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(* Title: ZF/ex/TF.thy
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1994 University of Cambridge
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Trees & forests, a mutually recursive type definition.
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*)
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TF = List +
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consts
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TF_rec :: "[i, [i,i,i]=>i, i, [i,i,i,i]=>i] => i"
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TF_map :: "[i=>i, i] => i"
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TF_size :: "i=>i"
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TF_preorder :: "i=>i"
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list_of_TF :: "i=>i"
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TF_of_list :: "i=>i"
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tree, forest, tree_forest :: "i=>i"
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datatype
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"tree(A)" = Tcons ("a: A", "f: forest(A)")
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and
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"forest(A)" = Fnil | Fcons ("t: tree(A)", "f: forest(A)")
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defs
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TF_rec_def
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"TF_rec(z,b,c,d) == Vrec(z, \
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\ %z r. tree_forest_case(%x f. b(x, f, r`f), \
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\ c, \
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\ %t f. d(t, f, r`t, r`f), z))"
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list_of_TF_def
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"list_of_TF(z) == TF_rec(z, %x f r. [Tcons(x,f)], [], \
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\ %t f r1 r2. Cons(t, r2))"
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TF_of_list_def
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"TF_of_list(f) == list_rec(f, Fnil, %t f r. Fcons(t,r))"
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TF_map_def
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"TF_map(h,z) == TF_rec(z, %x f r.Tcons(h(x),r), Fnil, \
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\ %t f r1 r2. Fcons(r1,r2))"
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TF_size_def
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"TF_size(z) == TF_rec(z, %x f r.succ(r), 0, %t f r1 r2. r1#+r2)"
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TF_preorder_def
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"TF_preorder(z) == TF_rec(z, %x f r.Cons(x,r), Nil, %t f r1 r2. r1@r2)"
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end
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