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(* Title: HOL/Sexp
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1992 University of Cambridge
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S-expressions, general binary trees for defining recursive data structures
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*)
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Sexp = Univ +
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consts
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sexp :: "'a item set"
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sexp_case :: "['a=>'b, nat=>'b, ['a item, 'a item]=>'b, \
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\ 'a item] => 'b"
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sexp_rec :: "['a item, 'a=>'b, nat=>'b, \
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\ ['a item, 'a item, 'b, 'b]=>'b] => 'b"
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pred_sexp :: "('a item * 'a item)set"
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inductive "sexp"
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intrs
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LeafI "Leaf(a): sexp"
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NumbI "Numb(a): sexp"
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SconsI "[| M: sexp; N: sexp |] ==> M$N : sexp"
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defs
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sexp_case_def
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"sexp_case c d e M == @ z. (? x. M=Leaf(x) & z=c(x)) \
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\ | (? k. M=Numb(k) & z=d(k)) \
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\ | (? N1 N2. M = N1 $ N2 & z=e N1 N2)"
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pred_sexp_def
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"pred_sexp == UN M: sexp. UN N: sexp. {<M, M$N>, <N, M$N>}"
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sexp_rec_def
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"sexp_rec M c d e == wfrec pred_sexp M \
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\ (%M g. sexp_case c d (%N1 N2. e N1 N2 (g N1) (g N2)) M)"
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end
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