Fundamental concepts.

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/basics.ML	Thu Nov 16 01:07:23 2006 +0100
@@ -0,0 +1,165 @@
+(*  Title:      Pure/General/basics.ML
+    ID:         $Id$
+    Author:     Florian Haftmann and Makarius, TU Muenchen
+
+Fundamental concepts.
+*)
+
+infix 1 |> |-> |>> ||> ||>>
+infix 1 #> #-> #>> ##> ##>>
+
+signature BASICS =
+sig
+  (*functions*)
+  val |> : 'a * ('a -> 'b) -> 'b
+  val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
+  val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
+  val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
+  val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
+  val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
+  val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
+  val #>> : ('a -> 'c * 'b) * ('c -> 'd) -> 'a -> 'd * 'b
+  val ##> : ('a -> 'c * 'b) * ('b -> 'd) -> 'a -> 'c * 'd
+  val ##>> : ('a -> 'c * 'b) * ('b -> 'e * 'd) -> 'a -> ('c * 'e) * 'd
+  val ` : ('b -> 'a) -> 'b -> 'a * 'b
+  val tap: ('b -> 'a) -> 'b -> 'b
+
+  (*options*)
+  val is_some: 'a option -> bool
+  val is_none: 'a option -> bool
+  val the: 'a option -> 'a
+  val these: 'a list option -> 'a list
+  val the_list: 'a option -> 'a list
+  val the_default: 'a -> 'a option -> 'a
+  val perhaps: ('a -> 'a option) -> 'a -> 'a
+
+  (*partiality*)
+  val try: ('a -> 'b) -> 'a -> 'b option
+  val can: ('a -> 'b) -> 'a -> bool
+
+  (*lists*)
+  val cons: 'a -> 'a list -> 'a list
+  val dest: 'a list -> 'a * 'a list
+  val append: 'a list -> 'a list -> 'a list
+  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
+  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
+  val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
+  val unfold: int -> ('b -> 'a * 'b) -> 'b -> 'a list * 'b
+  val unfold_rev: int -> ('b -> 'a * 'b) -> 'b -> 'a list * 'b
+end;
+
+structure Basics: BASICS =
+struct
+
+(* functions *)
+
+(*application and structured results*)
+fun x |> f = f x;
+fun (x, y) |-> f = f x y;
+fun (x, y) |>> f = (f x, y);
+fun (x, y) ||> f = (x, f y);
+fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
+
+(*composition and structured results*)
+fun (f #> g) x   = x |> f |> g;
+fun (f #-> g) x  = x |> f |-> g;
+fun (f #>> g) x  = x |> f |>> g;
+fun (f ##> g) x  = x |> f ||> g;
+fun (f ##>> g) x = x |> f ||>> g;
+
+(*result views*)
+fun `f = fn x => (f x, x);
+fun tap f = fn x => (f x; x);
+
+
+(* options *)
+
+fun is_some (SOME _) = true
+  | is_some NONE = false;
+
+fun is_none (SOME _) = false
+  | is_none NONE = true;
+
+fun the (SOME x) = x
+  | the NONE = raise Option;
+
+fun these (SOME x) = x
+  | these _ = [];
+
+fun the_list (SOME x) = [x]
+  | the_list _ = []
+
+fun the_default x (SOME y) = y
+  | the_default x _ = x;
+
+fun perhaps f x = the_default x (f x);
+
+
+(* partiality *)
+
+exception Interrupt = Interrupt;   (*signals intruding execution :-[*)
+
+fun try f x = SOME (f x)
+  handle Interrupt => raise Interrupt | _ => NONE;
+
+fun can f x = is_some (try f x);
+
+
+(* lists *)
+
+fun cons x xs = x :: xs;
+
+fun dest (x :: xs) = (x, xs)
+  | dest [] = raise Empty;
+
+fun append xs ys = xs @ ys;
+
+
+(* fold *)
+
+fun fold f =
+  let
+    fun fld [] y = y
+      | fld (x :: xs) y = fld xs (f x y);
+  in fld end;
+
+fun fold_rev f =
+  let
+    fun fld [] y = y
+      | fld (x :: xs) y = f x (fld xs y);
+  in fld end;
+
+fun fold_map f =
+  let
+    fun fld [] y = ([], y)
+      | fld (x :: xs) y =
+          let
+            val (x', y') = f x y;
+            val (xs', y'') = fld xs y';
+          in (x' :: xs', y'') end;
+  in fld end;
+
+
+(* unfold -- with optional limit *)
+
+fun unfold lim f =
+  let
+    fun unfld 0 ys x = (ys, x)
+      | unfld n ys x =
+          (case try f x of
+            NONE => (ys, x)
+          | SOME (y, x') => unfld (n - 1) (y :: ys) x');
+  in unfld lim [] end;
+
+fun unfold_rev lim f =
+  let
+    fun unfld 0 x = ([], x)
+      | unfld n x =
+          (case try f x of
+            NONE => ([], x)
+          | SOME (y, x') => unfld (n - 1) x' |>> cons y);
+  in unfld lim end;
+
+end;
+
+open Basics;