--- a/src/LK/LK.thy Thu Oct 10 10:57:33 1996 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,135 +0,0 @@
-(* Title: LK/lk.thy
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-Classical First-Order Sequent Calculus
-
-There may be printing problems if a seqent is in expanded normal form
- (eta-expanded, beta-contracted)
-*)
-
-LK = Pure +
-
-classes term < logic
-
-default term
-
-types
- o sequence seqobj seqcont sobj
-
-arities
- o :: logic
-
-consts
- True,False :: o
- "=" :: ['a,'a] => o (infixl 50)
- Not :: o => o ("~ _" [40] 40)
- "&" :: [o,o] => o (infixr 35)
- "|" :: [o,o] => o (infixr 30)
- "-->","<->" :: [o,o] => o (infixr 25)
- The :: ('a => o) => 'a (binder "THE " 10)
- All :: ('a => o) => o (binder "ALL " 10)
- Ex :: ('a => o) => o (binder "EX " 10)
-
- (*Representation of sequents*)
- Trueprop :: [sobj=>sobj, sobj=>sobj] => prop
- Seqof :: [o, sobj] => sobj
-
-syntax
- "@Trueprop" :: [sequence,sequence] => prop ("((_)/ |- (_))" [6,6] 5)
- NullSeq :: sequence ("" [] 1000)
- NonNullSeq :: [seqobj,seqcont] => sequence ("__" [] 1000)
- NullSeqCont :: seqcont ("" [] 1000)
- SeqCont :: [seqobj,seqcont] => seqcont (",/ __" [] 1000)
- "" :: o => seqobj ("_" [] 1000)
- SeqId :: id => seqobj ("$_" [] 1000)
- SeqVar :: var => seqobj ("$_")
-
-rules
- (*Structural rules*)
-
- basic "$H, P, $G |- $E, P, $F"
-
- thinR "$H |- $E, $F ==> $H |- $E, P, $F"
- thinL "$H, $G |- $E ==> $H, P, $G |- $E"
-
- cut "[| $H |- $E, P; $H, P |- $E |] ==> $H |- $E"
-
- (*Propositional rules*)
-
- conjR "[| $H|- $E, P, $F; $H|- $E, Q, $F |] ==> $H|- $E, P&Q, $F"
- conjL "$H, P, Q, $G |- $E ==> $H, P & Q, $G |- $E"
-
- disjR "$H |- $E, P, Q, $F ==> $H |- $E, P|Q, $F"
- disjL "[| $H, P, $G |- $E; $H, Q, $G |- $E |] ==> $H, P|Q, $G |- $E"
-
- impR "$H, P |- $E, Q, $F ==> $H |- $E, P-->Q, $F"
- impL "[| $H,$G |- $E,P; $H, Q, $G |- $E |] ==> $H, P-->Q, $G |- $E"
-
- notR "$H, P |- $E, $F ==> $H |- $E, ~P, $F"
- notL "$H, $G |- $E, P ==> $H, ~P, $G |- $E"
-
- FalseL "$H, False, $G |- $E"
-
- True_def "True == False-->False"
- iff_def "P<->Q == (P-->Q) & (Q-->P)"
-
- (*Quantifiers*)
-
- allR "(!!x.$H |- $E, P(x), $F) ==> $H |- $E, ALL x.P(x), $F"
- allL "$H, P(x), $G, ALL x.P(x) |- $E ==> $H, ALL x.P(x), $G |- $E"
-
- exR "$H |- $E, P(x), $F, EX x.P(x) ==> $H |- $E, EX x.P(x), $F"
- exL "(!!x.$H, P(x), $G |- $E) ==> $H, EX x.P(x), $G |- $E"
-
- (*Equality*)
-
- refl "$H |- $E, a=a, $F"
- sym "$H |- $E, a=b, $F ==> $H |- $E, b=a, $F"
- trans "[| $H|- $E, a=b, $F; $H|- $E, b=c, $F |] ==> $H|- $E, a=c, $F"
-
-
- (*Descriptions*)
-
- The "[| $H |- $E, P(a), $F; !!x.$H, P(x) |- $E, x=a, $F |] ==>
- $H |- $E, P(THE x.P(x)), $F"
-end
-
-ML
-
-(*Abstract over "sobj" -- representation of a sequence of formulae *)
-fun abs_sobj t = Abs("sobj", Type("sobj",[]), t);
-
-(*Representation of empty sequence*)
-val Sempty = abs_sobj (Bound 0);
-
-fun seq_obj_tr (Const("SeqId",_)$id) = id
- | seq_obj_tr (Const("SeqVar",_)$id) = id
- | seq_obj_tr (fm) = Const("Seqof",dummyT)$fm;
-
-fun seq_tr (_$obj$seq) = seq_obj_tr(obj)$seq_tr(seq)
- | seq_tr (_) = Bound 0;
-
-fun seq_tr1 (Const("NullSeq",_)) = Sempty
- | seq_tr1 (seq) = abs_sobj(seq_tr seq);
-
-fun true_tr[s1,s2] = Const("Trueprop",dummyT)$seq_tr1 s1$seq_tr1 s2;
-
-fun seq_obj_tr' (Const("Seqof",_)$fm) = fm
- | seq_obj_tr' (id) = Const("SeqId",dummyT)$id;
-
-fun seq_tr' (obj$sq,C) =
- let val sq' = case sq of
- Bound 0 => Const("NullSeqCont",dummyT)
- | _ => seq_tr'(sq,Const("SeqCont",dummyT))
- in C $ seq_obj_tr' obj $ sq' end;
-
-fun seq_tr1' (Bound 0) = Const("NullSeq",dummyT)
- | seq_tr1' s = seq_tr'(s,Const("NonNullSeq",dummyT));
-
-fun true_tr' [Abs(_,_,s1),Abs(_,_,s2)] =
- Const("@Trueprop",dummyT)$seq_tr1' s1$seq_tr1' s2;
-
-val parse_translation = [("@Trueprop",true_tr)];
-val print_translation = [("Trueprop",true_tr')];