src/FOL/ex/prop.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/prop.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,153 @@
+(*  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 thy "P & Q  -->  Q & P";
+by tac;
+result();
+
+goal thy "P | Q  -->  Q | P";
+by tac;
+result();
+
+
+writeln"associative laws of & and | ";
+goal thy "(P & Q) & R  -->  P & (Q & R)";
+by tac;
+result();
+
+goal thy "(P | Q) | R  -->  P | (Q | R)";
+by tac;
+result();
+
+
+
+writeln"distributive laws of & and | ";
+goal thy "(P & Q) | R  --> (P | R) & (Q | R)";
+by tac;
+result();
+
+goal thy "(P | R) & (Q | R)  --> (P & Q) | R";
+by tac;
+result();
+
+goal thy "(P | Q) & R  --> (P & R) | (Q & R)";
+by tac;
+result();
+
+
+goal thy "(P & R) | (Q & R)  --> (P | Q) & R";
+by tac;
+result();
+
+
+writeln"Laws involving implication";
+
+goal thy "(P-->R) & (Q-->R) <-> (P|Q --> R)";
+by tac;
+result();
+
+
+goal thy "(P & Q --> R) <-> (P--> (Q-->R))";
+by tac;
+result();
+
+
+goal thy "((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R";
+by tac;
+result();
+
+goal thy "~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)";
+by tac;
+result();
+
+goal thy "(P --> Q & R) <-> (P-->Q)  &  (P-->R)";
+by tac;
+result();
+
+
+writeln"Propositions-as-types";
+
+(*The combinator K*)
+goal thy "P --> (Q --> P)";
+by tac;
+result();
+
+(*The combinator S*)
+goal thy "(P-->Q-->R)  --> (P-->Q) --> (P-->R)";
+by tac;
+result();
+
+
+(*Converse is classical*)
+goal thy "(P-->Q) | (P-->R)  -->  (P --> Q | R)";
+by tac;
+result();
+
+goal thy "(P-->Q)  -->  (~Q --> ~P)";
+by tac;
+result();
+
+
+writeln"Schwichtenberg's examples (via T. Nipkow)";
+
+(* stab-imp *)
+goal thy "(((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q";
+by tac;
+result();
+
+(* stab-to-peirce *)
+goal thy "(((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \
+\	      --> ((P --> Q) --> P) --> P";
+by tac;
+result();
+
+(* peirce-imp1 *)
+goal thy "(((Q --> R) --> Q) --> Q) \
+\	       --> (((P --> Q) --> R) --> P --> Q) --> P --> Q";
+by tac;
+result();
+  
+(* peirce-imp2 *)
+goal thy "(((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P";
+by tac;
+result();
+
+(* mints  *)
+goal thy "((((P --> Q) --> P) --> P) --> Q) --> Q";
+by tac;
+result();
+
+(* mints-solovev *)
+goal thy "(P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R";
+by tac;
+result();
+
+(* tatsuta *)
+goal thy "(((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 thy "(((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.";