4832
|
1 |
(* Title: HOL/Lex/NAe.thy
|
|
2 |
ID: $Id$
|
|
3 |
Author: Tobias Nipkow
|
|
4 |
Copyright 1998 TUM
|
|
5 |
|
|
6 |
Nondeterministic automata with epsilon transitions
|
|
7 |
*)
|
|
8 |
|
|
9 |
NAe = List + Option + NA +
|
|
10 |
|
|
11 |
types ('a,'s)nae = ('a option,'s)na
|
|
12 |
|
|
13 |
constdefs
|
|
14 |
step :: "('a,'s)nae => 'a option => ('s * 's)set"
|
|
15 |
"step A a == {(p,q) . q : next A a p}"
|
|
16 |
|
|
17 |
syntax eps :: "('a,'s)nae => ('s * 's)set"
|
|
18 |
translations "eps A" == "step A None"
|
|
19 |
|
|
20 |
consts steps :: "('a,'s)nae => 'a list => ('s * 's)set"
|
|
21 |
primrec steps list
|
|
22 |
"steps A [] = (eps A)^*"
|
|
23 |
"steps A (a#w) = steps A w O step A (Some a) O (eps A)^*"
|
|
24 |
|
|
25 |
consts delta :: "('a,'s)nae => 'a list => 's => 's set"
|
|
26 |
primrec delta list
|
|
27 |
"delta A [] s = (eps A)^* ^^ {s}"
|
|
28 |
"delta A (a#w) s = lift(delta A w) (lift(next A (Some a)) ((eps A)^* ^^ {s}))"
|
|
29 |
|
|
30 |
constdefs
|
|
31 |
accepts :: ('a,'s)nae => 'a list => bool
|
|
32 |
"accepts A w == ? q. (start A,q) : steps A w & fin A q"
|
|
33 |
|
|
34 |
end
|