X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=code%2Fmonads.ml;h=3fba1f3216414caa0419bc04527f7bb6b2f64cbb;hp=34ad1cef5771d3ea8caf3c1dc7d1f27bfdc8756a;hb=a1a38a5cfaede25b7e6299cac3275e1ccfd9b2db;hpb=ef6e90fdda821a1d071c93dc50587d1a0fd207b9

diff --git a/code/monads.ml b/code/monads.ml
index 34ad1cef..3fba1f32 100644
--- a/code/monads.ml
+++ b/code/monads.ml
@@ -42,6 +42,17 @@
  * have to use operations like `run` to convert the abstract monadic types
  * to types whose internals you have free access to.
  *
+ * Acknowledgements: This is largely based on the mtl library distributed
+ * 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/>
+ * - Ken Shan "Monads for natural language semantics" <http://arxiv.org/abs/cs/0205026v1>
+ * - 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 this is partly
+ * derived from)
  *)
 
 exception Undefined
@@ -63,7 +74,7 @@ module Util = struct
     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
 
@@ -140,6 +151,10 @@ module Monad = struct
     let run_exn u =
       if u == Util.undef then raise Undefined else B.run_exn u
     let (>>=) = bind
+    (* expressions after >> will be evaluated before they're passed to
+     * bind, so you can't do `zero () >> assert false`
+     * this works though: `zero () >>= fun _ -> assert false`
+     *)
     let (>>) u v = u >>= fun _ -> v
     let lift f u = u >>= fun a -> unit (f a)
     (* lift is called listM, fmap, and <$> in Haskell *)
@@ -155,10 +170,21 @@ module Monad = struct
     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
-    (* not in tail position, will Stack overflow *)
+    (* A Haskell-like version works:
+         let rec forever uthunk = uthunk () >>= fun _ -> forever uthunk
+     * but the recursive call is not in tail position so this can stack overflow. *)
     let forever uthunk =
-        let rec loop () = uthunk () >>= fun _ -> loop ()
-        in loop ()
+        let z = zero () in
+        let id result = result in
+        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 [])
@@ -432,18 +458,10 @@ end = struct
       | Success a -> a
       | Error e -> raise (Err.Exc e)
     let zero () = Util.undef
-    let plus u v = u
-    (*
-    let zero () = Error Err.zero
-    let plus u v = match (u, v) with
-      | Success _, _ -> u
-      (* to satisfy (Catch) laws, plus u zero = u, even if u = Error _
-       * otherwise, plus (Error _) v = v *)
-      | Error _, _ when v = zero -> u
-      (* combine errors *)
-      | Error e1, Error e2 when u <> zero -> Error (Err.plus e1 e2)
-      | Error _, _ -> v
-    *)
+    (* satisfies Catch *)
+    let plus u v = match u with
+      | Success _ -> u
+      | Error _ -> if v == Util.undef then u else v
   end
   include Monad.Make(Base)
   (* include (Monad.MakeCatch(Base) : Monad.PLUS with type 'a m := 'a m) *)
@@ -472,7 +490,7 @@ end = struct
           | Error e -> raise (Err.Exc e))
         in Wrapped.run_exn w
       let plus u v = Wrapped.plus u v
-      let zero () = elevate (Wrapped.zero ())
+      let zero () = Wrapped.zero () (* elevate (Wrapped.zero ()) *)
     end)
     let throw e = Wrapped.unit (Error e)
     let catch u handler = Wrapped.bind u (fun t -> match t with
@@ -491,26 +509,6 @@ module Failure = Error_monad(struct
   *)
 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
@@ -557,15 +555,15 @@ end = struct
       type ('x,'a) result = env -> ('x,'a) Wrapped.result
       type ('x,'a) result_exn = env -> ('x,'a) Wrapped.result_exn
       let elevate w = fun e -> w
-      let bind u f = fun e -> Wrapped.bind (u e) (fun v -> f v e)
+      let bind u f = fun e -> Wrapped.bind (u e) (fun a -> f a e)
       let run u = fun e -> Wrapped.run (u e)
       let run_exn u = fun e -> Wrapped.run_exn (u e)
       (* satisfies Distrib *)
-      let plus u v = fun s -> Wrapped.plus (u s) (v s)
-      let zero () = elevate (Wrapped.zero ())
+      let plus u v = fun e -> Wrapped.plus (u e) (v e)
+      let zero () = fun e -> Wrapped.zero () (* elevate (Wrapped.zero ()) *)
     end
     include Monad.MakeT(BaseT)
-    let ask = fun e -> Wrapped.unit e
+    let ask = Wrapped.unit
     let local modifier u = fun e -> u (modifier e)
     let asks selector = ask >>= (fun e ->
       try unit (selector e)
@@ -630,7 +628,7 @@ end = struct
         in Wrapped.run_exn w
       (* satisfies Distrib *)
       let plus u v = fun s -> Wrapped.plus (u s) (v s)
-      let zero () = elevate (Wrapped.zero ())
+      let zero () = fun s -> Wrapped.zero () (* elevate (Wrapped.zero ()) *)
     end
     include Monad.MakeT(BaseT)
     let get = fun s -> Wrapped.unit (s, s)
@@ -642,6 +640,7 @@ end = struct
   end
 end
 
+
 (* State monad with different interface (structured store) *)
 module Ref_monad(V : sig
   type value
@@ -709,7 +708,7 @@ end = struct
         in Wrapped.run_exn w
       (* satisfies Distrib *)
       let plus u v = fun s -> Wrapped.plus (u s) (v s)
-      let zero () = elevate (Wrapped.zero ())
+      let zero () = fun s -> Wrapped.zero () (* elevate (Wrapped.zero ()) *)
     end
     include Monad.MakeT(BaseT)
     let newref value = fun s -> Wrapped.unit (alloc value s)
@@ -718,7 +717,7 @@ end = struct
   end
 end
 
-(* TODO needs a T *)
+
 (* must be parameterized on (struct type log = ... end) *)
 module Writer_monad(Log : sig
   type log
@@ -735,6 +734,17 @@ end) : sig
   val listens : (log -> 'b) -> ('x,'a) m -> ('x,'a * 'b) m
   (* val pass : ('x,'a * (log -> log)) m -> ('x,'a) m *)
   val censor : (log -> log) -> ('x,'a) m -> ('x,'a) m
+  (* WriterT transformer *)
+  module T : functor (Wrapped : Monad.S) -> sig
+    type ('x,'a) result = ('x,'a * log) Wrapped.result
+    type ('x,'a) result_exn = ('x,'a * log) Wrapped.result_exn
+    include Monad.S 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 tell : log -> ('x,unit) m
+    val listen : ('x,'a) m -> ('x,'a * log) m
+    val listens : (log -> 'b) -> ('x,'a) m -> ('x,'a * 'b) m
+    val censor : (log -> log) -> ('x,'a) m -> ('x,'a) m
+  end
 end = struct
   type log = Log.log
   module Base = struct
@@ -742,7 +752,7 @@ end = struct
     type ('x,'a) result = 'a * log
     type ('x,'a) result_exn = 'a * log
     let unit a = (a, Log.zero)
-    let bind (a, w) f = let (a', w') = f a in (a', Log.plus w w')
+    let bind (a, w) f = let (b, w') = f a in (b, Log.plus w w')
     let run u = u
     let run_exn = run
     let zero () = Util.undef
@@ -754,6 +764,31 @@ end = struct
   let listens selector u = listen u >>= fun (a, w) -> unit (a, selector w) (* filter listen through selector *)
   let pass ((a, f), w) = (a, f w) (* usually use censor helper *)
   let censor f u = pass (u >>= fun a -> unit (a, f))
+  module T(Wrapped : Monad.S) = struct
+    module BaseT = struct
+      module Wrapped = Wrapped
+      type ('x,'a) m = ('x,'a * log) Wrapped.m
+      type ('x,'a) result = ('x,'a * log) Wrapped.result
+      type ('x,'a) result_exn = ('x,'a * log) Wrapped.result_exn
+      let elevate w =
+        Wrapped.bind w (fun a -> Wrapped.unit (a, Log.zero))
+      let bind u f =
+        Wrapped.bind u (fun (a, w) ->
+        Wrapped.bind (f a) (fun (b, w') ->
+        Wrapped.unit (b, Log.plus w w')))
+      let zero () = elevate (Wrapped.zero ())
+      let plus u v = Wrapped.plus u v
+      let run u = Wrapped.run u
+      let run_exn u = Wrapped.run_exn u
+    end
+    include Monad.MakeT(BaseT)
+    let tell entries = Wrapped.unit ((), entries)
+    let listen u = Wrapped.bind u (fun (a, w) -> Wrapped.unit ((a, w), w))
+    let pass u = Wrapped.bind u (fun ((a, f), w) -> Wrapped.unit (a, f w))
+    (* rest are derived in same way as before *)
+    let listens selector u = listen u >>= fun (a, w) -> unit (a, selector w)
+    let censor f u = pass (u >>= fun a -> unit (a, f))
+  end
 end
 
 (* pre-define simple Writer *)
@@ -812,7 +847,6 @@ end = struct
 end
 
 
-(* TODO needs a T *)
 module Continuation_monad : sig
   (* expose only the implementation of type `('r,'a) result` *)
   type ('r,'a) m
@@ -825,6 +859,16 @@ module Continuation_monad : sig
   (* val abort : ('a,'a) m -> ('a,'b) m *)
   val abort : 'a -> ('a,'b) m
   val run0 : ('a,'a) m -> 'a
+  (* ContinuationT transformer *)
+  module T : functor (Wrapped : Monad.S) -> sig
+    type ('r,'a) m
+    type ('r,'a) result = ('a -> ('r,'r) Wrapped.m) -> ('r,'r) Wrapped.result
+    type ('r,'a) result_exn = ('a -> ('r,'r) Wrapped.m) -> ('r,'r) Wrapped.result_exn
+    include Monad.S with type ('r,'a) result := ('r,'a) result and type ('r,'a) result_exn := ('r,'a) result_exn and type ('r,'a) m := ('r,'a) m
+    val elevate : ('x,'a) Wrapped.m -> ('x,'a) m
+    val callcc : (('a -> ('r,'b) m) -> ('r,'a) m) -> ('r,'a) m
+    (* TODO: reset,shift,abort,run0 *)
+  end
 end = struct
   let id = fun i -> i
   module Base = struct
@@ -863,6 +907,24 @@ end = struct
   (* let abort a = shift (fun _ -> a) *)
   let abort a = shift (fun _ -> unit a)
   let run0 (u : ('a,'a) m) = (u) id
+  module T(Wrapped : Monad.S) = struct
+    module BaseT = struct
+      module Wrapped = Wrapped
+      type ('r,'a) m = ('a -> ('r,'r) Wrapped.m) -> ('r,'r) Wrapped.m
+      type ('r,'a) result = ('a -> ('r,'r) Wrapped.m) -> ('r,'r) Wrapped.result
+      type ('r,'a) result_exn = ('a -> ('r,'r) Wrapped.m) -> ('r,'r) Wrapped.result_exn
+      let elevate w = fun k -> Wrapped.bind w k
+      let bind u f = fun k -> u (fun a -> f a k)
+      let run u k = Wrapped.run (u k)
+      let run_exn u k = Wrapped.run_exn (u k)
+      let zero () = Util.undef
+      let plus u v = u
+    end
+    include Monad.MakeT(BaseT)
+    let callcc f = (fun k ->
+      let usek a = (fun _ -> k a)
+      in (f usek) k)
+  end
 end
 
 
@@ -887,53 +949,17 @@ end
  *   >>= 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
@@ -1001,211 +1027,6 @@ end = struct
     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)))) );;