equal
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inserted
replaced
13 type_synonym 'a predicate = "'a \<Rightarrow> bool" |
13 type_synonym 'a predicate = "'a \<Rightarrow> bool" |
14 |
14 |
15 definition satisfies :: "'a \<Rightarrow> 'a predicate \<Rightarrow> bool" ("_ \<Turnstile> _" [100, 9] 8) |
15 definition satisfies :: "'a \<Rightarrow> 'a predicate \<Rightarrow> bool" ("_ \<Turnstile> _" [100, 9] 8) |
16 where "(s \<Turnstile> P) \<longleftrightarrow> P s" |
16 where "(s \<Turnstile> P) \<longleftrightarrow> P s" |
17 |
17 |
18 definition valid :: "'a predicate \<Rightarrow> bool" (* ("|-") *) |
18 definition valid :: "'a predicate \<Rightarrow> bool" (* FIXME ("|-") *) |
19 where "valid P \<longleftrightarrow> (\<forall>s. (s \<Turnstile> P))" |
19 where "valid P \<longleftrightarrow> (\<forall>s. (s \<Turnstile> P))" |
20 |
20 |
21 definition NOT :: "'a predicate \<Rightarrow> 'a predicate" ("\<^bold>\<not> _" [40] 40) |
21 definition NOT :: "'a predicate \<Rightarrow> 'a predicate" ("\<^bold>\<not> _" [40] 40) |
22 where "NOT P s \<longleftrightarrow> \<not> P s" |
22 where "NOT P s \<longleftrightarrow> \<not> P s" |
23 |
23 |