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Diffstat (limited to 'old-examples/logic/Logic.gf')
| -rw-r--r-- | old-examples/logic/Logic.gf | 60 |
1 files changed, 0 insertions, 60 deletions
diff --git a/old-examples/logic/Logic.gf b/old-examples/logic/Logic.gf deleted file mode 100644 index f7bb4ab57..000000000 --- a/old-examples/logic/Logic.gf +++ /dev/null @@ -1,60 +0,0 @@ --- 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 ; - -} ; |
