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(* Title: Pure/General/basics.ML
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
val merge_options: 'a option * 'a option -> 'a option
val eq_option: ('a * 'b -> bool) -> 'a option * 'b option -> bool
(*partiality*)
val try: ('a -> 'b) -> 'a -> 'b option
val can: ('a -> 'b) -> 'a -> bool
(*lists*)
val cons: 'a -> 'a list -> '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
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.Option;
fun these (SOME x) = x
| these NONE = [];
fun the_list (SOME x) = [x]
| the_list NONE = []
fun the_default x (SOME y) = y
| the_default x NONE = x;
fun perhaps f x = the_default x (f x);
fun merge_options (x, y) = if is_some x then x else y;
fun eq_option eq (SOME x, SOME y) = eq (x, y)
| eq_option _ (NONE, NONE) = true
| eq_option _ _ = false;
(* partiality *)
fun try f x = SOME (f x)
handle exn => if Exn.is_interrupt exn then Exn.reraise exn else NONE;
fun can f x = is_some (try f x);
(* lists *)
fun cons x xs = x :: xs;
fun append xs ys = xs @ ys;
fun fold _ [] y = y
| fold f (x :: xs) y = fold f xs (f x y);
fun fold_rev _ [] y = y
| fold_rev f (x :: xs) y = f x (fold_rev f xs y);
fun fold_map _ [] y = ([], y)
| fold_map f (x :: xs) y =
let
val (x', y') = f x y;
val (xs', y'') = fold_map f xs y';
in (x' :: xs', y'') end;
end;
open Basics;
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