13 type_synonym |
13 type_synonym |
14 'a predicate = "'a => bool" |
14 'a predicate = "'a => bool" |
15 |
15 |
16 consts |
16 consts |
17 |
17 |
18 satisfies ::"'a => 'a predicate => bool" ("_ |= _" [100,9] 8) |
18 satisfies ::"'a => 'a predicate => bool" ("_ \<Turnstile> _" [100,9] 8) |
19 valid ::"'a predicate => bool" (* ("|-") *) |
19 valid ::"'a predicate => bool" (* ("|-") *) |
20 |
20 |
21 NOT ::"'a predicate => 'a predicate" (".~ _" [40] 40) |
21 NOT ::"'a predicate => 'a predicate" ("\<^bold>\<not> _" [40] 40) |
22 AND ::"'a predicate => 'a predicate => 'a predicate" (infixr ".&" 35) |
22 AND ::"'a predicate => 'a predicate => 'a predicate" (infixr "\<^bold>\<and>" 35) |
23 OR ::"'a predicate => 'a predicate => 'a predicate" (infixr ".|" 30) |
23 OR ::"'a predicate => 'a predicate => 'a predicate" (infixr "\<^bold>\<or>" 30) |
24 IMPLIES ::"'a predicate => 'a predicate => 'a predicate" (infixr ".-->" 25) |
24 IMPLIES ::"'a predicate => 'a predicate => 'a predicate" (infixr "\<^bold>\<longrightarrow>" 25) |
25 |
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26 |
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27 notation (output) |
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28 NOT ("~ _" [40] 40) and |
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29 AND (infixr "&" 35) and |
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30 OR (infixr "|" 30) and |
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31 IMPLIES (infixr "-->" 25) |
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32 |
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33 notation (xsymbols output) |
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34 NOT ("\<not> _" [40] 40) and |
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35 AND (infixr "\<and>" 35) and |
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36 OR (infixr "\<or>" 30) and |
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37 IMPLIES (infixr "\<longrightarrow>" 25) |
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38 |
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39 notation (xsymbols) |
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40 satisfies ("_ \<Turnstile> _" [100,9] 8) |
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41 |
25 |
42 |
26 |
43 defs |
27 defs |
44 |
28 |
45 satisfies_def: |
29 satisfies_def: |
46 "s |= P == P s" |
30 "s \<Turnstile> P == P s" |
47 |
31 |
48 (* priority einfuegen, da clash mit |=, wenn graphisches Symbol *) |
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49 valid_def: |
32 valid_def: |
50 "valid P == (! s. (s |= P))" |
33 "valid P == (! s. (s \<Turnstile> P))" |
51 |
34 |
52 NOT_def: |
35 NOT_def: |
53 "NOT P s == ~ (P s)" |
36 "NOT P s == ~ (P s)" |
54 |
37 |
55 AND_def: |
38 AND_def: |
56 "(P .& Q) s == (P s) & (Q s)" |
39 "(P \<^bold>\<and> Q) s == (P s) & (Q s)" |
57 |
40 |
58 OR_def: |
41 OR_def: |
59 "(P .| Q) s == (P s) | (Q s)" |
42 "(P \<^bold>\<or> Q) s == (P s) | (Q s)" |
60 |
43 |
61 IMPLIES_def: |
44 IMPLIES_def: |
62 "(P .--> Q) s == (P s) --> (Q s)" |
45 "(P \<^bold>\<longrightarrow> Q) s == (P s) --> (Q s)" |
63 |
46 |
64 end |
47 end |