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src/HOLCF/IOA/meta_theory/Pred.thy
author wenzelm
Wed, 29 Jun 2005 15:13:35 +0200
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(*  Title:      HOLCF/IOA/meta_theory/Pred.thy
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    ID:         $Id$
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    Author:     Olaf Müller
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Logical Connectives lifted to predicates.













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*)   













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Pred = Main +








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default type








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types













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'a predicate      = "'a => bool"













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consts













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satisfies    ::"'a  => 'a predicate => bool"    ("_ |= _" [100,9] 8)













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valid        ::"'a predicate => bool"           (*  ("|-") *)         













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NOT          ::"'a predicate => 'a predicate"  (".~ _" [40] 40)













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AND          ::"'a predicate => 'a predicate => 'a predicate"    (infixr ".&" 35)













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OR           ::"'a predicate => 'a predicate => 'a predicate"    (infixr ".|" 30)













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IMPLIES      ::"'a predicate => 'a predicate => 'a predicate"    (infixr ".-->" 25)













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syntax ("" output)













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  "NOT"     ::"'a predicate => 'a predicate" ("~ _" [40] 40)













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  "AND"     ::"'a predicate => 'a predicate => 'a predicate"    (infixr "&" 35)













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  "OR"      ::"'a predicate => 'a predicate => 'a predicate"    (infixr "|" 30)













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  "IMPLIES" ::"'a predicate => 'a predicate => 'a predicate"    (infixr "-->" 25)













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syntax (xsymbols output)








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  "NOT"    ::"'a predicate => 'a predicate" ("\\<not> _" [40] 40)













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  "AND"    ::"'a predicate => 'a predicate => 'a predicate"    (infixr "\\<and>" 35)













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  "OR"     ::"'a predicate => 'a predicate => 'a predicate"    (infixr "\\<or>" 30)








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  "IMPLIES" ::"'a predicate => 'a predicate => 'a predicate"    (infixr "\\<longrightarrow>" 25)








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syntax (xsymbols)








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  "satisfies"  ::"'a => 'a predicate => bool"    ("_ \\<Turnstile> _" [100,9] 8)













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syntax (HTML output)













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  "NOT"    ::"'a predicate => 'a predicate" ("\\<not> _" [40] 40)








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  "AND"    ::"'a predicate => 'a predicate => 'a predicate"    (infixr "\\<and>" 35)













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  "OR"     ::"'a predicate => 'a predicate => 'a predicate"    (infixr "\\<or>" 30)








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defs













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satisfies_def













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   "s |= P  == P s" 













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(* priority einfuegen, da clash mit |=, wenn graphisches Symbol *)













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valid_def













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   "valid P == (! s. (s |= P))"













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NOT_def













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  "NOT P s ==  ~ (P s)"













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AND_def













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  "(P .& Q) s == (P s) & (Q s)"













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OR_def













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  "(P .| Q) s ==  (P s) | (Q s)"













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IMPLIES_def













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  "(P .--> Q) s == (P s) --> (Q s)"













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end















isabelle