
diff -r fd19f77dcf60 -r 75166ebb619b src/Sequents/LK0.thy
--- a/src/Sequents/LK0.thy	Sun Sep 18 14:25:48 2005 +0200
+++ b/src/Sequents/LK0.thy	Sun Sep 18 15:20:08 2005 +0200
@@ -1,136 +1,139 @@
-(*  Title:      LK/LK0
+(*  Title:      LK/LK0.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)
+        (eta-expanded, beta-contracted)
 *)
 
-LK0 = Sequents +
+header {* Classical First-Order Sequent Calculus *}
+
+theory LK0
+imports Sequents
+begin
 
 global
 
-classes term
-default term
+classes "term"
+defaultsort "term"
 
 consts
 
- Trueprop	:: "two_seqi"
+ Trueprop       :: "two_seqi"
 
-  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)
+  True         :: o
+  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)
+  "<->"        :: "[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)
 
 syntax
- "@Trueprop"	:: "two_seqe" ("((_)/ |- (_))" [6,6] 5)
-  "_not_equal" :: ['a, 'a] => o                (infixl "~=" 50)
+ "@Trueprop"    :: "two_seqe" ("((_)/ |- (_))" [6,6] 5)
+  "_not_equal" :: "['a, 'a] => o"              (infixl "~=" 50)
+
+parse_translation {* [("@Trueprop", two_seq_tr "Trueprop")] *}
+print_translation {* [("Trueprop", two_seq_tr' "@Trueprop")] *}
 
 translations
   "x ~= y"      == "~ (x = y)"
 
 syntax (xsymbols)
-  Not           :: o => o               ("\\<not> _" [40] 40)
-  "op &"        :: [o, o] => o          (infixr "\\<and>" 35)
-  "op |"        :: [o, o] => o          (infixr "\\<or>" 30)
-  "op -->"      :: [o, o] => o          (infixr "\\<longrightarrow>" 25)
-  "op <->"      :: [o, o] => o          (infixr "\\<longleftrightarrow>" 25)
-  "ALL "        :: [idts, o] => o       ("(3\\<forall>_./ _)" [0, 10] 10)
-  "EX "         :: [idts, o] => o       ("(3\\<exists>_./ _)" [0, 10] 10)
-  "EX! "        :: [idts, o] => o       ("(3\\<exists>!_./ _)" [0, 10] 10)
-  "_not_equal"  :: ['a, 'a] => o        (infixl "\\<noteq>" 50)
+  Not           :: "o => o"               ("\<not> _" [40] 40)
+  "op &"        :: "[o, o] => o"          (infixr "\<and>" 35)
+  "op |"        :: "[o, o] => o"          (infixr "\<or>" 30)
+  "op -->"      :: "[o, o] => o"          (infixr "\<longrightarrow>" 25)
+  "op <->"      :: "[o, o] => o"          (infixr "\<longleftrightarrow>" 25)
+  "ALL "        :: "[idts, o] => o"       ("(3\<forall>_./ _)" [0, 10] 10)
+  "EX "         :: "[idts, o] => o"       ("(3\<exists>_./ _)" [0, 10] 10)
+  "EX! "        :: "[idts, o] => o"       ("(3\<exists>!_./ _)" [0, 10] 10)
+  "_not_equal"  :: "['a, 'a] => o"        (infixl "\<noteq>" 50)
 
 syntax (HTML output)
-  Not           :: o => o               ("\\<not> _" [40] 40)
-  "op &"        :: [o, o] => o          (infixr "\\<and>" 35)
-  "op |"        :: [o, o] => o          (infixr "\\<or>" 30)
-  "ALL "        :: [idts, o] => o       ("(3\\<forall>_./ _)" [0, 10] 10)
-  "EX "         :: [idts, o] => o       ("(3\\<exists>_./ _)" [0, 10] 10)
-  "EX! "        :: [idts, o] => o       ("(3\\<exists>!_./ _)" [0, 10] 10)
-  "_not_equal"  :: ['a, 'a] => o        (infixl "\\<noteq>" 50)
-
+  Not           :: "o => o"               ("\<not> _" [40] 40)
+  "op &"        :: "[o, o] => o"          (infixr "\<and>" 35)
+  "op |"        :: "[o, o] => o"          (infixr "\<or>" 30)
+  "ALL "        :: "[idts, o] => o"       ("(3\<forall>_./ _)" [0, 10] 10)
+  "EX "         :: "[idts, o] => o"       ("(3\<exists>_./ _)" [0, 10] 10)
+  "EX! "        :: "[idts, o] => o"       ("(3\<exists>!_./ _)" [0, 10] 10)
+  "_not_equal"  :: "['a, 'a] => o"        (infixl "\<noteq>" 50)
 
 local
-  
-rules
+
+axioms
 
   (*Structural rules: contraction, thinning, exchange [Soren Heilmann] *)
 
-  contRS "$H |- $E, $S, $S, $F ==> $H |- $E, $S, $F"
-  contLS "$H, $S, $S, $G |- $E ==> $H, $S, $G |- $E"
+  contRS: "$H |- $E, $S, $S, $F ==> $H |- $E, $S, $F"
+  contLS: "$H, $S, $S, $G |- $E ==> $H, $S, $G |- $E"
 
-  thinRS "$H |- $E, $F ==> $H |- $E, $S, $F"
-  thinLS "$H, $G |- $E ==> $H, $S, $G |- $E"
+  thinRS: "$H |- $E, $F ==> $H |- $E, $S, $F"
+  thinLS: "$H, $G |- $E ==> $H, $S, $G |- $E"
 
-  exchRS "$H |- $E, $R, $S, $F ==> $H |- $E, $S, $R, $F"
-  exchLS "$H, $R, $S, $G |- $E ==> $H, $S, $R, $G |- $E"
+  exchRS: "$H |- $E, $R, $S, $F ==> $H |- $E, $S, $R, $F"
+  exchLS: "$H, $R, $S, $G |- $E ==> $H, $S, $R, $G |- $E"
 
-  cut   "[| $H |- $E, P;  $H, P |- $E |] ==> $H |- $E"
+  cut:   "[| $H |- $E, P;  $H, P |- $E |] ==> $H |- $E"
 
   (*Propositional rules*)
 
-  basic "$H, P, $G |- $E, P, $F"
+  basic: "$H, P, $G |- $E, P, $F"
 
-  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"
+  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 |- $E"
+  disjR: "$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 |- $E"
+  impR:  "$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 |- $E"
+  notR:  "$H, P |- $E, $F ==> $H |- $E, ~P, $F"
+  notL:  "$H, $G |- $E, P ==> $H, ~P, $G |- $E"
 
-  FalseL "$H, False, $G |- $E"
+  FalseL: "$H, False, $G |- $E"
 
-  True_def "True == False-->False"
-  iff_def  "P<->Q == (P-->Q) & (Q-->P)"
+  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 |- $E"
+  allR:  "(!!x.$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 |- $E"
+  exR:   "$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, $F"
-  subst "$H(a), $G(a) |- $E(a) ==> $H(b), a=b, $G(b) |- $E(b)"
+  refl:  "$H |- $E, a=a, $F"
+  subst: "$H(a), $G(a) |- $E(a) ==> $H(b), a=b, $G(b) |- $E(b)"
 
   (* Reflection *)
 
-  eq_reflection  "|- x=y ==> (x==y)"
-  iff_reflection "|- P<->Q ==> (P==Q)"
+  eq_reflection:  "|- x=y ==> (x==y)"
+  iff_reflection: "|- P<->Q ==> (P==Q)"
 
   (*Descriptions*)
 
-  The "[| $H |- $E, P(a), $F;  !!x.$H, P(x) |- $E, x=a, $F |] ==> 
+  The: "[| $H |- $E, P(a), $F;  !!x.$H, P(x) |- $E, x=a, $F |] ==>
           $H |- $E, P(THE x. P(x)), $F"
 
 constdefs
-  If :: [o, 'a, 'a] => 'a   ("(if (_)/ then (_)/ else (_))" 10)
+  If :: "[o, 'a, 'a] => 'a"   ("(if (_)/ then (_)/ else (_))" 10)
    "If(P,x,y) == THE z::'a. (P --> z=x) & (~P --> z=y)"
 
 setup
   prover_setup
 
+ML {* use_legacy_bindings (the_context ()) *}
+
 end
 
-ML
 
-
-val parse_translation = [("@Trueprop",Sequents.two_seq_tr "Trueprop")];
-val print_translation = [("Trueprop",Sequents.two_seq_tr' "@Trueprop")];
-




