MuPAD Pro Computing Essentials - Examples 

Example 11.2 - Polish Notation in Logic 

Here is a nice example showing how Polish notation for logical expressions can be implemented in MuPAD.

• C := (p,q) -> (not p) or q;

• unprotect(E):
  E := (p,q) -> C(p,q) and C(q,p);

• N := p -> not p:
  K := (p,q) -> p and q:
  A := (p,q) -> p or q:
    
• taut := proc(lexpr)

    local p, q, r, BV, bval;

begin

   BV := {TRUE, FALSE};

   bval:=TRUE;

   for p in BV do

      for q in BV do

         for r in BV do

            bval:=bval and bool(lexpr(p,q,r))

         end;

      end;

   end;

   return(bval);

end:

• lexpr1 := (p,q)-> E(N(A(p,q)),K(N(q),N(p)));

• taut(lexpr1);

• lexpr2 := (p,q)-> E(N(K(p,q)),A(N(q),N(p)));

• taut(lexpr2);

• lexpr3 := (p,q)-> E(K(p,A(p,q)),p);

• taut(lexpr3);

• lexpr4 := (p,q)-> E(A(p,K(p,q)),p);

• taut(lexpr4);

• lexpr5 := (p,q)-> E(A(p,K(p,q)),q);

• taut(lexpr5);