* 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 Glaskow 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).
*)
exception Undefined
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 *)
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:
+ let rec forever uthunk = uthunk () >>= fun _ -> forever uthunk
+ * is not in tail position and will stack overflow. *)
let forever uthunk =
- let rec loop () = uthunk () >>= fun _ -> loop ()
+ 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 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
| 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) *)
| 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
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)
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)
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)
end
end
-(* TODO needs a T *)
+
(* must be parameterized on (struct type log = ... end) *)
module Writer_monad(Log : sig
type log
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
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
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 *)
end
-(* TODO needs a T *)
module Continuation_monad : sig
(* expose only the implementation of type `('r,'a) result` *)
type ('r,'a) m
(* 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
(* 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