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(* Title: HOL/ex/Term
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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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Terms over a given alphabet -- function applications; illustrates list functor
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(essentially the same type as in Trees & Forests)
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There is no constructor APP because it is simply cons ($)
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*)
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Term = SList +
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types 'a term
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arities term :: (term)term
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consts
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term :: "'a item set => 'a item set"
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Rep_term :: "'a term => 'a item"
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Abs_term :: "'a item => 'a term"
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Rep_Tlist :: "'a term list => 'a item"
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Abs_Tlist :: "'a item => 'a term list"
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App :: "['a, ('a term)list] => 'a term"
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Term_rec :: "['a item, ['a item , 'a item, 'b list]=>'b] => 'b"
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term_rec :: "['a term, ['a ,'a term list, 'b list]=>'b] => 'b"
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inductive "term(A)"
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intrs
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APP_I "[| M: A; N : list(term(A)) |] ==> M$N : term(A)"
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monos "[list_mono]"
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defs
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(*defining abstraction/representation functions for term list...*)
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Rep_Tlist_def "Rep_Tlist == Rep_map(Rep_term)"
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Abs_Tlist_def "Abs_Tlist == Abs_map(Abs_term)"
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(*defining the abstract constants*)
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App_def "App a ts == Abs_term(Leaf(a) $ Rep_Tlist(ts))"
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(*list recursion*)
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Term_rec_def
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"Term_rec M d == wfrec (trancl pred_sexp) M \
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\ (Split(%x y g. d x y (Abs_map g y)))"
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term_rec_def
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"term_rec t d == \
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\ Term_rec (Rep_term t) (%x y r. d (Inv Leaf x) (Abs_Tlist(y)) r)"
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rules
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(*faking a type definition for term...*)
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Rep_term "Rep_term(n): term(range(Leaf))"
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Rep_term_inverse "Abs_term(Rep_term(t)) = t"
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Abs_term_inverse "M: term(range(Leaf)) ==> Rep_term(Abs_term(M)) = M"
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end
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