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authoraarne <aarne@cs.chalmers.se>2008-06-25 16:54:35 +0000
committeraarne <aarne@cs.chalmers.se>2008-06-25 16:54:35 +0000
commite9e80fc389365e24d4300d7d5390c7d833a96c50 (patch)
treef0b58473adaa670bd8fc52ada419d8cad470ee03 /examples/logic/Logic.gf
parentb96b36f43de3e2f8b58d5f539daa6f6d47f25870 (diff)
changed names of resource-1.3; added a note on homepage on release
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--- many-sorted predicate calculus
--- AR 1999, revised 2001 and 2006
-
-abstract Logic = {
-
-cat
- Prop ; -- proposition
- Dom ; -- domain of quantification
- Elem Dom ; -- individual element of a domain
- Proof Prop ; -- proof of a proposition
- Hypo Prop ; -- hypothesis of a proposition
- Text ; -- theorem with proof etc.
-
-fun
- -- texts
- Statement : Prop -> Text ;
- ThmWithProof : (A : Prop) -> Proof A -> Text ;
- ThmWithTrivialProof : (A : Prop) -> Proof A -> Text ;
-
- -- logically complex propositions
- Disj : (A,B : Prop) -> Prop ;
- Conj : (A,B : Prop) -> Prop ;
- Impl : (A,B : Prop) -> Prop ;
- Abs : Prop ;
- Neg : Prop -> Prop ;
-
- Univ : (A : Dom) -> (Elem A -> Prop) -> Prop ;
- Exist : (A : Dom) -> (Elem A -> Prop) -> Prop ;
-
- -- inference rules
-
- ConjI : (A,B : Prop) -> Proof A -> Proof B -> Proof (Conj A B) ;
- ConjEl : (A,B : Prop) -> Proof (Conj A B) -> Proof A ;
- ConjEr : (A,B : Prop) -> Proof (Conj A B) -> Proof B ;
- DisjIl : (A,B : Prop) -> Proof A -> Proof (Disj A B) ;
- DisjIr : (A,B : Prop) -> Proof B -> Proof (Disj A B) ;
- DisjE : (A,B,C : Prop) -> Proof (Disj A B) ->
- (Hypo A -> Proof C) -> (Hypo B -> Proof C) -> Proof C ;
- ImplI : (A,B : Prop) -> (Hypo A -> Proof B) -> Proof (Impl A B) ;
- ImplE : (A,B : Prop) -> Proof (Impl A B) -> Proof A -> Proof B ;
- NegI : (A : Prop) -> (Hypo A -> Proof Abs) -> Proof (Neg A) ;
- NegE : (A : Prop) -> Proof (Neg A) -> Proof A -> Proof Abs ;
- AbsE : (C : Prop) -> Proof Abs -> Proof C ;
- UnivI : (A : Dom) -> (B : Elem A -> Prop) ->
- ((x : Elem A) -> Proof (B x)) -> Proof (Univ A B) ;
- UnivE : (A : Dom) -> (B : Elem A -> Prop) ->
- Proof (Univ A B) -> (a : Elem A) -> Proof (B a) ;
- ExistI : (A : Dom) -> (B : Elem A -> Prop) ->
- (a : Elem A) -> Proof (B a) -> Proof (Exist A B) ;
- ExistE : (A : Dom) -> (B : Elem A -> Prop) -> (C : Prop) ->
- Proof (Exist A B) -> ((x : Elem A) -> Proof (B x) -> Proof C) ->
- Proof C ;
-
- -- use a hypothesis
- Hypoth : (A : Prop) -> Hypo A -> Proof A ;
-
- -- pronoun
- Pron : (A : Dom) -> Elem A -> Elem A ;
-
-} ;