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By Michael J. Gordon, Arthur J. Milner, Christopher P. Wadsworth (auth.)

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Extra info for Edinburgh LCF: A Mechanised Logic of Computation

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N o t i c e that functions. Type values of an a b s t r a c t type are printed as * "-" like # 0perators B o t h "list" and "#" are e x a m p l e s of type o p e r a t o r s ; "list" has one argument (hence "* list") w h e r e a s "#" has two (hence "* # **"). E a c h type o p e r a t o r has v a r i o u s p r i m i t i v e o p e r a t i o n s a s s o c i a t e d w i t h it, for example "list" has "null", "hd", "tl",... etc, and "#" has "fst", "snd" and the infix "," * .

For e x a m p l e trees a n a l o g o u s to LISP S - e x p r e s s i o n s c o u l d be d e f i n e d by: 4-- . . . . . . . . . 4 # a b s r e c t y p e * s e x p = 4 + (, sexp) # (* sexp) # with cons(sl,s2) = abssexp(inr(sl,s2)) # and car s = f s t ( o u t r ( r e p s e x p s)) # and cdr s = s n d ( o u t r ( r e p s e x p s)) # and a t o m s = i s l ( r e p s e x p s) # and m a k e a t o m a = a b s s e x p ( i n l a);; cons = - : (((* sexp) # (* sexp)) -> (* sexp)) car = - : ((** sexp) -> (** sexp)) cdr = - : ((*** sexp) -> (*** sexp)) a t o m = - : ((**** sexp) -> bool) m a k e a t o m = - : (***** -> (***** sexp)) * .

E. to the beginning of "if el ... "). In the case that all of el,e2 ... ,en return false, and there is a phrase following en', then if this is "else e'" control is passed to e', whilst if it is "loop e'" then e' is evaluated for its side effects and control is then passed back to the beginning of the whole expression again. e. ") is returned. but no phrase is absent - then 42 .... \id} e'} e is evaluated and if this succeeds its value is returned. In the case that e fails, with failure token tok say, then each of el,e2 ...

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