this paper we present a formal system for deriving assertions about programs with memory. The assertions we consider are of the following three forms: (i) e diverges (i.e. fails to reduce to a value), written " e; (ii) e 0 and e 1 reduce to the same value and have exactly the same effect on memory, written e 0 ¸ e 1 ; and (iii) e 0 and e 1 reduce to the same value and have the same effect on memory up to production of garbage (are strongly isomorphic), written e 0 ' e 1 . The e, e j are expressions of a first-order Scheme- or Lisp-like language with the data operations atom ; eq; car ; cdr ; cons; setcar; setcdr , the control primitives let