--- 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")];
-