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1 (* Title: HOLCF/one.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 atomic type one = (void)u |
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7 |
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8 This is the first type that is introduced using a domain isomorphism. |
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9 The type axiom |
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10 |
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11 arities one :: pcpo |
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12 |
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13 and the continuity of the Isomorphisms are taken for granted. Since the |
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14 type is not recursive, it could be easily introduced in a purely conservative |
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15 style as it was used for the types sprod, ssum, lift. The definition of the |
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16 ordering is canonical using abstraction and representation, but this would take |
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17 again a lot of internal constants. It can easily be seen that the axioms below |
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18 are consistent. |
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19 |
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20 The partial ordering on type one is implicitly defined via the |
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21 isomorphism axioms and the continuity of abs_one and rep_one. |
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22 |
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23 We could also introduce the function less_one with definition |
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24 |
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25 less_one(x,y) = rep_one[x] << rep_one[y] |
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26 |
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27 |
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28 *) |
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29 |
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30 One = ccc1+ |
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31 |
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32 types one 0 |
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33 arities one :: pcpo |
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34 |
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35 consts |
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36 abs_one :: "(void)u -> one" |
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37 rep_one :: "one -> (void)u" |
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38 one :: "one" |
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39 one_when :: "'c -> one -> 'c" |
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40 |
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41 rules |
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42 abs_one_iso "abs_one[rep_one[u]] = u" |
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43 rep_one_iso "rep_one[abs_one[x]] = x" |
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44 |
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45 one_def "one == abs_one[up[UU]]" |
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46 one_when_def "one_when == (LAM c u.lift[LAM x.c][rep_one[u]])" |
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47 |
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48 end |
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49 |
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50 |
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51 |
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52 |
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53 |
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