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1 (* Title: ZF/ex/Term.thy |
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2 ID: $Id$ |
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3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 Copyright 1994 University of Cambridge |
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5 |
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6 Terms over an alphabet. |
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7 Illustrates the list functor (essentially the same type as in Trees & Forests) |
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8 *) |
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9 |
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10 Term = List + |
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11 consts |
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12 term_rec :: "[i, [i,i,i]=>i] => i" |
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13 term_map :: "[i=>i, i] => i" |
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14 term_size :: "i=>i" |
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15 reflect :: "i=>i" |
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16 preorder :: "i=>i" |
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17 |
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18 term :: "i=>i" |
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19 |
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20 datatype |
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21 "term(A)" = Apply ("a: A", "l: list(term(A))") |
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22 monos "[list_mono]" |
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23 type_intrs "[list_univ RS subsetD]" |
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24 |
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25 rules |
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26 term_rec_def |
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27 "term_rec(t,d) == \ |
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28 \ Vrec(t, %t g. term_case(%x zs. d(x, zs, map(%z.g`z, zs)), t))" |
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29 |
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30 term_map_def "term_map(f,t) == term_rec(t, %x zs rs. Apply(f(x), rs))" |
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31 |
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32 term_size_def "term_size(t) == term_rec(t, %x zs rs. succ(list_add(rs)))" |
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33 |
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34 reflect_def "reflect(t) == term_rec(t, %x zs rs. Apply(x, rev(rs)))" |
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35 |
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36 preorder_def "preorder(t) == term_rec(t, %x zs rs. Cons(x, flat(rs)))" |
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37 |
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38 end |