21394
|
1 |
(* Title: Pure/General/basics.ML
|
|
2 |
ID: $Id$
|
|
3 |
Author: Florian Haftmann and Makarius, TU Muenchen
|
|
4 |
|
|
5 |
Fundamental concepts.
|
|
6 |
*)
|
|
7 |
|
|
8 |
infix 1 |> |-> |>> ||> ||>>
|
|
9 |
infix 1 #> #-> #>> ##> ##>>
|
|
10 |
|
|
11 |
signature BASICS =
|
|
12 |
sig
|
|
13 |
(*functions*)
|
|
14 |
val |> : 'a * ('a -> 'b) -> 'b
|
|
15 |
val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
|
|
16 |
val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
|
|
17 |
val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
|
|
18 |
val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
|
|
19 |
val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
|
|
20 |
val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
|
|
21 |
val #>> : ('a -> 'c * 'b) * ('c -> 'd) -> 'a -> 'd * 'b
|
|
22 |
val ##> : ('a -> 'c * 'b) * ('b -> 'd) -> 'a -> 'c * 'd
|
|
23 |
val ##>> : ('a -> 'c * 'b) * ('b -> 'e * 'd) -> 'a -> ('c * 'e) * 'd
|
|
24 |
val ` : ('b -> 'a) -> 'b -> 'a * 'b
|
|
25 |
val tap: ('b -> 'a) -> 'b -> 'b
|
|
26 |
|
|
27 |
(*options*)
|
|
28 |
val is_some: 'a option -> bool
|
|
29 |
val is_none: 'a option -> bool
|
|
30 |
val the: 'a option -> 'a
|
|
31 |
val these: 'a list option -> 'a list
|
|
32 |
val the_list: 'a option -> 'a list
|
|
33 |
val the_default: 'a -> 'a option -> 'a
|
|
34 |
val perhaps: ('a -> 'a option) -> 'a -> 'a
|
|
35 |
|
|
36 |
(*partiality*)
|
|
37 |
val try: ('a -> 'b) -> 'a -> 'b option
|
|
38 |
val can: ('a -> 'b) -> 'a -> bool
|
|
39 |
|
|
40 |
(*lists*)
|
|
41 |
val cons: 'a -> 'a list -> 'a list
|
|
42 |
val dest: 'a list -> 'a * 'a list
|
|
43 |
val append: 'a list -> 'a list -> 'a list
|
|
44 |
val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
|
|
45 |
val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
|
|
46 |
val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
|
|
47 |
val unfold: int -> ('b -> 'a * 'b) -> 'b -> 'a list * 'b
|
|
48 |
val unfold_rev: int -> ('b -> 'a * 'b) -> 'b -> 'a list * 'b
|
|
49 |
end;
|
|
50 |
|
|
51 |
structure Basics: BASICS =
|
|
52 |
struct
|
|
53 |
|
|
54 |
(* functions *)
|
|
55 |
|
|
56 |
(*application and structured results*)
|
|
57 |
fun x |> f = f x;
|
|
58 |
fun (x, y) |-> f = f x y;
|
|
59 |
fun (x, y) |>> f = (f x, y);
|
|
60 |
fun (x, y) ||> f = (x, f y);
|
|
61 |
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
|
|
62 |
|
|
63 |
(*composition and structured results*)
|
|
64 |
fun (f #> g) x = x |> f |> g;
|
|
65 |
fun (f #-> g) x = x |> f |-> g;
|
|
66 |
fun (f #>> g) x = x |> f |>> g;
|
|
67 |
fun (f ##> g) x = x |> f ||> g;
|
|
68 |
fun (f ##>> g) x = x |> f ||>> g;
|
|
69 |
|
|
70 |
(*result views*)
|
|
71 |
fun `f = fn x => (f x, x);
|
|
72 |
fun tap f = fn x => (f x; x);
|
|
73 |
|
|
74 |
|
|
75 |
(* options *)
|
|
76 |
|
|
77 |
fun is_some (SOME _) = true
|
|
78 |
| is_some NONE = false;
|
|
79 |
|
|
80 |
fun is_none (SOME _) = false
|
|
81 |
| is_none NONE = true;
|
|
82 |
|
|
83 |
fun the (SOME x) = x
|
|
84 |
| the NONE = raise Option;
|
|
85 |
|
|
86 |
fun these (SOME x) = x
|
|
87 |
| these _ = [];
|
|
88 |
|
|
89 |
fun the_list (SOME x) = [x]
|
|
90 |
| the_list _ = []
|
|
91 |
|
|
92 |
fun the_default x (SOME y) = y
|
|
93 |
| the_default x _ = x;
|
|
94 |
|
|
95 |
fun perhaps f x = the_default x (f x);
|
|
96 |
|
|
97 |
|
|
98 |
(* partiality *)
|
|
99 |
|
|
100 |
exception Interrupt = Interrupt; (*signals intruding execution :-[*)
|
|
101 |
|
|
102 |
fun try f x = SOME (f x)
|
|
103 |
handle Interrupt => raise Interrupt | _ => NONE;
|
|
104 |
|
|
105 |
fun can f x = is_some (try f x);
|
|
106 |
|
|
107 |
|
|
108 |
(* lists *)
|
|
109 |
|
|
110 |
fun cons x xs = x :: xs;
|
|
111 |
|
|
112 |
fun dest (x :: xs) = (x, xs)
|
|
113 |
| dest [] = raise Empty;
|
|
114 |
|
|
115 |
fun append xs ys = xs @ ys;
|
|
116 |
|
|
117 |
|
|
118 |
(* fold *)
|
|
119 |
|
|
120 |
fun fold f =
|
|
121 |
let
|
|
122 |
fun fld [] y = y
|
|
123 |
| fld (x :: xs) y = fld xs (f x y);
|
|
124 |
in fld end;
|
|
125 |
|
|
126 |
fun fold_rev f =
|
|
127 |
let
|
|
128 |
fun fld [] y = y
|
|
129 |
| fld (x :: xs) y = f x (fld xs y);
|
|
130 |
in fld end;
|
|
131 |
|
|
132 |
fun fold_map f =
|
|
133 |
let
|
|
134 |
fun fld [] y = ([], y)
|
|
135 |
| fld (x :: xs) y =
|
|
136 |
let
|
|
137 |
val (x', y') = f x y;
|
|
138 |
val (xs', y'') = fld xs y';
|
|
139 |
in (x' :: xs', y'') end;
|
|
140 |
in fld end;
|
|
141 |
|
|
142 |
|
|
143 |
(* unfold -- with optional limit *)
|
|
144 |
|
|
145 |
fun unfold lim f =
|
|
146 |
let
|
|
147 |
fun unfld 0 ys x = (ys, x)
|
|
148 |
| unfld n ys x =
|
|
149 |
(case try f x of
|
|
150 |
NONE => (ys, x)
|
|
151 |
| SOME (y, x') => unfld (n - 1) (y :: ys) x');
|
|
152 |
in unfld lim [] end;
|
|
153 |
|
|
154 |
fun unfold_rev lim f =
|
|
155 |
let
|
|
156 |
fun unfld 0 x = ([], x)
|
|
157 |
| unfld n x =
|
|
158 |
(case try f x of
|
|
159 |
NONE => ([], x)
|
|
160 |
| SOME (y, x') => unfld (n - 1) x' |>> cons y);
|
|
161 |
in unfld lim end;
|
|
162 |
|
|
163 |
end;
|
|
164 |
|
|
165 |
open Basics;
|