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(* Title: HOL/Lex/NAe.thy
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ID: $Id$
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Author: Tobias Nipkow
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Copyright 1998 TUM
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Nondeterministic automata with epsilon transitions
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*)
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NAe = List + Option + NA +
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types ('a,'s)nae = ('a option,'s)na
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syntax eps :: "('a,'s)nae => ('s * 's)set"
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translations "eps A" == "step A None"
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consts steps :: "('a,'s)nae => 'a list => ('s * 's)set"
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primrec
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"steps A [] = (eps A)^*"
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"steps A (a#w) = steps A w O step A (Some a) O (eps A)^*"
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constdefs
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accepts :: ('a,'s)nae => 'a list => bool
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"accepts A w == ? q. (start A,q) : steps A w & fin A q"
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(* not really used:
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consts delta :: "('a,'s)nae => 'a list => 's => 's set"
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primrec
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"delta A [] s = (eps A)^* ^^ {s}"
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"delta A (a#w) s = lift(delta A w) (lift(next A (Some a)) ((eps A)^* ^^ {s}))"
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*)
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end
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