msyds/gf-core
1
0
Fork 0
forked from GitHub/gf-core
Code Pull Requests Activity

gfcm header

Browse Source
This commit is contained in:
aarne
2004-09-14 17:05:46 +00:00
parent 25f95fcfc3
commit 6c372cc599
27 changed files with 1350 additions and 883 deletions
Download Patch File Download Diff File Expand all files Collapse all files

16
grammars/logic/Logic.gf
View File

@@ -32,25 +32,36 @@ fun
ImplP : (A : Prop) -> (Proof A -> Prop) -> Prop ;
-- inference rules
data
ConjI : (A,B : Prop) -> Proof A -> Proof B -> Proof (Conj A B) ;
fun
ConjEl : (A,B : Prop) -> Proof (Conj A B) -> Proof A ;
ConjEr : (A,B : Prop) -> Proof (Conj A B) -> Proof B ;
data
DisjIl : (A,B : Prop) -> Proof A -> Proof (Disj A B) ;
DisjIr : (A,B : Prop) -> Proof B -> Proof (Disj A B) ;
fun
DisjE : (A,B,C : Prop) -> Proof (Disj A B) ->
(Proof A -> Proof C) -> (Proof B -> Proof C) -> Proof C ;
data
ImplI : (A,B : Prop) -> (Proof A -> Proof B) -> Proof (Impl A B) ;
fun
ImplE : (A,B : Prop) -> Proof (Impl A B) -> Proof A -> Proof B ;
data
NegI : (A : Prop) -> (Proof A -> Proof Abs) -> Proof (Neg A) ;
fun
NegE : (A : Prop) -> Proof (Neg A) -> Proof A -> Proof Abs ;
AbsE : (C : Prop) -> Proof Abs -> Proof C ;
data
UnivI : (A : Dom) -> (B : Elem A -> Prop) ->
((x : Elem A) -> Proof (B x)) -> Proof (Univ A B) ;
fun
UnivE : (A : Dom) -> (B : Elem A -> Prop) ->
Proof (Univ A B) -> (a : Elem A) -> Proof (B a) ;
data
ExistI : (A : Dom) -> (B : Elem A -> Prop) ->
(a : Elem A) -> Proof (B a) -> Proof (Exist A B) ;
fun
ExistE : (A : Dom) -> (B : Elem A -> Prop) -> (C : Prop) ->
Proof (Exist A B) -> ((x : Elem A) -> Proof (B x) -> Proof C) ->
Proof C ;
@@ -61,9 +72,6 @@ fun
-- pronoun
Pron : (A : Dom) -> Elem A -> Elem A ;
data
Proof = ConjI | DisjIl | DisjIr ;
def
-- proof normalization
ConjEl _ _ (ConjI _ _ a _) = a ;