␈⊃
␈⊃
␈⊃
␈⊃                     SYNTAX DIRECTED COMPUTATION
␈⊃
␈⊃        It  is often  more convenient  to describe  certain  kinds of
␈⊃computation  with  symbolic expressions  by  "syntax transformations"
␈⊃than  by  recursive  LISP  functions.   For  example,   consider  the
␈⊃simplification of  expressions in a  binary  PLUS  and   TIMES  where
␈⊃the number  0  is to be eliminated from sums, the number  1  is to be
␈⊃eliminated from products, products containing  0  are to  be replaced
␈⊃by  0, and  sums and products  of one element  are to be  replaced by
␈⊃that element.   This may be  accomplished by the  function  simplifya
␈⊃defined by
␈⊃        simplifya e ← __ __ e ____ e
                      if at   then
␈⊃                        ____ {simplifya __ e,simplifya ___ e}
                        else            ad             add
␈⊃                        [λwz. __ _ e __ PLUS ____
                              if a   eq      then
␈⊃                                [__ w = 0 ____ z
                                 if       then
␈⊃                                ____ __ z = 0 ____ w
                                else if       then
␈⊃                                ____ _____ _ ___
                                else <PLUS w z>]
␈⊃                                ____ __ w = 0 ∨ z = 0 ____ 0
                                else if               then
␈⊃                                ____ __ w = 1 ____ z
                                else if       then
␈⊃                                ____ __ z = 1 ____ w
                                else if       then
␈⊃                                ____ <TIMES w z>.
                                else
␈⊃