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1 (* Title: HOL/ex/Recdefs.ML |
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2 ID: $Id$ |
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3 Author: Konrad Slind and Lawrence C Paulson |
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4 Copyright 1997 University of Cambridge |
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5 |
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6 A few proofs to demonstrate the functions defined in Recdefs.thy |
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7 Lemma statements from Konrad Slind's Web site |
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8 *) |
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9 |
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10 (** The silly g function: example of nested recursion **) |
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11 |
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12 Addsimps g.simps; |
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13 |
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14 Goal "g x < Suc x"; |
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15 by (induct_thm_tac g.induct "x" 1); |
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16 by Auto_tac; |
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17 qed "g_terminates"; |
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18 |
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19 Goal "g x = 0"; |
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20 by (induct_thm_tac g.induct "x" 1); |
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21 by (ALLGOALS (asm_simp_tac (simpset() addsimps [g_terminates]))); |
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22 qed "g_zero"; |
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23 |
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24 (*** the contrived `mapf' ***) |
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25 |
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26 (* proving the termination condition: *) |
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27 val [tc] = mapf.tcs; |
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28 goalw_cterm [] (cterm_of (sign_of thy) (HOLogic.mk_Trueprop tc)); |
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29 by (rtac allI 1); |
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30 by (case_tac "n=0" 1); |
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31 by (ALLGOALS Asm_simp_tac); |
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32 val lemma = result(); |
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33 |
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34 (* removing the termination condition from the generated thms: *) |
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35 val [mapf_0,mapf_Suc] = mapf.simps; |
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36 val mapf_Suc = lemma RS mapf_Suc; |
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37 |
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38 val mapf_induct = lemma RS mapf.induct; |
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