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1 (* Title: HOLCF/tr1.thy |
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2 ID: $Id$ |
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3 Author: Franz Regensburger |
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4 Copyright 1993 Technische Universitaet Muenchen |
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5 |
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6 Introduve the domain of truth values tr = {UU,TT,FF} |
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7 |
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8 This type is introduced using a domain isomorphism. |
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9 |
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10 The type axiom |
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11 |
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12 arities tr :: pcpo |
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13 |
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14 and the continuity of the Isomorphisms are taken for granted. Since the |
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15 type is not recursive, it could be easily introduced in a purely conservative |
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16 style as it was used for the types sprod, ssum, lift. The definition of the |
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17 ordering is canonical using abstraction and representation, but this would take |
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18 again a lot of internal constants. It can be easily seen that the axioms below |
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19 are consistent. |
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20 |
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21 Partial Ordering is implicit in isomorphims abs_tr,rep_tr and their continuity |
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22 |
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23 *) |
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24 |
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25 Tr1 = One + |
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26 |
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27 types tr 0 |
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28 arities tr :: pcpo |
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29 |
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30 consts |
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31 abs_tr :: "one ++ one -> tr" |
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32 rep_tr :: "tr -> one ++ one" |
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33 TT :: "tr" |
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34 FF :: "tr" |
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35 tr_when :: "'c -> 'c -> tr -> 'c" |
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36 |
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37 rules |
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38 |
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39 abs_tr_iso "abs_tr[rep_tr[u]] = u" |
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40 rep_tr_iso "rep_tr[abs_tr[x]] = x" |
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41 |
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42 TT_def "TT == abs_tr[sinl[one]]" |
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43 FF_def "FF == abs_tr[sinr[one]]" |
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44 |
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45 tr_when_def "tr_when == (LAM e1 e2 t.when[LAM x.e1][LAM y.e2][rep_tr[t]])" |
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46 |
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47 end |
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48 |
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49 |
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53 |
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57 |