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1 (* Title: Substitutions/uterm.thy |
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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 Simple term structure for unifiation. |
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6 Binary trees with leaves that are constants or variables. |
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7 *) |
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8 |
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9 UTerm = Sexp + |
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10 |
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11 types uterm 1 |
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12 |
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13 arities |
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14 uterm :: (term)term |
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15 |
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16 consts |
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17 UTerm :: "'a node set set => 'a node set set" |
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18 Rep_UTerm :: "'a uterm => 'a node set" |
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19 Abs_UTerm :: "'a node set => 'a uterm" |
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20 VAR :: "'a node set => 'a node set" |
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21 CONST :: "'a node set => 'a node set" |
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22 COMB :: "['a node set, 'a node set] => 'a node set" |
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23 Var :: "'a => 'a uterm" |
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24 Const :: "'a => 'a uterm" |
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25 Comb :: "['a uterm, 'a uterm] => 'a uterm" |
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26 UTerm_rec :: "['a node set, 'a node set => 'b, 'a node set => 'b, \ |
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27 \ ['a node set , 'a node set, 'b, 'b]=>'b] => 'b" |
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28 uterm_rec :: "['a uterm, 'a => 'b, 'a => 'b, \ |
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29 \ ['a uterm, 'a uterm,'b,'b]=>'b] => 'b" |
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30 |
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31 rules |
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32 UTerm_def "UTerm(A) == lfp(%Z. A <+> A <+> Z <*> Z)" |
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33 (*faking a type definition...*) |
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34 Rep_UTerm "Rep_UTerm(xs): UTerm(range(Leaf))" |
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35 Rep_UTerm_inverse "Abs_UTerm(Rep_UTerm(xs)) = xs" |
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36 Abs_UTerm_inverse "M: UTerm(range(Leaf)) ==> Rep_UTerm(Abs_UTerm(M)) = M" |
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37 (*defining the concrete constructors*) |
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38 VAR_def "VAR(v) == In0(v)" |
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39 CONST_def "CONST(v) == In1(In0(v))" |
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40 COMB_def "COMB(t,u) == In1(In1(t . u))" |
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41 (*defining the abstract constructors*) |
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42 Var_def "Var(v) == Abs_UTerm(VAR(Leaf(v)))" |
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43 Const_def "Const(c) == Abs_UTerm(CONST(Leaf(c)))" |
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44 Comb_def "Comb(t,u) == Abs_UTerm(COMB(Rep_UTerm(t),Rep_UTerm(u)))" |
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45 |
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46 (*uterm recursion*) |
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47 UTerm_rec_def |
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48 "UTerm_rec(M,b,c,d) == wfrec(trancl(pred_Sexp), M, \ |
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49 \ %z g. Case(z, %x. b(x), \ |
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50 \ %w. Case(w, %x. c(x), \ |
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51 \ %v. Split(v, %x y. d(x,y,g(x),g(y))))))" |
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52 |
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53 uterm_rec_def |
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54 "uterm_rec(t,b,c,d) == \ |
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55 \ UTerm_rec(Rep_UTerm(t), %x.b(Inv(Leaf,x)), %x.c(Inv(Leaf,x)), \ |
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56 \ %x y q r.d(Abs_UTerm(x),Abs_UTerm(y),q,r))" |
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57 |
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58 end |