diff -r f04b33ce250f -r a4dc62a46ee4 ex/PropLog.thy --- a/ex/PropLog.thy Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,45 +0,0 @@ -(* Title: HOL/ex/PropLog.thy - ID: $Id$ - Author: Tobias Nipkow - Copyright 1994 TU Muenchen - -Inductive definition of propositional logic. -*) - -PropLog = Finite + -datatype - 'a pl = false | var ('a) ("#_" [1000]) | "->" ('a pl,'a pl) (infixr 90) -consts - thms :: "'a pl set => 'a pl set" - "|-" :: "['a pl set, 'a pl] => bool" (infixl 50) - "|=" :: "['a pl set, 'a pl] => bool" (infixl 50) - eval2 :: "['a pl, 'a set] => bool" - eval :: "['a set, 'a pl] => bool" ("_[_]" [100,0] 100) - hyps :: "['a pl, 'a set] => 'a pl set" - -translations - "H |- p" == "p : thms(H)" - -inductive "thms(H)" - intrs - H "p:H ==> H |- p" - K "H |- p->q->p" - S "H |- (p->q->r) -> (p->q) -> p->r" - DN "H |- ((p->false) -> false) -> p" - MP "[| H |- p->q; H |- p |] ==> H |- q" - -defs - sat_def "H |= p == (!tt. (!q:H. tt[q]) --> tt[p])" - eval_def "tt[p] == eval2(p,tt)" - -primrec eval2 pl - eval2_false "eval2(false) = (%x.False)" - eval2_var "eval2(#v) = (%tt.v:tt)" - eval2_imp "eval2(p->q) = (%tt.eval2(p,tt)-->eval2(q,tt))" - -primrec hyps pl - hyps_false "hyps(false) = (%tt.{})" - hyps_var "hyps(#v) = (%tt.{if(v:tt, #v, #v->false)})" - hyps_imp "hyps(p->q) = (%tt.hyps(p,tt) Un hyps(q,tt))" - -end