summary |
shortlog |
changelog |
graph |
tags |
bookmarks |
branches |
files |
changeset |
file |
latest |
revisions |
annotate |
diff |
comparison |
raw |
help

src/HOL/TLA/Intensional.thy

author | berghofe |

Fri, 13 Oct 2006 18:15:18 +0200 | |

changeset 21020 | 9af9ceb16d58 |

parent 17309 | c43ed29bd197 |

child 21624 | 6f79647cf536 |

permissions | -rw-r--r-- |

Adapted to changes in FixedPoint theory.

(* File: TLA/Intensional.thy ID: $Id$ Author: Stephan Merz Copyright: 1998 University of Munich Theory Name: Intensional Logic Image: HOL Define a framework for "intensional" (possible-world based) logics on top of HOL, with lifting of constants and functions. *) theory Intensional imports Main begin axclass world < type (** abstract syntax **) types ('w,'a) expr = "'w => 'a" (* intention: 'w::world, 'a::type *) 'w form = "('w, bool) expr" consts Valid :: "('w::world) form => bool" const :: "'a => ('w::world, 'a) expr" lift :: "['a => 'b, ('w::world, 'a) expr] => ('w,'b) expr" lift2 :: "['a => 'b => 'c, ('w::world,'a) expr, ('w,'b) expr] => ('w,'c) expr" lift3 :: "['a => 'b => 'c => 'd, ('w::world,'a) expr, ('w,'b) expr, ('w,'c) expr] => ('w,'d) expr" (* "Rigid" quantification (logic level) *) RAll :: "('a => ('w::world) form) => 'w form" (binder "Rall " 10) REx :: "('a => ('w::world) form) => 'w form" (binder "Rex " 10) REx1 :: "('a => ('w::world) form) => 'w form" (binder "Rex! " 10) (** concrete syntax **) nonterminals lift liftargs syntax "" :: "id => lift" ("_") "" :: "longid => lift" ("_") "" :: "var => lift" ("_") "_applC" :: "[lift, cargs] => lift" ("(1_/ _)" [1000, 1000] 999) "" :: "lift => lift" ("'(_')") "_lambda" :: "[idts, 'a] => lift" ("(3%_./ _)" [0, 3] 3) "_constrain" :: "[lift, type] => lift" ("(_::_)" [4, 0] 3) "" :: "lift => liftargs" ("_") "_liftargs" :: "[lift, liftargs] => liftargs" ("_,/ _") "_Valid" :: "lift => bool" ("(|- _)" 5) "_holdsAt" :: "['a, lift] => bool" ("(_ |= _)" [100,10] 10) (* Syntax for lifted expressions outside the scope of |- or |= *) "LIFT" :: "lift => 'a" ("LIFT _") (* generic syntax for lifted constants and functions *) "_const" :: "'a => lift" ("(#_)" [1000] 999) "_lift" :: "['a, lift] => lift" ("(_<_>)" [1000] 999) "_lift2" :: "['a, lift, lift] => lift" ("(_<_,/ _>)" [1000] 999) "_lift3" :: "['a, lift, lift, lift] => lift" ("(_<_,/ _,/ _>)" [1000] 999) (* concrete syntax for common infix functions: reuse same symbol *) "_liftEqu" :: "[lift, lift] => lift" ("(_ =/ _)" [50,51] 50) "_liftNeq" :: "[lift, lift] => lift" ("(_ ~=/ _)" [50,51] 50) "_liftNot" :: "lift => lift" ("(~ _)" [40] 40) "_liftAnd" :: "[lift, lift] => lift" ("(_ &/ _)" [36,35] 35) "_liftOr" :: "[lift, lift] => lift" ("(_ |/ _)" [31,30] 30) "_liftImp" :: "[lift, lift] => lift" ("(_ -->/ _)" [26,25] 25) "_liftIf" :: "[lift, lift, lift] => lift" ("(if (_)/ then (_)/ else (_))" 10) "_liftPlus" :: "[lift, lift] => lift" ("(_ +/ _)" [66,65] 65) "_liftMinus" :: "[lift, lift] => lift" ("(_ -/ _)" [66,65] 65) "_liftTimes" :: "[lift, lift] => lift" ("(_ */ _)" [71,70] 70) "_liftDiv" :: "[lift, lift] => lift" ("(_ div _)" [71,70] 70) "_liftMod" :: "[lift, lift] => lift" ("(_ mod _)" [71,70] 70) "_liftLess" :: "[lift, lift] => lift" ("(_/ < _)" [50, 51] 50) "_liftLeq" :: "[lift, lift] => lift" ("(_/ <= _)" [50, 51] 50) "_liftMem" :: "[lift, lift] => lift" ("(_/ : _)" [50, 51] 50) "_liftNotMem" :: "[lift, lift] => lift" ("(_/ ~: _)" [50, 51] 50) "_liftFinset" :: "liftargs => lift" ("{(_)}") (** TODO: syntax for lifted collection / comprehension **) "_liftPair" :: "[lift,liftargs] => lift" ("(1'(_,/ _'))") (* infix syntax for list operations *) "_liftCons" :: "[lift, lift] => lift" ("(_ #/ _)" [65,66] 65) "_liftApp" :: "[lift, lift] => lift" ("(_ @/ _)" [65,66] 65) "_liftList" :: "liftargs => lift" ("[(_)]") (* Rigid quantification (syntax level) *) "_ARAll" :: "[idts, lift] => lift" ("(3! _./ _)" [0, 10] 10) "_AREx" :: "[idts, lift] => lift" ("(3? _./ _)" [0, 10] 10) "_AREx1" :: "[idts, lift] => lift" ("(3?! _./ _)" [0, 10] 10) "_RAll" :: "[idts, lift] => lift" ("(3ALL _./ _)" [0, 10] 10) "_REx" :: "[idts, lift] => lift" ("(3EX _./ _)" [0, 10] 10) "_REx1" :: "[idts, lift] => lift" ("(3EX! _./ _)" [0, 10] 10) translations "_const" == "const" "_lift" == "lift" "_lift2" == "lift2" "_lift3" == "lift3" "_Valid" == "Valid" "_RAll x A" == "Rall x. A" "_REx x A" == "Rex x. A" "_REx1 x A" == "Rex! x. A" "_ARAll" => "_RAll" "_AREx" => "_REx" "_AREx1" => "_REx1" "w |= A" => "A w" "LIFT A" => "A::_=>_" "_liftEqu" == "_lift2 (op =)" "_liftNeq u v" == "_liftNot (_liftEqu u v)" "_liftNot" == "_lift Not" "_liftAnd" == "_lift2 (op &)" "_liftOr" == "_lift2 (op | )" "_liftImp" == "_lift2 (op -->)" "_liftIf" == "_lift3 If" "_liftPlus" == "_lift2 (op +)" "_liftMinus" == "_lift2 (op -)" "_liftTimes" == "_lift2 (op *)" "_liftDiv" == "_lift2 (op div)" "_liftMod" == "_lift2 (op mod)" "_liftLess" == "_lift2 (op <)" "_liftLeq" == "_lift2 (op <=)" "_liftMem" == "_lift2 (op :)" "_liftNotMem x xs" == "_liftNot (_liftMem x xs)" "_liftFinset (_liftargs x xs)" == "_lift2 insert x (_liftFinset xs)" "_liftFinset x" == "_lift2 insert x (_const {})" "_liftPair x (_liftargs y z)" == "_liftPair x (_liftPair y z)" "_liftPair" == "_lift2 Pair" "_liftCons" == "lift2 Cons" "_liftApp" == "lift2 (op @)" "_liftList (_liftargs x xs)" == "_liftCons x (_liftList xs)" "_liftList x" == "_liftCons x (_const [])" "w |= ~A" <= "_liftNot A w" "w |= A & B" <= "_liftAnd A B w" "w |= A | B" <= "_liftOr A B w" "w |= A --> B" <= "_liftImp A B w" "w |= u = v" <= "_liftEqu u v w" "w |= ALL x. A" <= "_RAll x A w" "w |= EX x. A" <= "_REx x A w" "w |= EX! x. A" <= "_REx1 x A w" syntax (xsymbols) "_Valid" :: "lift => bool" ("(\<turnstile> _)" 5) "_holdsAt" :: "['a, lift] => bool" ("(_ \<Turnstile> _)" [100,10] 10) "_liftNeq" :: "[lift, lift] => lift" (infixl "\<noteq>" 50) "_liftNot" :: "lift => lift" ("\<not> _" [40] 40) "_liftAnd" :: "[lift, lift] => lift" (infixr "\<and>" 35) "_liftOr" :: "[lift, lift] => lift" (infixr "\<or>" 30) "_liftImp" :: "[lift, lift] => lift" (infixr "\<longrightarrow>" 25) "_RAll" :: "[idts, lift] => lift" ("(3\<forall>_./ _)" [0, 10] 10) "_REx" :: "[idts, lift] => lift" ("(3\<exists>_./ _)" [0, 10] 10) "_REx1" :: "[idts, lift] => lift" ("(3\<exists>!_./ _)" [0, 10] 10) "_liftLeq" :: "[lift, lift] => lift" ("(_/ \<le> _)" [50, 51] 50) "_liftMem" :: "[lift, lift] => lift" ("(_/ \<in> _)" [50, 51] 50) "_liftNotMem" :: "[lift, lift] => lift" ("(_/ \<notin> _)" [50, 51] 50) syntax (HTML output) "_liftNeq" :: "[lift, lift] => lift" (infixl "\<noteq>" 50) "_liftNot" :: "lift => lift" ("\<not> _" [40] 40) "_liftAnd" :: "[lift, lift] => lift" (infixr "\<and>" 35) "_liftOr" :: "[lift, lift] => lift" (infixr "\<or>" 30) "_RAll" :: "[idts, lift] => lift" ("(3\<forall>_./ _)" [0, 10] 10) "_REx" :: "[idts, lift] => lift" ("(3\<exists>_./ _)" [0, 10] 10) "_REx1" :: "[idts, lift] => lift" ("(3\<exists>!_./ _)" [0, 10] 10) "_liftLeq" :: "[lift, lift] => lift" ("(_/ \<le> _)" [50, 51] 50) "_liftMem" :: "[lift, lift] => lift" ("(_/ \<in> _)" [50, 51] 50) "_liftNotMem" :: "[lift, lift] => lift" ("(_/ \<notin> _)" [50, 51] 50) axioms Valid_def: "|- A == ALL w. w |= A" unl_con: "LIFT #c w == c" unl_lift: "lift f x w == f (x w)" unl_lift2: "LIFT f<x, y> w == f (x w) (y w)" unl_lift3: "LIFT f<x, y, z> w == f (x w) (y w) (z w)" unl_Rall: "w |= ALL x. A x == ALL x. (w |= A x)" unl_Rex: "w |= EX x. A x == EX x. (w |= A x)" unl_Rex1: "w |= EX! x. A x == EX! x. (w |= A x)" ML {* use_legacy_bindings (the_context ()) *} end