By David Gries
Describes the strategies taken with writing compilers for high-level languages resembling FORTRAN or PL/1. Treats either idea and useful elements of compiler writing. Discusses semantic exercises, their reasons and their connection to syntax acceptance.
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C) (C,D) consists it w i l l follow f r o m d e s c r i b e d in this section a l r e a d y gives W h a t w e w i l l do here is to show that w h e n D = d i s c r e t e spaces, w e do not get a c l o s e d category. V(A,-) Thus Thus to show that limits, i t is s u f f i c i e n t to show it has the r i g h t topology. 9) It is n o w a n easy a p p l i c a t i o n o f the s p e c i a l a d j o i n t functor t h e o r e m to show that ~(A,-) has an a d j o i n t w h i c h w e will designate -~A .
4) [ I,B] ~ B b y the Yoneda lemma. This implies that A(C,D)-+ (C,D) is It is easy to see that both of these maps lie over the identity m a p on . Proposition. Proof. The b i f u n c t o r A(-,-) : A_°p x A + A is (or lifts to) a V_-functor. We m u s t s h o w that there are natural maps V(A',A)--+ V(A(A,B),A__(A',B)) V(B,B')--+ V ( A ( A , B ) , A ( A , B ' ) ) for all A,A',A,B'{A . We do the first, the second b e i n g similar. 13). 5) Proposition. (c ,D~)] Suppose A(A,B) is e m b e d d e d in the p r o d u c t 9[V(C .
Be Then f. ) which 3 13 for each j is r a p i d l y d e c r e a s i n g . r.. E D i 13 c r e a s i n g in sufficient . double j . Although sequence versely, into a sequence. logy, it follows hoods of 0 Chapter this m u s t be done (i n ) . for all Thus Clearly (rij) (s i) in IV, C and j < k(i,j) vector space of D especially . ) 13 ~ inj TM Irij I < £ iff of fundamental to i---~ ~ . C a Since Con- or as j ÷~. As for the topo- sequence . ) form a f u n d a m e n t a l takes . function. k---+ ~ . n 2n i ] r..