1 (* Title: ZF/ex/TF.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 1993 University of Cambridge |
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5 |
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6 Trees & forests, a mutually recursive type definition. |
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7 *) |
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8 |
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9 TF_Fn = TF + ListFn + |
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10 consts |
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11 TF_rec :: "[i, [i,i,i]=>i, i, [i,i,i,i]=>i] => i" |
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12 TF_map :: "[i=>i, i] => i" |
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13 TF_size :: "i=>i" |
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14 TF_preorder :: "i=>i" |
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15 list_of_TF :: "i=>i" |
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16 TF_of_list :: "i=>i" |
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17 |
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18 rules |
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19 TF_rec_def |
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20 "TF_rec(z,b,c,d) == Vrec(z, \ |
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21 \ %z r. tree_forest_case(%x f. b(x, f, r`f), \ |
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22 \ c, \ |
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23 \ %t f. d(t, f, r`t, r`f), z))" |
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24 |
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25 list_of_TF_def |
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26 "list_of_TF(z) == TF_rec(z, %x f r. [Tcons(x,f)], [], \ |
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27 \ %t f r1 r2. Cons(t, r2))" |
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28 |
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29 TF_of_list_def |
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30 "TF_of_list(f) == list_rec(f, Fnil, %t f r. Fcons(t,r))" |
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31 |
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32 TF_map_def |
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33 "TF_map(h,z) == TF_rec(z, %x f r.Tcons(h(x),r), Fnil, \ |
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34 \ %t f r1 r2. Fcons(r1,r2))" |
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35 |
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36 TF_size_def |
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37 "TF_size(z) == TF_rec(z, %x f r.succ(r), 0, %t f r1 r2. r1#+r2)" |
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38 |
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39 TF_preorder_def |
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40 "TF_preorder(z) == TF_rec(z, %x f r.Cons(x,r), Nil, %t f r1 r2. r1@r2)" |
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41 |
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42 end |
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