--- a/src/FOL/IsaMakefile Sun Jul 22 21:20:58 2007 +0200
+++ b/src/FOL/IsaMakefile Sun Jul 22 22:01:30 2007 +0200
@@ -50,7 +50,9 @@
ex/If.thy ex/IffOracle.thy ex/LocaleTest.thy \
ex/Nat.thy ex/Natural_Numbers.thy ex/Miniscope.thy \
ex/Prolog.thy ex/ROOT.ML ex/Classical.thy ex/document/root.tex \
- ex/Foundation.thy ex/Intuitionistic.thy ex/Intro.thy ex/prop.ML ex/quant.ML
+ ex/Foundation.thy ex/Intuitionistic.thy ex/Intro.thy \
+ ex/Propositional_Int.thy ex/Propositional_Cla.thy \
+ ex/Quantifiers_Int.thy ex/Quantifiers_Cla.thy
@$(ISATOOL) usedir $(OUT)/FOL ex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Propositional_Cla.thy Sun Jul 22 22:01:30 2007 +0200
@@ -0,0 +1,118 @@
+(* Title: FOL/ex/Propositional_Cla.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1991 University of Cambridge
+*)
+
+header {* First-Order Logic: propositional examples (classical version) *}
+
+theory Propositional_Cla
+imports FOL
+begin
+
+text {* commutative laws of @{text "&"} and @{text "|"} *}
+
+lemma "P & Q --> Q & P"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "P | Q --> Q | P"
+ by fast
+
+
+text {* associative laws of @{text "&"} and @{text "|"} *}
+lemma "(P & Q) & R --> P & (Q & R)"
+ by fast
+
+lemma "(P | Q) | R --> P | (Q | R)"
+ by fast
+
+
+text {* distributive laws of @{text "&"} and @{text "|"} *}
+lemma "(P & Q) | R --> (P | R) & (Q | R)"
+ by fast
+
+lemma "(P | R) & (Q | R) --> (P & Q) | R"
+ by fast
+
+lemma "(P | Q) & R --> (P & R) | (Q & R)"
+ by fast
+
+lemma "(P & R) | (Q & R) --> (P | Q) & R"
+ by fast
+
+
+text {* Laws involving implication *}
+
+lemma "(P-->R) & (Q-->R) <-> (P|Q --> R)"
+ by fast
+
+lemma "(P & Q --> R) <-> (P--> (Q-->R))"
+ by fast
+
+lemma "((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
+ by fast
+
+lemma "~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
+ by fast
+
+lemma "(P --> Q & R) <-> (P-->Q) & (P-->R)"
+ by fast
+
+
+text {* Propositions-as-types *}
+
+-- {* The combinator K *}
+lemma "P --> (Q --> P)"
+ by fast
+
+-- {* The combinator S *}
+lemma "(P-->Q-->R) --> (P-->Q) --> (P-->R)"
+ by fast
+
+
+-- {* Converse is classical *}
+lemma "(P-->Q) | (P-->R) --> (P --> Q | R)"
+ by fast
+
+lemma "(P-->Q) --> (~Q --> ~P)"
+ by fast
+
+
+text {* Schwichtenberg's examples (via T. Nipkow) *}
+
+lemma stab_imp: "(((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
+ by fast
+
+lemma stab_to_peirce:
+ "(((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)
+ --> ((P --> Q) --> P) --> P"
+ by fast
+
+lemma peirce_imp1: "(((Q --> R) --> Q) --> Q)
+ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
+ by fast
+
+lemma peirce_imp2: "(((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
+ by fast
+
+lemma mints: "((((P --> Q) --> P) --> P) --> Q) --> Q"
+ by fast
+
+lemma mints_solovev: "(P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
+ by fast
+
+lemma tatsuta: "(((P7 --> P1) --> P10) --> P4 --> P5)
+ --> (((P8 --> P2) --> P9) --> P3 --> P10)
+ --> (P1 --> P8) --> P6 --> P7
+ --> (((P3 --> P2) --> P9) --> P4)
+ --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5"
+ by fast
+
+lemma tatsuta1: "(((P8 --> P2) --> P9) --> P3 --> P10)
+ --> (((P3 --> P2) --> P9) --> P4)
+ --> (((P6 --> P1) --> P2) --> P9)
+ --> (((P7 --> P1) --> P10) --> P4 --> P5)
+ --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5"
+ by fast
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Propositional_Int.thy Sun Jul 22 22:01:30 2007 +0200
@@ -0,0 +1,118 @@
+(* Title: FOL/ex/Propositional_Int.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1991 University of Cambridge
+*)
+
+header {* First-Order Logic: propositional examples (intuitionistic version) *}
+
+theory Propositional_Int
+imports IFOL
+begin
+
+text {* commutative laws of @{text "&"} and @{text "|"} *}
+
+lemma "P & Q --> Q & P"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "P | Q --> Q | P"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* associative laws of @{text "&"} and @{text "|"} *}
+lemma "(P & Q) & R --> P & (Q & R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P | Q) | R --> P | (Q | R)"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* distributive laws of @{text "&"} and @{text "|"} *}
+lemma "(P & Q) | R --> (P | R) & (Q | R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P | R) & (Q | R) --> (P & Q) | R"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P | Q) & R --> (P & R) | (Q & R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P & R) | (Q & R) --> (P | Q) & R"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Laws involving implication *}
+
+lemma "(P-->R) & (Q-->R) <-> (P|Q --> R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P & Q --> R) <-> (P--> (Q-->R))"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P --> Q & R) <-> (P-->Q) & (P-->R)"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Propositions-as-types *}
+
+-- {* The combinator K *}
+lemma "P --> (Q --> P)"
+ by (tactic "IntPr.fast_tac 1")
+
+-- {* The combinator S *}
+lemma "(P-->Q-->R) --> (P-->Q) --> (P-->R)"
+ by (tactic "IntPr.fast_tac 1")
+
+
+-- {* Converse is classical *}
+lemma "(P-->Q) | (P-->R) --> (P --> Q | R)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(P-->Q) --> (~Q --> ~P)"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Schwichtenberg's examples (via T. Nipkow) *}
+
+lemma stab_imp: "(((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma stab_to_peirce:
+ "(((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)
+ --> ((P --> Q) --> P) --> P"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma peirce_imp1: "(((Q --> R) --> Q) --> Q)
+ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma peirce_imp2: "(((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma mints: "((((P --> Q) --> P) --> P) --> Q) --> Q"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma mints_solovev: "(P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma tatsuta: "(((P7 --> P1) --> P10) --> P4 --> P5)
+ --> (((P8 --> P2) --> P9) --> P3 --> P10)
+ --> (P1 --> P8) --> P6 --> P7
+ --> (((P3 --> P2) --> P9) --> P4)
+ --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma tatsuta1: "(((P8 --> P2) --> P9) --> P3 --> P10)
+ --> (((P3 --> P2) --> P9) --> P4)
+ --> (((P6 --> P1) --> P2) --> P9)
+ --> (((P7 --> P1) --> P10) --> P4 --> P5)
+ --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5"
+ by (tactic "IntPr.fast_tac 1")
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Quantifiers_Cla.thy Sun Jul 22 22:01:30 2007 +0200
@@ -0,0 +1,101 @@
+(* Title: FOL/ex/Quantifiers_Int.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1991 University of Cambridge
+*)
+
+header {* First-Order Logic: quantifier examples (classical version) *}
+
+theory Quantifiers_Cla
+imports FOL
+begin
+
+lemma "(ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
+ by fast
+
+lemma "(EX x y. P(x,y)) --> (EX y x. P(x,y))"
+ by fast
+
+
+-- {* Converse is false *}
+lemma "(ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
+ by fast
+
+lemma "(ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
+ by fast
+
+
+lemma "(ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
+ by fast
+
+
+text {* Some harder ones *}
+
+lemma "(EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
+ by fast
+
+-- {* Converse is false *}
+lemma "(EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"
+ by fast
+
+
+text {* Basic test of quantifier reasoning *}
+
+-- {* TRUE *}
+lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
+ by fast
+
+lemma "(ALL x. Q(x)) --> (EX x. Q(x))"
+ by fast
+
+
+text {* The following should fail, as they are false! *}
+
+lemma "(ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
+ apply fast?
+ oops
+
+lemma "(EX x. Q(x)) --> (ALL x. Q(x))"
+ apply fast?
+ oops
+
+lemma "P(?a) --> (ALL x. P(x))"
+ apply fast?
+ oops
+
+lemma "(P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"
+ apply fast?
+ oops
+
+
+text {* Back to things that are provable \dots *}
+
+lemma "(ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"
+ by fast
+
+-- {* An example of why exI should be delayed as long as possible *}
+lemma "(P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
+ by fast
+
+lemma "(ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"
+ by fast
+
+lemma "(ALL x. Q(x)) --> (EX x. Q(x))"
+ by fast
+
+
+text {* Some slow ones *}
+
+-- {* Principia Mathematica *11.53 *}
+lemma "(ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"
+ by fast
+
+(*Principia Mathematica *11.55 *)
+lemma "(EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"
+ by fast
+
+(*Principia Mathematica *11.61 *)
+lemma "(EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"
+ by fast
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Quantifiers_Int.thy Sun Jul 22 22:01:30 2007 +0200
@@ -0,0 +1,101 @@
+(* Title: FOL/ex/Quantifiers_Int.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1991 University of Cambridge
+*)
+
+header {* First-Order Logic: quantifier examples (intuitionistic version) *}
+
+theory Quantifiers_Int
+imports IFOL
+begin
+
+lemma "(ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(EX x y. P(x,y)) --> (EX y x. P(x,y))"
+ by (tactic "IntPr.fast_tac 1")
+
+
+-- {* Converse is false *}
+lemma "(ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
+ by (tactic "IntPr.fast_tac 1")
+
+
+lemma "(ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Some harder ones *}
+
+lemma "(EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+-- {* Converse is false *}
+lemma "(EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Basic test of quantifier reasoning *}
+
+-- {* TRUE *}
+lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* The following should fail, as they are false! *}
+
+lemma "(ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
+ apply (tactic "IntPr.fast_tac 1")?
+ oops
+
+lemma "(EX x. Q(x)) --> (ALL x. Q(x))"
+ apply (tactic "IntPr.fast_tac 1")?
+ oops
+
+lemma "P(?a) --> (ALL x. P(x))"
+ apply (tactic "IntPr.fast_tac 1")?
+ oops
+
+lemma "(P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"
+ apply (tactic "IntPr.fast_tac 1")?
+ oops
+
+
+text {* Back to things that are provable \dots *}
+
+lemma "(ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+-- {* An example of why exI should be delayed as long as possible *}
+lemma "(P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"
+ by (tactic "IntPr.fast_tac 1")
+
+lemma "(ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic "IntPr.fast_tac 1")
+
+
+text {* Some slow ones *}
+
+-- {* Principia Mathematica *11.53 *}
+lemma "(ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"
+ by (tactic "IntPr.fast_tac 1")
+
+(*Principia Mathematica *11.55 *)
+lemma "(EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"
+ by (tactic "IntPr.fast_tac 1")
+
+(*Principia Mathematica *11.61 *)
+lemma "(EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"
+ by (tactic "IntPr.fast_tac 1")
+
+end
--- a/src/FOL/ex/ROOT.ML Sun Jul 22 21:20:58 2007 +0200
+++ b/src/FOL/ex/ROOT.ML Sun Jul 22 22:01:30 2007 +0200
@@ -6,31 +6,27 @@
Examples for First-Order Logic.
*)
-time_use_thy "First_Order_Logic";
-time_use_thy "Natural_Numbers";
-time_use_thy "Intro";
-time_use_thy "Nat";
-time_use_thy "Foundation";
-time_use_thy "Prolog";
-
-time_use_thy "Intuitionistic";
-
-val thy = theory "IFOL" and tac = IntPr.fast_tac 1;
-time_use "prop.ML";
-time_use "quant.ML";
+use_thys [
+ "First_Order_Logic",
+ "Natural_Numbers",
+ "Intro",
+ "Nat",
+ "Foundation",
+ "Prolog",
-writeln"\n** Classical examples **\n";
-time_use_thy "Miniscope";
-time_use_thy "Classical";
-time_use_thy "If";
+ "Intuitionistic",
+ "Propositional_Int",
+ "Quantifiers_Int",
-val thy = theory "FOL" and tac = Cla.fast_tac FOL_cs 1;
-time_use "prop.ML";
-time_use "quant.ML";
+ "Classical",
+ "Propositional_Cla",
+ "Quantifiers_Cla",
+ "Miniscope",
+ "If",
-time_use_thy "NatClass";
-
-time_use_thy "IffOracle";
+ "NatClass",
+ "IffOracle"
+];
(*regression test for locales -- sets several global flags!*)
-time_use_thy "LocaleTest";
+no_document use_thy "LocaleTest";
--- a/src/FOL/ex/prop.ML Sun Jul 22 21:20:58 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,153 +0,0 @@
-(* Title: FOL/ex/prop
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1991 University of Cambridge
-
-First-Order Logic: propositional examples (intuitionistic and classical)
-Needs declarations of the theory "thy" and the tactic "tac"
-*)
-
-writeln"File FOL/ex/prop.";
-
-
-writeln"commutative laws of & and | ";
-Goal "P & Q --> Q & P";
-by tac;
-result();
-
-Goal "P | Q --> Q | P";
-by tac;
-result();
-
-
-writeln"associative laws of & and | ";
-Goal "(P & Q) & R --> P & (Q & R)";
-by tac;
-result();
-
-Goal "(P | Q) | R --> P | (Q | R)";
-by tac;
-result();
-
-
-
-writeln"distributive laws of & and | ";
-Goal "(P & Q) | R --> (P | R) & (Q | R)";
-by tac;
-result();
-
-Goal "(P | R) & (Q | R) --> (P & Q) | R";
-by tac;
-result();
-
-Goal "(P | Q) & R --> (P & R) | (Q & R)";
-by tac;
-result();
-
-
-Goal "(P & R) | (Q & R) --> (P | Q) & R";
-by tac;
-result();
-
-
-writeln"Laws involving implication";
-
-Goal "(P-->R) & (Q-->R) <-> (P|Q --> R)";
-by tac;
-result();
-
-
-Goal "(P & Q --> R) <-> (P--> (Q-->R))";
-by tac;
-result();
-
-
-Goal "((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R";
-by tac;
-result();
-
-Goal "~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)";
-by tac;
-result();
-
-Goal "(P --> Q & R) <-> (P-->Q) & (P-->R)";
-by tac;
-result();
-
-
-writeln"Propositions-as-types";
-
-(*The combinator K*)
-Goal "P --> (Q --> P)";
-by tac;
-result();
-
-(*The combinator S*)
-Goal "(P-->Q-->R) --> (P-->Q) --> (P-->R)";
-by tac;
-result();
-
-
-(*Converse is classical*)
-Goal "(P-->Q) | (P-->R) --> (P --> Q | R)";
-by tac;
-result();
-
-Goal "(P-->Q) --> (~Q --> ~P)";
-by tac;
-result();
-
-
-writeln"Schwichtenberg's examples (via T. Nipkow)";
-
-(* stab-imp *)
-Goal "(((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q";
-by tac;
-result();
-
-(* stab-to-peirce *)
-Goal "(((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \
-\ --> ((P --> Q) --> P) --> P";
-by tac;
-result();
-
-(* peirce-imp1 *)
-Goal "(((Q --> R) --> Q) --> Q) \
-\ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q";
-by tac;
-result();
-
-(* peirce-imp2 *)
-Goal "(((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P";
-by tac;
-result();
-
-(* mints *)
-Goal "((((P --> Q) --> P) --> P) --> Q) --> Q";
-by tac;
-result();
-
-(* mints-solovev *)
-Goal "(P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R";
-by tac;
-result();
-
-(* tatsuta *)
-Goal "(((P7 --> P1) --> P10) --> P4 --> P5) \
-\ --> (((P8 --> P2) --> P9) --> P3 --> P10) \
-\ --> (P1 --> P8) --> P6 --> P7 \
-\ --> (((P3 --> P2) --> P9) --> P4) \
-\ --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5";
-by tac;
-result();
-
-(* tatsuta1 *)
-Goal "(((P8 --> P2) --> P9) --> P3 --> P10) \
-\ --> (((P3 --> P2) --> P9) --> P4) \
-\ --> (((P6 --> P1) --> P2) --> P9) \
-\ --> (((P7 --> P1) --> P10) --> P4 --> P5) \
-\ --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5";
-by tac;
-result();
-
-writeln"Reached end of file.";
--- a/src/FOL/ex/quant.ML Sun Jul 22 21:20:58 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,129 +0,0 @@
-(* Title: FOL/ex/quant
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1991 University of Cambridge
-
-First-Order Logic: quantifier examples (intuitionistic and classical)
-Needs declarations of the theory "thy" and the tactic "tac"
-*)
-
-writeln"File FOL/ex/quant.";
-
-Goal "(ALL x y. P(x,y)) --> (ALL y x. P(x,y))";
-by tac;
-result();
-
-
-Goal "(EX x y. P(x,y)) --> (EX y x. P(x,y))";
-by tac;
-result();
-
-
-(*Converse is false*)
-Goal "(ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
-by tac;
-result();
-
-Goal "(ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))";
-by tac;
-result();
-
-
-Goal "(ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)";
-by tac;
-result();
-
-
-writeln"Some harder ones";
-
-Goal "(EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
-by tac;
-result();
-(*6 secs*)
-
-(*Converse is false*)
-Goal "(EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"Basic test of quantifier reasoning";
-(*TRUE*)
-Goal "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))";
-by tac;
-result();
-
-
-Goal "(ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"The following should fail, as they are false!";
-
-Goal "(ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-Goal "(EX x. Q(x)) --> (ALL x. Q(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-getgoal 1;
-
-Goal "P(?a) --> (ALL x. P(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-Goal
- "(P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-getgoal 1;
-
-
-writeln"Back to things that are provable...";
-
-Goal "(ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-(*An example of why exI should be delayed as long as possible*)
-Goal "(P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
-by tac;
-result();
-
-Goal "(ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)";
-by tac;
-(*Verify that no subgoals remain.*)
-uresult();
-
-
-Goal "(ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"Some slow ones";
-
-
-(*Principia Mathematica *11.53 *)
-Goal "(ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))";
-by tac;
-result();
-(*6 secs*)
-
-(*Principia Mathematica *11.55 *)
-Goal "(EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))";
-by tac;
-result();
-(*9 secs*)
-
-(*Principia Mathematica *11.61 *)
-Goal "(EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
-by tac;
-result();
-(*3 secs*)
-
-writeln"Reached end of file.";
-