LISP I Programmer's Manual - Software Preservation Group

h,~~,pand)Y,SP5a. Rule4>: If j,++h,ly,f,then3 w~,b>q,~.P5b. Rule>+: If h,I/f,pw~and h,P+~,q,thenh,$2v,P+rr.P6a.~6b.Rule +=: 1f 9,s ++ h,cfi~,p,thenS 4 h,Q~*p.~f~,~,h,~+~andh,P~a,$,~,thenh,~~\Y,9(2) The LISP Program. We define a function theorem [s]whose value is truth or falsity according to whether the sequent,- s is theorem.The sequent-is represented by the S-expressionwhere in each case the ellipsis ... denotes missing terms, andwhere y* denotes the S-expression for 9.Propositional formulae are represented as follows:1. For "atomic formulae" (Wangls terminology) we useItatomic symbols l1 (LISP terminology) ,2, The following table gives our "cambridge ~olish" wayof representing propositional formulae with given main connectives.1. W Cf becomes (NOT, y*)2 . ~ 4 becomes ~(AND, 9% y*)3. 9 V becomes (OR, y*, p)4. 3 y becomes (IMPLIES, v*, *)5. 9 Y/ becomes (EQUIV, Cf*, p)Thus the sequentY P & &Q4is represented byPf Q,RVS(ARR~W,((AND,(N~T,P>,(NOT,Q))),((EQ~I~,P,Q),(~R,R,~)))