src/ZF/ex/PropLog.thy
changeset 0 a5a9c433f639
child 501 9c724f7085f9
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/ZF/ex/PropLog.thy	Thu Sep 16 12:20:38 1993 +0200
     1.3 @@ -0,0 +1,43 @@
     1.4 +(*  Title: 	ZF/ex/prop-log.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Tobias Nipkow & Lawrence C Paulson
     1.7 +    Copyright   1993  University of Cambridge
     1.8 +
     1.9 +Inductive definition of propositional logic.
    1.10 +*)
    1.11 +
    1.12 +PropLog = Prop + Fin +
    1.13 +consts
    1.14 +  (*semantics*)
    1.15 +  prop_rec :: "[i, i, i=>i, [i,i,i,i]=>i] => i"
    1.16 +  is_true  :: "[i,i] => o"
    1.17 +  "|="     :: "[i,i] => o"    			(infixl 50)
    1.18 +  hyps     :: "[i,i] => i"
    1.19 +
    1.20 +  (*proof theory*)
    1.21 +  thms     :: "i => i"
    1.22 +  "|-"     :: "[i,i] => o"    			(infixl 50)
    1.23 +
    1.24 +translations
    1.25 +  "H |- p" == "p : thms(H)"
    1.26 +
    1.27 +rules
    1.28 +
    1.29 +  prop_rec_def
    1.30 +   "prop_rec(p,b,c,h) == \
    1.31 +\   Vrec(p, %p g.prop_case(b, c, %x y. h(x, y, g`x, g`y), p))"
    1.32 +
    1.33 +  (** Semantics of propositional logic **)
    1.34 +  is_true_def
    1.35 +   "is_true(p,t) == prop_rec(p, 0,  %v. if(v:t, 1, 0), \
    1.36 +\                               %p q tp tq. if(tp=1,tq,1))         =  1"
    1.37 +
    1.38 +  (*For every valuation, if all elements of H are true then so is p*)
    1.39 +  sat_def     "H |= p == ALL t. (ALL q:H. is_true(q,t)) --> is_true(p,t)"
    1.40 +
    1.41 +  (** A finite set of hypotheses from t and the Vars in p **)
    1.42 +  hyps_def
    1.43 +   "hyps(p,t) == prop_rec(p, 0,  %v. {if(v:t, #v, #v=>Fls)}, \
    1.44 +\                            %p q Hp Hq. Hp Un Hq)"
    1.45 +
    1.46 +end