = ask >>= (fun e ->
module TP2(Wrapped : Monad.P2) = struct
module TransP = struct
include T2(Wrapped)
+ (* code repetition, ugh *)
let plus u v = fun s -> Wrapped.plus (u s) (v s)
let zero () = elevate (Wrapped.zero ())
end
module TP2(Wrapped : Monad.P2) = struct
module TransP = struct
include T2(Wrapped)
+ (* code repetition, ugh *)
let plus u v = fun s -> Wrapped.plus (u s) (v s)
let zero () = elevate (Wrapped.zero ())
end
val callcc : (('a -> ('r,'b) m) -> ('r,'a) m) -> ('r,'a) m
val reset : ('a,'a) m -> ('r,'a) m
val shift : (('a -> ('q,'r) m) -> ('r,'r) m) -> ('r,'a) m
- val abort : ('a,'a) m -> ('a,'b) m
+ (* val abort : ('a,'a) m -> ('a,'b) m *)
+ val abort : 'a -> ('a,'b) m
val run0 : ('a,'a) m -> 'a
end = struct
let id = fun i -> i
let callcc f = fun k -> f k k
let throw k a = fun _ -> k a
*)
- (* from http://www.haskell.org/haskellwiki/MonadCont_done_right *)
+
+ (* from http://www.haskell.org/haskellwiki/MonadCont_done_right
+ *
+ * reset :: (Monad m) => ContT a m a -> ContT r m a
+ * reset e = ContT $ \k -> runContT e return >>= k
+ *
+ * shift :: (Monad m) => ((a -> ContT r m b) -> ContT b m b) -> ContT b m a
+ * shift e = ContT $ \k ->
+ * runContT (e $ \v -> ContT $ \c -> k v >>= c) return *)
let reset u = unit ((u) id)
let shift f = (fun k -> (f (fun a -> unit (k a))) id)
- let abort a = shift (fun _ -> a)
+ (* let abort a = shift (fun _ -> a) *)
+ let abort a = shift (fun _ -> unit a)
let run0 (u : ('a,'a) m) = (u) id
end
module TC = T.T2(C);;
-print_endline "================================================";;
+print_endline "=== test Leaf(...).distribute ==================";;
let t1 = Some (T.Node (T.Node (T.Leaf 2, T.Leaf 3), T.Node (T.Leaf 5, T.Node (T.Leaf 7, T.Leaf 11))));;
- : S.store list * S.store = ([10; 0; 0; 1; 20], 1)
*)
+print_endline "=== test Leaf(Continuation).distribute ==================";;
let id : 'z. 'z -> 'z = fun x -> x
(* (+ 100 (prompt (+ 10 (shift k (k (k 1)))))) ~~> 121 *)
let example5 () : int =
Continuation_monad.(let v = reset (
- let u = shift (fun k -> k 1 >>= fun x -> k x)
+ let u = shift (fun k -> k 1 >>= k)
in u >>= fun x -> unit (10 + x)
) in let w = v >>= fun x -> unit (100 + x)
in run0 w)
-
;;
+print_endline "=== test bare Continuation ============";;
+
(1011, 1111, 1111, 121);;
(example1(), example2(), example3(), example5());;
((111,0), (0,0));;
testc C.(fun a -> shift (fun k -> k (a,a+1))) (fun t -> t);;
+print_endline "=== pa_monad's Continuation Tests ============";;
+
+(1, 5 = C.(run0 (unit 1 >>= fun x -> unit (x+4))) );;
+(2, 9 = C.(run0 (reset (unit 5 >>= fun x -> unit (x+4)))) );;
+(3, 9 = C.(run0 (reset (abort 5 >>= fun y -> unit (y+6)) >>= fun x -> unit (x+4))) );;
+(4, 9 = C.(run0 (reset (reset (abort 5 >>= fun y -> unit (y+6))) >>= fun x -> unit (x+4))) );;
+(5, 27 = C.(run0 (
+ let c = reset(abort 5 >>= fun y -> unit (y+6))
+ in reset(c >>= fun v1 -> abort 7 >>= fun v2 -> unit (v2+10) ) >>= fun x -> unit (x+20))) );;
+
+(7, 117 = C.(run0 (reset (shift (fun sk -> sk 3 >>= sk >>= fun v3 -> unit (v3+100) ) >>= fun v1 -> unit (v1+2)) >>= fun x -> unit (x+10))) );;
+
+(8, 115 = C.(run0 (reset (shift (fun sk -> sk 3 >>= fun v3 -> unit (v3+100)) >>= fun v1 -> unit (v1+2)) >>= fun x -> unit (x+10))) );;
+
+(12, ["a"] = C.(run0 (reset (shift (fun f -> f [] >>= fun t -> unit ("a"::t) ) >>= fun xv -> shift (fun _ -> unit xv)))) );;
+
+
+(0, 15 = C.(run0 (let f k = k 10 >>= fun v-> unit (v+100) in reset (callcc f >>= fun v -> unit (v+5)))) );;
+