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1 (* Title: Substitutions/alist.ML |
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2 Author: Martin Coen, Cambridge University Computer Laboratory |
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3 Copyright 1993 University of Cambridge |
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4 |
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5 For alist.thy. |
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6 *) |
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7 |
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8 open AList; |
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9 |
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10 (*********) |
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11 |
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12 val al_defs = [alist_rec_def,assoc_def]; |
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13 |
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14 val alist_ss = pair_ss addsimps [Nil_not_Cons,Cons_not_Nil,Cons_Cons_eq, |
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15 list_rec_Nil,list_rec_Cons]; |
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16 |
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17 val al_rews = |
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18 let fun mk_thm s = prove_goalw AList.thy al_defs s |
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19 (fn _ => [simp_tac alist_ss 1]) |
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20 in map mk_thm |
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21 ["alist_rec(Nil,c,d) = c", |
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22 "alist_rec(Cons(<a,b>,al),c,d) = d(a,b,al,alist_rec(al,c,d))", |
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23 "assoc(v,d,Nil) = d", |
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24 "assoc(v,d,Cons(<a,b>,al)) = if(v=a,b,assoc(v,d,al))"] end; |
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25 |
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26 (*********) |
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27 |
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28 val prems = goal AList.thy |
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29 "[| P(Nil); \ |
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30 \ !!x y xs. P(xs) ==> P(Cons(<x,y>,xs)) |] ==> P(l)"; |
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31 by (list_ind_tac "l" 1); |
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32 by (resolve_tac prems 1); |
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33 by (rtac PairE 1); |
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34 by (etac ssubst 1); |
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35 by (resolve_tac prems 1); |
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36 by (assume_tac 1); |
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37 val alist_induct = result(); |
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38 |
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39 (*Perform induction on xs. *) |
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40 fun alist_ind_tac a M = |
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41 EVERY [res_inst_tac [("l",a)] alist_induct M, |
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42 rename_last_tac a ["1"] (M+1)]; |
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43 |
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44 (* |
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45 val prems = goal AList.thy |
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46 "[| P(Nil); !! x y xs. P(xs) --> P(Cons(<x,y>,xs)) |] ==> P(a)"; |
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47 by (alist_ind_tac "a" 1); |
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48 by (ALLGOALS (cut_facts_tac prems THEN' fast_tac HOL_cs)); |
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49 val alist_induct2 = result(); |
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50 |
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51 add_inds alist_induct2; |
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52 *) |