--- a/src/FOLP/IsaMakefile Wed Mar 26 22:38:17 2008 +0100
+++ b/src/FOLP/IsaMakefile Wed Mar 26 22:38:55 2008 +0100
@@ -26,8 +26,8 @@
Pure:
@cd $(SRC)/Pure; $(ISATOOL) make Pure
-$(OUT)/FOLP: $(OUT)/Pure FOLP.thy IFOLP.thy ROOT.ML \
- classical.ML hypsubst.ML intprover.ML simp.ML simpdata.ML
+$(OUT)/FOLP: $(OUT)/Pure FOLP.thy IFOLP.thy ROOT.ML classical.ML \
+ hypsubst.ML intprover.ML simp.ML simpdata.ML
@$(ISATOOL) usedir -b $(OUT)/Pure FOLP
@@ -35,10 +35,11 @@
FOLP-ex: FOLP $(LOG)/FOLP-ex.gz
-$(LOG)/FOLP-ex.gz: $(OUT)/FOLP ex/ROOT.ML ex/Foundation.thy \
- ex/If.thy ex/Intro.thy ex/Nat.thy ex/Intuitionistic.thy \
- ex/Classical.thy \
- ex/Prolog.ML ex/Prolog.thy ex/prop.ML ex/quant.ML
+$(LOG)/FOLP-ex.gz: $(OUT)/FOLP ex/ROOT.ML ex/Foundation.thy ex/If.thy \
+ ex/Intro.thy ex/Nat.thy ex/Intuitionistic.thy ex/Classical.thy \
+ ex/Prolog.ML ex/Prolog.thy ex/Propositional_Int.thy \
+ ex/Propositional_Cla.thy ex/Quantifiers_Int.thy \
+ ex/Quantifiers_Cla.thy
@$(ISATOOL) usedir $(OUT)/FOLP ex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/ex/Propositional_Cla.thy Wed Mar 26 22:38:55 2008 +0100
@@ -0,0 +1,118 @@
+(* Title: FOLP/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 *}
+
+theory Propositional_Cla
+imports FOLP
+begin
+
+
+text "commutative laws of & and | "
+lemma "?p : P & Q --> Q & P"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : P | Q --> Q | P"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "associative laws of & and | "
+lemma "?p : (P & Q) & R --> P & (Q & R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P | Q) | R --> P | (Q | R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "distributive laws of & and | "
+lemma "?p : (P & Q) | R --> (P | R) & (Q | R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P | R) & (Q | R) --> (P & Q) | R"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P | Q) & R --> (P & R) | (Q & R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+lemma "?p : (P & R) | (Q & R) --> (P | Q) & R"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Laws involving implication"
+
+lemma "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P & Q --> R) <-> (P--> (Q-->R))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P --> Q & R) <-> (P-->Q) & (P-->R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Propositions-as-types"
+
+(*The combinator K*)
+lemma "?p : P --> (Q --> P)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+(*The combinator S*)
+lemma "?p : (P-->Q-->R) --> (P-->Q) --> (P-->R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+(*Converse is classical*)
+lemma "?p : (P-->Q) | (P-->R) --> (P --> Q | R)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (P-->Q) --> (~Q --> ~P)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Schwichtenberg's examples (via T. Nipkow)"
+
+lemma stab_imp: "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma stab_to_peirce: "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)
+ --> ((P --> Q) --> P) --> P"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma peirce_imp1: "?p : (((Q --> R) --> Q) --> Q)
+ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma peirce_imp2: "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma mints: "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma mints_solovev: "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma tatsuta: "?p : (((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 {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma tatsuta1: "?p : (((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 {* Cla.fast_tac FOLP_cs 1 *})
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/ex/Propositional_Int.thy Wed Mar 26 22:38:55 2008 +0100
@@ -0,0 +1,118 @@
+(* Title: FOLP/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 *}
+
+theory Propositional_Int
+imports IFOLP
+begin
+
+
+text "commutative laws of & and | "
+lemma "?p : P & Q --> Q & P"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : P | Q --> Q | P"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "associative laws of & and | "
+lemma "?p : (P & Q) & R --> P & (Q & R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P | Q) | R --> P | (Q | R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "distributive laws of & and | "
+lemma "?p : (P & Q) | R --> (P | R) & (Q | R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P | R) & (Q | R) --> (P & Q) | R"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P | Q) & R --> (P & R) | (Q & R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+lemma "?p : (P & R) | (Q & R) --> (P | Q) & R"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "Laws involving implication"
+
+lemma "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P & Q --> R) <-> (P--> (Q-->R))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P --> Q & R) <-> (P-->Q) & (P-->R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "Propositions-as-types"
+
+(*The combinator K*)
+lemma "?p : P --> (Q --> P)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+(*The combinator S*)
+lemma "?p : (P-->Q-->R) --> (P-->Q) --> (P-->R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+(*Converse is classical*)
+lemma "?p : (P-->Q) | (P-->R) --> (P --> Q | R)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (P-->Q) --> (~Q --> ~P)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "Schwichtenberg's examples (via T. Nipkow)"
+
+lemma stab_imp: "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma stab_to_peirce: "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)
+ --> ((P --> Q) --> P) --> P"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma peirce_imp1: "?p : (((Q --> R) --> Q) --> Q)
+ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma peirce_imp2: "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma mints: "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma mints_solovev: "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma tatsuta: "?p : (((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: "?p : (((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/FOLP/ex/Quantifiers_Cla.thy Wed Mar 26 22:38:55 2008 +0100
@@ -0,0 +1,102 @@
+(* Title: FOLP/ex/Quantifiers_Cla.thy
+ 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"
+*)
+
+theory Quantifiers_Cla
+imports FOLP
+begin
+
+lemma "?p : (ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+(*Converse is false*)
+lemma "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+lemma "?p : (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Some harder ones"
+
+lemma "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+(*Converse is false*)
+lemma "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x)) & (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Basic test of quantifier reasoning"
+(*TRUE*)
+lemma "?p : (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "The following should fail, as they are false!"
+
+lemma "?p : (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
+ apply (tactic {* Cla.fast_tac FOLP_cs 1 *})?
+ oops
+
+lemma "?p : (EX x. Q(x)) --> (ALL x. Q(x))"
+ apply (tactic {* Cla.fast_tac FOLP_cs 1 *})?
+ oops
+
+lemma "?p : P(?a) --> (ALL x. P(x))"
+ apply (tactic {* Cla.fast_tac FOLP_cs 1 *})?
+ oops
+
+lemma "?p : (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))"
+ apply (tactic {* Cla.fast_tac FOLP_cs 1 *})?
+ oops
+
+
+text "Back to things that are provable..."
+
+lemma "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+(*An example of why exI should be delayed as long as possible*)
+lemma "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+lemma "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+
+text "Some slow ones"
+
+(*Principia Mathematica *11.53 *)
+lemma "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+(*Principia Mathematica *11.55 *)
+lemma "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+(*Principia Mathematica *11.61 *)
+lemma "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))"
+ by (tactic {* Cla.fast_tac FOLP_cs 1 *})
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/ex/Quantifiers_Int.thy Wed Mar 26 22:38:55 2008 +0100
@@ -0,0 +1,102 @@
+(* Title: FOLP/ex/Quantifiers_Int.thy
+ 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"
+*)
+
+theory Quantifiers_Int
+imports IFOLP
+begin
+
+lemma "?p : (ALL x y. P(x,y)) --> (ALL y x. P(x,y))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+(*Converse is false*)
+lemma "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+lemma "?p : (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "Some harder ones"
+
+lemma "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+(*Converse is false*)
+lemma "?p : (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 "?p : (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "The following should fail, as they are false!"
+
+lemma "?p : (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))"
+ apply (tactic {* IntPr.fast_tac 1 *})?
+ oops
+
+lemma "?p : (EX x. Q(x)) --> (ALL x. Q(x))"
+ apply (tactic {* IntPr.fast_tac 1 *})?
+ oops
+
+lemma "?p : P(?a) --> (ALL x. P(x))"
+ apply (tactic {* IntPr.fast_tac 1 *})?
+ oops
+
+lemma "?p : (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..."
+
+lemma "?p : (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 : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+lemma "?p : (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 "?p : (ALL x. Q(x)) --> (EX x. Q(x))"
+ by (tactic {* IntPr.fast_tac 1 *})
+
+
+text "Some slow ones"
+
+(*Principia Mathematica *11.53 *)
+lemma "?p : (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 "?p : (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 "?p : (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/FOLP/ex/ROOT.ML Wed Mar 26 22:38:17 2008 +0100
+++ b/src/FOLP/ex/ROOT.ML Wed Mar 26 22:38:55 2008 +0100
@@ -12,13 +12,9 @@
"Foundation",
"If",
"Intuitionistic",
- "Classical"
+ "Classical",
+ "Propositional_Int",
+ "Quantifiers_Int",
+ "Propositional_Cla",
+ "Quantifiers_Cla"
];
-
-val thy = theory "IFOLP" and tac = IntPr.fast_tac 1;
-time_use "prop.ML";
-time_use "quant.ML";
-
-val thy = theory "FOLP" and tac = Cla.fast_tac FOLP_cs 1;
-time_use "prop.ML";
-time_use "quant.ML";
--- a/src/FOLP/ex/prop.ML Wed Mar 26 22:38:17 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,151 +0,0 @@
-(* Title: FOLP/ex/prop.ML
- 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"
-*)
-
-ML_Context.set_context (SOME (Context.Theory thy));
-
-
-writeln"commutative laws of & and | ";
-Goal "?p : P & Q --> Q & P";
-by tac;
-result();
-
-Goal "?p : P | Q --> Q | P";
-by tac;
-result();
-
-
-writeln"associative laws of & and | ";
-Goal "?p : (P & Q) & R --> P & (Q & R)";
-by tac;
-result();
-
-Goal "?p : (P | Q) | R --> P | (Q | R)";
-by tac;
-result();
-
-
-
-writeln"distributive laws of & and | ";
-Goal "?p : (P & Q) | R --> (P | R) & (Q | R)";
-by tac;
-result();
-
-Goal "?p : (P | R) & (Q | R) --> (P & Q) | R";
-by tac;
-result();
-
-Goal "?p : (P | Q) & R --> (P & R) | (Q & R)";
-by tac;
-result();
-
-
-Goal "?p : (P & R) | (Q & R) --> (P | Q) & R";
-by tac;
-result();
-
-
-writeln"Laws involving implication";
-
-Goal "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)";
-by tac;
-result();
-
-
-Goal "?p : (P & Q --> R) <-> (P--> (Q-->R))";
-by tac;
-result();
-
-
-Goal "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R";
-by tac;
-result();
-
-Goal "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)";
-by tac;
-result();
-
-Goal "?p : (P --> Q & R) <-> (P-->Q) & (P-->R)";
-by tac;
-result();
-
-
-writeln"Propositions-as-types";
-
-(*The combinator K*)
-Goal "?p : P --> (Q --> P)";
-by tac;
-result();
-
-(*The combinator S*)
-Goal "?p : (P-->Q-->R) --> (P-->Q) --> (P-->R)";
-by tac;
-result();
-
-
-(*Converse is classical*)
-Goal "?p : (P-->Q) | (P-->R) --> (P --> Q | R)";
-by tac;
-result();
-
-Goal "?p : (P-->Q) --> (~Q --> ~P)";
-by tac;
-result();
-
-
-writeln"Schwichtenberg's examples (via T. Nipkow)";
-
-(* stab-imp *)
-Goal "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q";
-by tac;
-result();
-
-(* stab-to-peirce *)
-Goal "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \
-\ --> ((P --> Q) --> P) --> P";
-by tac;
-result();
-
-(* peirce-imp1 *)
-Goal "?p : (((Q --> R) --> Q) --> Q) \
-\ --> (((P --> Q) --> R) --> P --> Q) --> P --> Q";
-by tac;
-result();
-
-(* peirce-imp2 *)
-Goal "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P";
-by tac;
-result();
-
-(* mints *)
-Goal "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q";
-by tac;
-result();
-
-(* mints-solovev *)
-Goal "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R";
-by tac;
-result();
-
-(* tatsuta *)
-Goal "?p : (((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 "?p : (((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();
--- a/src/FOLP/ex/quant.ML Wed Mar 26 22:38:17 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,124 +0,0 @@
-(* Title: FOLP/ex/quant.ML
- 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"
-*)
-
-Goal "?p : (ALL x y. P(x,y)) --> (ALL y x. P(x,y))";
-by tac;
-result();
-
-
-Goal "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))";
-by tac;
-result();
-
-
-(*Converse is false*)
-Goal "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
-by tac;
-result();
-
-Goal "?p : (ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))";
-by tac;
-result();
-
-
-Goal "?p : (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)";
-by tac;
-result();
-
-
-writeln"Some harder ones";
-
-Goal "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
-by tac;
-result();
-(*6 secs*)
-
-(*Converse is false*)
-Goal "?p : (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 "?p : (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))";
-by tac;
-result();
-
-
-Goal "?p : (ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"The following should fail, as they are false!";
-
-Goal "?p : (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 "?p : (EX x. Q(x)) --> (ALL x. Q(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-getgoal 1;
-
-Goal "?p : P(?a) --> (ALL x. P(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-Goal
- "?p : (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 "?p : (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 : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
-by tac;
-result();
-
-Goal "?p : (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 "?p : (ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"Some slow ones";
-
-
-(*Principia Mathematica *11.53 *)
-Goal "?p : (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 "?p : (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 "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
-by tac;
-result();
-(*3 secs*)