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(* Title: ZF/ex/bt-fn.thy
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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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Binary trees
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*)
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935
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BT = Datatype +
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consts
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bt_rec :: "[i, i, [i,i,i,i,i]=>i] => i"
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n_nodes :: "i=>i"
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n_leaves :: "i=>i"
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bt_reflect :: "i=>i"
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bt :: "i=>i"
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datatype
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"bt(A)" = Lf | Br ("a: A", "t1: bt(A)", "t2: bt(A)")
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defs
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bt_rec_def
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"bt_rec(t,c,h) == Vrec(t, %t g.bt_case(c, %x y z. h(x,y,z,g`y,g`z), t))"
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n_nodes_def "n_nodes(t) == bt_rec(t, 0, %x y z r s. succ(r#+s))"
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n_leaves_def "n_leaves(t) == bt_rec(t, succ(0), %x y z r s. r#+s)"
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bt_reflect_def "bt_reflect(t) == bt_rec(t, Lf, %x y z r s. Br(x,s,r))"
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end
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