In Scheme

Here is the entire functionality in Scheme:

(define (cef f) (let ((x '()) (y '())) (cons
  (lambda () (if (null? y) (set! y (f x))) y) ; getter
  (lambda (nx) (set! y '()) (set! x nx))  ; setter
  )))

f is the function to be continuously evaluated. The function cef above, given f, returns a pair of functions, a getter and a setter. We presume that f never returns '() and that what f yields depends only on its argument. The getter always returns what ever f would yield given the most recent argument to the setter.

(define gs (cef (lambda (x) (display "Ugh ") (expt 10 x))))
((cdr gs) 100)
((cdr gs) 10)
((car gs)) ⇒ Ugh 10000000000
((car gs)) ⇒ 10000000000

Note that the substantial work of computing 10¹⁰⁰ was entirely avoided because no one asked for that value. 10¹⁰ was needed twice but computed (Ugh) only once.

Of course this version does not support mutation of x by machine store commands. Here is the more general pattern.