# HG changeset patch
# User nipkow
# Date 764321311 -3600
# Node ID 385d51d74f7183bde49285ee9733cdb6b8e668c7
# Parent  d9096849bd8efe9df8278377f76bdfb74990aad4
Used Datatype functor to define propositional logic terms.

diff -r d9096849bd8e -r 385d51d74f71 ex/PL.ML
--- a/ex/PL.ML	Tue Mar 22 08:26:25 1994 +0100
+++ b/ex/PL.ML	Tue Mar 22 08:28:31 1994 +0100
@@ -1,10 +1,9 @@
-(*  Title: 	HOL/ex/prop-log.ML
+(*  Title: 	HOL/ex/pl.ML
     ID:         $Id$
     Author: 	Tobias Nipkow & Lawrence C Paulson
-    Copyright   1993  TU Muenchen & University of Cambridge
+    Copyright   1994  TU Muenchen & University of Cambridge
 
-For ex/prop-log.thy.  Inductive definition of propositional logic.
-Soundness and completeness w.r.t. truth-tables.
+Soundness and completeness of propositional logic w.r.t. truth-tables.
 
 Prove: If H|=p then G|=p where G:Fin(H)
 *)
@@ -136,7 +135,8 @@
 
 (** The function eval **)
 
-val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp];
+val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp]
+                            @ PL0.inject @ PL0.ineq;
 
 goalw PL.thy [eval_def] "tt[false] = False";
 by (simp_tac pl_ss 1);
@@ -213,8 +213,7 @@
 (*This formulation is required for strong induction hypotheses*)
 goal PL.thy "hyps(p,tt) |- if(tt[p], p, p->false)";
 by (rtac (expand_if RS iffD2) 1);
-by(res_inst_tac[("x","p")]spec 1);
-by (rtac pl_ind 1);
+by(PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss addsimps [conseq_I, conseq_H])));
 by (fast_tac (set_cs addIs [weaken_left_Un1, weaken_left_Un2, 
 			   weaken_right, imp_false]
@@ -250,25 +249,24 @@
 
 (*For the case hyps(p,t)-insert(#v,Y) |- p;
   we also have hyps(p,t)-{#v} <= hyps(p, t-{v}) *)
-goal PL.thy "!p.hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
 by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [sym RS var_neq_imp] addSDs [var_inject]) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_Diff = result() RS spec;
+val hyps_Diff = result();
 
 (*For the case hyps(p,t)-insert(#v -> false,Y) |- p;
   we also have hyps(p,t)-{(#v)->false} <= hyps(p, insert(v,t)) *)
-goal PL.thy "!p.hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
-by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [var_neq_imp, imp_inject] addSDs [var_inject]) 1);
+by (simp_tac (pl_ss addsimps [insert_subset]
+                    setloop (split_tac [expand_if])) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_insert = result() RS spec;
+val hyps_insert = result();
 
 (** Two lemmas for use with weaken_left **)
 
@@ -282,11 +280,11 @@
 
 (*The set hyps(p,t) is finite, and elements have the form #v or #v->false;
  could probably prove the stronger hyps(p,t) : Fin(hyps(p,{}) Un hyps(p,nat))*)
-goal PL.thy "!p.hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss setloop (split_tac [expand_if])) THEN'
               fast_tac (set_cs addSIs [Fin_0I, Fin_insertI, Fin_UnI])));
-val hyps_finite = result() RS spec;
+val hyps_finite = result();
 
 val Diff_weaken_left = subset_refl RSN (2, Diff_mono) RS weaken_left;
 
@@ -341,4 +339,3 @@
 
 writeln"Reached end of file.";
 
-
diff -r d9096849bd8e -r 385d51d74f71 ex/PL.thy
--- a/ex/PL.thy	Tue Mar 22 08:26:25 1994 +0100
+++ b/ex/PL.thy	Tue Mar 22 08:28:31 1994 +0100
@@ -1,24 +1,18 @@
-(*  Title: 	HOL/ex/prop-log
+(*  Title: 	HOL/ex/pl.thy
     ID:         $Id$
     Author: 	Tobias Nipkow
-    Copyright   1991  University of Cambridge
+    Copyright   1994  TU Muenchen
 
 Inductive definition of propositional logic.
-
 *)
 
-PL = Finite +
-types pl 1
-arities pl :: (term)term
+PL = Finite + PL0 +
 consts
-    false	:: "'a pl"
-    "->"	:: "['a pl,'a pl] => 'a pl"	(infixr 90)
-    var		:: "'a => 'a pl"		("#_")
-    pl_rec	:: "['a pl,'a => 'b, 'b, ['b,'b] => 'b] => 'b"
     axK,axS,axDN:: "'a pl set"
     ruleMP,thms :: "'a pl set => 'a pl set"
     "|-" 	:: "['a pl set, 'a pl] => bool"	(infixl 50)
     "|="	:: "['a pl set, 'a pl] => bool"	(infixl 50)
+    pl_rec	:: "['a pl,'a => 'b, 'b, ['b,'b] => 'b] => 'b"
     eval	:: "['a set, 'a pl] => bool"	("_[_]" [100,0] 100)
     hyps	:: "['a pl, 'a set] => 'a pl set"
 rules
@@ -39,17 +33,13 @@
 
     sat_def "H |= p  ==  (!tt. (!q:H. tt[q]) --> tt[p])"
 
-pl_rec_var   "pl_rec(#v,f,y,z)    = f(v)"
-pl_rec_false "pl_rec(false,f,y,z) = y"
-pl_rec_imp   "pl_rec(p->q,f,y,g)  = g(pl_rec(p,f,y,g),pl_rec(q,f,y,g))"
-
-eval_def "tt[p] == pl_rec(p, %v.v:tt, False, op -->)"
+    pl_rec_var   "pl_rec(#v,f,y,z)    = f(v)"
+    pl_rec_false "pl_rec(false,f,y,z) = y"
+    pl_rec_imp   "pl_rec(p->q,f,y,g)  = g(pl_rec(p,f,y,g),pl_rec(q,f,y,g))"
 
-hyps_def
- "hyps(p,tt) == pl_rec(p, %a. {if(a:tt, #a, (#a)->false)}, {}, op Un)"
+    eval_def "tt[p] == pl_rec(p, %v.v:tt, False, op -->)"
 
-var_inject "(#v = #w) ==> v = w"
-imp_inject "[| (p -> q) = (p' -> q'); [| p = p'; q = q' |] ==> R |] ==> R"
-var_neq_imp "(#v = (p -> q)) ==> R"
-pl_ind "[| P(false); !!v. P(#v); !!p q. P(p)-->P(q)-->P(p->q)|] ==> !t.P(t)"
+    hyps_def
+      "hyps(p,tt) == pl_rec(p, %a. {if(a:tt, #a, (#a)->false)}, {}, op Un)"
+
 end
diff -r d9096849bd8e -r 385d51d74f71 ex/PL0.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/PL0.ML	Tue Mar 22 08:28:31 1994 +0100
@@ -0,0 +1,12 @@
+(*  Title: 	HOL/ex/pl0.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994  TU Muenchen
+
+Inductive definition of propositional logic formulae.
+*)
+
+structure PL0 = DeclaredDatatype
+(val base = PL0.thy
+ val data = "'a pl = false | var('a) | \"op->\"('a pl,'a pl)"
+);
diff -r d9096849bd8e -r 385d51d74f71 ex/PL0.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/PL0.thy	Tue Mar 22 08:28:31 1994 +0100
@@ -0,0 +1,16 @@
+(*  Title: 	HOL/ex/pl0.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994  TU Muenchen
+
+Syntax of propositional logic formulae.
+*)
+
+PL0 = HOL +
+types 'a pl
+arities pl :: (term)term
+consts
+    false	:: "'a pl"
+    "->"	:: "['a pl,'a pl] => 'a pl"	(infixr 90)
+    var		:: "'a => 'a pl"		("#_")
+end
diff -r d9096849bd8e -r 385d51d74f71 ex/pl.ML
--- a/ex/pl.ML	Tue Mar 22 08:26:25 1994 +0100
+++ b/ex/pl.ML	Tue Mar 22 08:28:31 1994 +0100
@@ -1,10 +1,9 @@
-(*  Title: 	HOL/ex/prop-log.ML
+(*  Title: 	HOL/ex/pl.ML
     ID:         $Id$
     Author: 	Tobias Nipkow & Lawrence C Paulson
-    Copyright   1993  TU Muenchen & University of Cambridge
+    Copyright   1994  TU Muenchen & University of Cambridge
 
-For ex/prop-log.thy.  Inductive definition of propositional logic.
-Soundness and completeness w.r.t. truth-tables.
+Soundness and completeness of propositional logic w.r.t. truth-tables.
 
 Prove: If H|=p then G|=p where G:Fin(H)
 *)
@@ -136,7 +135,8 @@
 
 (** The function eval **)
 
-val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp];
+val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp]
+                            @ PL0.inject @ PL0.ineq;
 
 goalw PL.thy [eval_def] "tt[false] = False";
 by (simp_tac pl_ss 1);
@@ -213,8 +213,7 @@
 (*This formulation is required for strong induction hypotheses*)
 goal PL.thy "hyps(p,tt) |- if(tt[p], p, p->false)";
 by (rtac (expand_if RS iffD2) 1);
-by(res_inst_tac[("x","p")]spec 1);
-by (rtac pl_ind 1);
+by(PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss addsimps [conseq_I, conseq_H])));
 by (fast_tac (set_cs addIs [weaken_left_Un1, weaken_left_Un2, 
 			   weaken_right, imp_false]
@@ -250,25 +249,24 @@
 
 (*For the case hyps(p,t)-insert(#v,Y) |- p;
   we also have hyps(p,t)-{#v} <= hyps(p, t-{v}) *)
-goal PL.thy "!p.hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
 by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [sym RS var_neq_imp] addSDs [var_inject]) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_Diff = result() RS spec;
+val hyps_Diff = result();
 
 (*For the case hyps(p,t)-insert(#v -> false,Y) |- p;
   we also have hyps(p,t)-{(#v)->false} <= hyps(p, insert(v,t)) *)
-goal PL.thy "!p.hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
-by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [var_neq_imp, imp_inject] addSDs [var_inject]) 1);
+by (simp_tac (pl_ss addsimps [insert_subset]
+                    setloop (split_tac [expand_if])) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_insert = result() RS spec;
+val hyps_insert = result();
 
 (** Two lemmas for use with weaken_left **)
 
@@ -282,11 +280,11 @@
 
 (*The set hyps(p,t) is finite, and elements have the form #v or #v->false;
  could probably prove the stronger hyps(p,t) : Fin(hyps(p,{}) Un hyps(p,nat))*)
-goal PL.thy "!p.hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss setloop (split_tac [expand_if])) THEN'
               fast_tac (set_cs addSIs [Fin_0I, Fin_insertI, Fin_UnI])));
-val hyps_finite = result() RS spec;
+val hyps_finite = result();
 
 val Diff_weaken_left = subset_refl RSN (2, Diff_mono) RS weaken_left;
 
@@ -341,4 +339,3 @@
 
 writeln"Reached end of file.";
 
-
diff -r d9096849bd8e -r 385d51d74f71 ex/pl.thy
--- a/ex/pl.thy	Tue Mar 22 08:26:25 1994 +0100
+++ b/ex/pl.thy	Tue Mar 22 08:28:31 1994 +0100
@@ -1,24 +1,18 @@
-(*  Title: 	HOL/ex/prop-log
+(*  Title: 	HOL/ex/pl.thy
     ID:         $Id$
     Author: 	Tobias Nipkow
-    Copyright   1991  University of Cambridge
+    Copyright   1994  TU Muenchen
 
 Inductive definition of propositional logic.
-
 *)
 
-PL = Finite +
-types pl 1
-arities pl :: (term)term
+PL = Finite + PL0 +
 consts
-    false	:: "'a pl"
-    "->"	:: "['a pl,'a pl] => 'a pl"	(infixr 90)
-    var		:: "'a => 'a pl"		("#_")
-    pl_rec	:: "['a pl,'a => 'b, 'b, ['b,'b] => 'b] => 'b"
     axK,axS,axDN:: "'a pl set"
     ruleMP,thms :: "'a pl set => 'a pl set"
     "|-" 	:: "['a pl set, 'a pl] => bool"	(infixl 50)
     "|="	:: "['a pl set, 'a pl] => bool"	(infixl 50)
+    pl_rec	:: "['a pl,'a => 'b, 'b, ['b,'b] => 'b] => 'b"
     eval	:: "['a set, 'a pl] => bool"	("_[_]" [100,0] 100)
     hyps	:: "['a pl, 'a set] => 'a pl set"
 rules
@@ -39,17 +33,13 @@
 
     sat_def "H |= p  ==  (!tt. (!q:H. tt[q]) --> tt[p])"
 
-pl_rec_var   "pl_rec(#v,f,y,z)    = f(v)"
-pl_rec_false "pl_rec(false,f,y,z) = y"
-pl_rec_imp   "pl_rec(p->q,f,y,g)  = g(pl_rec(p,f,y,g),pl_rec(q,f,y,g))"
-
-eval_def "tt[p] == pl_rec(p, %v.v:tt, False, op -->)"
+    pl_rec_var   "pl_rec(#v,f,y,z)    = f(v)"
+    pl_rec_false "pl_rec(false,f,y,z) = y"
+    pl_rec_imp   "pl_rec(p->q,f,y,g)  = g(pl_rec(p,f,y,g),pl_rec(q,f,y,g))"
 
-hyps_def
- "hyps(p,tt) == pl_rec(p, %a. {if(a:tt, #a, (#a)->false)}, {}, op Un)"
+    eval_def "tt[p] == pl_rec(p, %v.v:tt, False, op -->)"
 
-var_inject "(#v = #w) ==> v = w"
-imp_inject "[| (p -> q) = (p' -> q'); [| p = p'; q = q' |] ==> R |] ==> R"
-var_neq_imp "(#v = (p -> q)) ==> R"
-pl_ind "[| P(false); !!v. P(#v); !!p q. P(p)-->P(q)-->P(p->q)|] ==> !t.P(t)"
+    hyps_def
+      "hyps(p,tt) == pl_rec(p, %a. {if(a:tt, #a, (#a)->false)}, {}, op Un)"
+
 end
diff -r d9096849bd8e -r 385d51d74f71 ex/pl0.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/pl0.ML	Tue Mar 22 08:28:31 1994 +0100
@@ -0,0 +1,12 @@
+(*  Title: 	HOL/ex/pl0.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994  TU Muenchen
+
+Inductive definition of propositional logic formulae.
+*)
+
+structure PL0 = DeclaredDatatype
+(val base = PL0.thy
+ val data = "'a pl = false | var('a) | \"op->\"('a pl,'a pl)"
+);
diff -r d9096849bd8e -r 385d51d74f71 ex/pl0.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/pl0.thy	Tue Mar 22 08:28:31 1994 +0100
@@ -0,0 +1,16 @@
+(*  Title: 	HOL/ex/pl0.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994  TU Muenchen
+
+Syntax of propositional logic formulae.
+*)
+
+PL0 = HOL +
+types 'a pl
+arities pl :: (term)term
+consts
+    false	:: "'a pl"
+    "->"	:: "['a pl,'a pl] => 'a pl"	(infixr 90)
+    var		:: "'a => 'a pl"		("#_")
+end