--- 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