53 lines
1.4 KiB
Plaintext
53 lines
1.4 KiB
Plaintext
(* Author: Tobias Nipkow
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Copyright 1998 TUM
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*)
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section "Automata based scanner"
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theory AutoMaxChop
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imports DA MaxChop
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begin
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primrec auto_split :: "('a,'s)da => 's => 'a list * 'a list => 'a list => 'a splitter" where
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"auto_split A q res ps [] = (if fin A q then (ps,[]) else res)" |
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"auto_split A q res ps (x#xs) =
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auto_split A (next A x q) (if fin A q then (ps,x#xs) else res) (ps@[x]) xs"
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definition
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auto_chop :: "('a,'s)da => 'a chopper" where
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"auto_chop A = chop (%xs. auto_split A (start A) ([],xs) [] xs)"
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lemma delta_snoc: "delta A (xs@[y]) q = next A y (delta A xs q)"
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by simp
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lemma auto_split_lemma:
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"!!q ps res. auto_split A (delta A ps q) res ps xs =
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maxsplit (%ys. fin A (delta A ys q)) res ps xs"
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apply (induct xs)
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apply simp
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apply (simp add: delta_snoc[symmetric] del: delta_append)
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done
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lemma auto_split_is_maxsplit:
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"auto_split A (start A) res [] xs = maxsplit (accepts A) res [] xs"
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apply (unfold accepts_def)
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apply (subst delta_Nil[where ?s = "start A", symmetric])
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apply (subst auto_split_lemma)
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apply simp
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done
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lemma is_maxsplitter_auto_split:
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"is_maxsplitter (accepts A) (%xs. auto_split A (start A) ([],xs) [] xs)"
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by (simp add: auto_split_is_maxsplit is_maxsplitter_maxsplit)
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lemma is_maxchopper_auto_chop:
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"is_maxchopper (accepts A) (auto_chop A)"
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apply (unfold auto_chop_def)
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apply (rule is_maxchopper_chop)
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apply (rule is_maxsplitter_auto_split)
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done
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end
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