By C A R Hoare

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Fortunately, LISP is very suitable for this purpose. Traces are represented in the obvious way by lists of atoms representing their events = NIL coin = (cons("COIN , NIL)) coin, choc = " (COIN CHOC) which means cons("COIN , cons("CHOC, NIL)) Operations on traces can be readily implemented as functions on lists. For example, the head and tail of a nonempty list are given by the primitive functions car and cdr t0 = car (t ) t = cdr (t ) s = cons(x, s) x General catenation is implemented as the familiar append function, which is defined by recursion s t = append(s, t ) where append(s, t ) = if s = NIL then t else cons(car (s), append(cdr (s), t )) The correctness of this definition follows from the laws t =t s t = s0 (s t) whenever s ≠ The termination of the LISP append function is guaranteed by the fact that the list supplied as the first argument of each recursive call is shorter than it was at the previous level of recursion.

For example, since STOP never engages in any event, this is the only result it can ever give, and so it is defined STOP = λ x • "BLEEP But if the actual argument is a possible event for the process, the function gives back as its result another function, representing the subsequent behaviour of the process. , STOP ) as the result of a function. LISP also allows a function to be passed as an argument to a function, a facility used in representing a general prefix operation (c → P) prefix(c, P ) = λ x • if x = c then P else "BLEEP A function to represent a general binary choice (c → P | d → Q) requires four parameters choice2(c, P , d, Q ) = λ x • if x = c then P else if x = d then Q else "BLEEP Recursively defined processes may be represented with the aid of the LABEL feature of LISP.

In this construction, x is a local variable, so (x : B → P (x)) = (y : B → P (y)) The set B defines the initial menu of the process, since it gives the set of actions between which a choice is to be made at the start. Examples X8 A process which at all times can engage in any event of its alphabet A αRUNA = A RUNA = (x : A → RUNA ) In the special case that the menu contains only one event e, (x : {e} → P (x)) = (e → P (e)) since e is the only possible initial event. 1 Introduction 11 Choice between three or more alternatives can be similarly expressed.