* to types whose internals you have free access to.
*
* Acknowledgements: This is largely based on the mtl library distributed
- * with the Glaskow Haskell Compiler. I've also been helped in
+ * with the Glasgow Haskell Compiler. I've also been helped in
* various ways by posts and direct feedback from Oleg Kiselyov and
* Chung-chieh Shan. The following were also useful:
* - <http://pauillac.inria.fr/~xleroy/mpri/progfunc/>
* - http://www.grabmueller.de/martin/www/pub/Transformers.pdf
* - http://en.wikibooks.org/wiki/Haskell/Monad_transformers
*
- * Licensing: MIT (if that's compatible with the ghc sources).
+ * Licensing: MIT (if that's compatible with the ghc sources this is partly
+ * derived from)
*)
exception Undefined
in loop len []
(* Dirty hack to be a default polymorphic zero.
* To implement this cleanly, monads without a natural zero
- * should always wrap themselves in an option layer (see Leaf_monad). *)
+ * should always wrap themselves in an option layer (see Tree_monad). *)
let undef = Obj.magic (fun () -> raise Undefined)
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
- (* A Haskell-like version:
+ (* A Haskell-like version works:
let rec forever uthunk = uthunk () >>= fun _ -> forever uthunk
- * is not in tail position and will stack overflow. *)
+ * but the recursive call is not in tail position so this can stack overflow. *)
let forever uthunk =
let z = zero () in
let id result = result in
- let newk = ref id in
- let rec loop () =
- let result = uthunk (newk := id) >>= chained
- in !newk result
- and chained =
- fun _ -> newk := (fun _ -> loop ()); z (* we use z only for its polymorphism *)
- in loop ()
- (* reimplementations of the preceding using a hand-rolled State or StateT also stack overflowed *)
+ let kcell = ref id in
+ let rec loop _ =
+ let result = uthunk (kcell := id) >>= chained
+ in !kcell result
+ and chained _ =
+ kcell := loop; z (* we use z only for its polymorphism *)
+ in loop z
+ (* Reimplementations of the preceding using a hand-rolled State or StateT
+can also stack overflow. *)
let sequence ms =
let op u v = u >>= fun x -> v >>= fun xs -> unit (x :: xs) in
Util.fold_right op ms (unit [])
end
end
-(*
-# LL.(run(plus (unit 1) (unit 2) >>= fun i -> plus (unit i) (unit(10*i)) ));;
-- : ('_a, int) LL.result = [[1; 10; 2; 20]]
-# LL.(run(plus (unit 1) (unit 2) >>= fun i -> elevate L.(plus (unit i) (unit(10*i)) )));;
-- : ('_a, int) LL.result = [[1; 2]; [1; 20]; [10; 2]; [10; 20]]
-*)
-
(* must be parameterized on (struct type err = ... end) *)
module Error_monad(Err : sig
*)
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
end
end
+
(* State monad with different interface (structured store) *)
module Ref_monad(V : sig
type value
* >>= fun x -> unit (x, 0)
* in run u)
*
- *
- * (* (+ 1000 (prompt (+ 100 (shift k (+ 10 1))))) ~~> 1011 *)
- * let example1 () : int =
- * Continuation_monad.(let v = reset (
- * let u = shift (fun k -> unit (10 + 1))
- * in u >>= fun x -> unit (100 + x)
- * ) in let w = v >>= fun x -> unit (1000 + x)
- * in run w)
- *
- * (* (+ 1000 (prompt (+ 100 (shift k (k (+ 10 1)))))) ~~> 1111 *)
- * let example2 () =
- * Continuation_monad.(let v = reset (
- * let u = shift (fun k -> k (10 :: [1]))
- * in u >>= fun x -> unit (100 :: x)
- * ) in let w = v >>= fun x -> unit (1000 :: x)
- * in run w)
- *
- * (* (+ 1000 (prompt (+ 100 (shift k (+ 10 (k 1)))))) ~~> 1111 but added differently *)
- * let example3 () =
- * Continuation_monad.(let v = reset (
- * let u = shift (fun k -> k [1] >>= fun x -> unit (10 :: x))
- * in u >>= fun x -> unit (100 :: x)
- * ) in let w = v >>= fun x -> unit (1000 :: x)
- * in run w)
- *
- * (* (+ 100 ((prompt (+ 10 (shift k k))) 1)) ~~> 111 *)
- * (* not sure if this example can be typed without a sum-type *)
- *
- * (* (+ 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)
- * in u >>= fun x -> unit (10 + x)
- * ) in let w = v >>= fun x -> unit (100 + x)
- * in run w)
- *
*)
-module Leaf_monad : sig
+module Tree_monad : sig
(* We implement the type as `'a tree option` because it has a natural`plus`,
* and the rest of the library expects that `plus` and `zero` will come together. *)
type 'a tree = Leaf of 'a | Node of ('a tree * 'a tree)
type ('x,'a) result = 'a tree option
type ('x,'a) result_exn = 'a tree
include Monad.S with type ('x,'a) result := ('x,'a) result and type ('x,'a) result_exn := ('x,'a) result_exn
- (* LeafT transformer *)
+ (* TreeT transformer *)
module T : functor (Wrapped : Monad.S) -> sig
type ('x,'a) result = ('x,'a tree option) Wrapped.result
type ('x,'a) result_exn = ('x,'a tree) Wrapped.result_exn
include BaseT
let distribute f t = mapT (fun a -> elevate (f a)) t zero plus
end
-end
-
-
-module L = List_monad;;
-module R = Reader_monad(struct type env = int -> int end);;
-module S = State_monad(struct type store = int end);;
-module T = Leaf_monad;;
-module LR = L.T(R);;
-module LS = L.T(S);;
-module TL = T.T(L);;
-module TR = T.T(R);;
-module TS = T.T(S);;
-module C = Continuation_monad
-module TC = T.T(C);;
-
-
-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))));;
-
-let ts = TS.distribute (fun i -> S.(puts succ >> unit i)) t1;;
-TS.run ts 0;;
-(*
-- : int T.tree option * S.store =
-(Some
- (T.Node
- (T.Node (T.Leaf 2, T.Leaf 3),
- T.Node (T.Leaf 5, T.Node (T.Leaf 7, T.Leaf 11)))),
- 5)
-*)
-
-let ts2 = TS.distribute (fun i -> S.(puts succ >> get >>= fun n -> unit (i,n))) t1;;
-TS.run_exn ts2 0;;
-(*
-- : (int * S.store) T.tree option * S.store =
-(Some
- (T.Node
- (T.Node (T.Leaf (2, 1), T.Leaf (3, 2)),
- T.Node (T.Leaf (5, 3), T.Node (T.Leaf (7, 4), T.Leaf (11, 5))))),
- 5)
-*)
-
-let tr = TR.distribute (fun i -> R.asks (fun e -> e i)) t1;;
-TR.run_exn tr (fun i -> i+i);;
-(*
-- : int T.tree option =
-Some
- (T.Node
- (T.Node (T.Leaf 4, T.Leaf 6),
- T.Node (T.Leaf 10, T.Node (T.Leaf 14, T.Leaf 22))))
-*)
-
-let tl = TL.distribute (fun i -> L.(unit (i,i+1))) t1;;
-TL.run_exn tl;;
-(*
-- : (int * int) TL.result =
-[Some
- (T.Node
- (T.Node (T.Leaf (2, 3), T.Leaf (3, 4)),
- T.Node (T.Leaf (5, 6), T.Node (T.Leaf (7, 8), T.Leaf (11, 12)))))]
-*)
-
-let l2 = [1;2;3;4;5];;
-let t2 = Some (T.Node (T.Leaf 1, (T.Node (T.Node (T.Node (T.Leaf 2, T.Leaf 3), T.Leaf 4), T.Leaf 5))));;
-
-LR.(run (distribute (fun i -> R.(asks (fun e -> e i))) l2 >>= fun j -> LR.(plus (unit j) (unit (succ j))))) (fun i -> i*10);;
-(* int list = [10; 11; 20; 21; 30; 31; 40; 41; 50; 51] *)
-
-TR.(run_exn (distribute (fun i -> R.(asks (fun e -> e i))) t2 >>= fun j -> TR.(plus (unit j) (unit (succ j))))) (fun i -> i*10);;
-(*
-int T.tree option =
-Some
- (T.Node
- (T.Node (T.Leaf 10, T.Leaf 11),
- T.Node
- (T.Node
- (T.Node (T.Node (T.Leaf 20, T.Leaf 21), T.Node (T.Leaf 30, T.Leaf 31)),
- T.Node (T.Leaf 40, T.Leaf 41)),
- T.Node (T.Leaf 50, T.Leaf 51))))
- *)
-
-LS.run (LS.distribute (fun i -> if i = -1 then S.get else if i < 0 then S.(puts succ >> unit 0) else S.unit i) [10;-1;-2;-1;20]) 0;;
-(*
-- : 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
-
-let example n : (int * int) =
- Continuation_monad.(let u = callcc (fun k ->
- (if n < 0 then k 0 else unit [n + 100])
- (* all of the following is skipped by k 0; the end type int is k's input type *)
- >>= fun [x] -> unit (x + 1)
- )
- (* k 0 starts again here, outside the callcc (...); the end type int * int is k's output type *)
- >>= fun x -> unit (x, 0)
- in run0 u)
-
-
-(* (+ 1000 (prompt (+ 100 (shift k (+ 10 1))))) ~~> 1011 *)
-let example1 () : int =
- Continuation_monad.(let v = reset (
- let u = shift (fun k -> unit (10 + 1))
- in u >>= fun x -> unit (100 + x)
- ) in let w = v >>= fun x -> unit (1000 + x)
- in run0 w)
-
-(* (+ 1000 (prompt (+ 100 (shift k (k (+ 10 1)))))) ~~> 1111 *)
-let example2 () =
- Continuation_monad.(let v = reset (
- let u = shift (fun k -> k (10 :: [1]))
- in u >>= fun x -> unit (100 :: x)
- ) in let w = v >>= fun x -> unit (1000 :: x)
- in run0 w)
-
-(* (+ 1000 (prompt (+ 100 (shift k (+ 10 (k 1)))))) ~~> 1111 but added differently *)
-let example3 () =
- Continuation_monad.(let v = reset (
- let u = shift (fun k -> k [1] >>= fun x -> unit (10 :: x))
- in u >>= fun x -> unit (100 :: x)
- ) in let w = v >>= fun x -> unit (1000 :: x)
- in run0 w)
-
-(* (+ 100 ((prompt (+ 10 (shift k k))) 1)) ~~> 111 *)
-(* not sure if this example can be typed without a sum-type *)
-
-(* (+ 100 (prompt (+ 10 (shift k (k (k 1)))))) ~~> 121 *)
-let example5 () : int =
- Continuation_monad.(let v = reset (
- 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));;
-(example ~+10, example ~-10);;
-
-let testc df ic =
- C.run_exn TC.(run (distribute df t1)) ic;;
-
-
-(*
-(* do nothing *)
-let initial_continuation = fun t -> t in
-TreeCont.monadize t1 Continuation_monad.unit initial_continuation;;
-*)
-testc (C.unit) id;;
-
-(*
-(* count leaves, using continuation *)
-let initial_continuation = fun t -> 0 in
-TreeCont.monadize t1 (fun a k -> 1 + k a) initial_continuation;;
-*)
-
-testc C.(fun a -> shift (fun k -> k a >>= fun v -> unit (1 + v))) (fun t -> 0);;
-
-(*
-(* convert tree to list of leaves *)
-let initial_continuation = fun t -> [] in
-TreeCont.monadize t1 (fun a k -> a :: k a) initial_continuation;;
-*)
-
-testc C.(fun a -> shift (fun k -> k a >>= fun v -> unit (a::v))) (fun t -> ([] : int list));;
-
-(*
-(* square each leaf using continuation *)
-let initial_continuation = fun t -> t in
-TreeCont.monadize t1 (fun a k -> k (a*a)) initial_continuation;;
-*)
-
-testc C.(fun a -> shift (fun k -> k (a*a))) (fun t -> t);;
-
-
-(*
-(* replace leaves with list, using continuation *)
-let initial_continuation = fun t -> t in
-TreeCont.monadize t1 (fun a k -> k [a; a*a]) initial_continuation;;
-*)
-
-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)))) );;
-
+end;;
-(0, 15 = C.(run0 (let f k = k 10 >>= fun v-> unit (v+100) in reset (callcc f >>= fun v -> unit (v+5)))) );;