Minimal function graphs are

R esum e: The minimal function graph semantics of Jones and Mycroft is a standard denotational semantics modiied to include only`reachable' parts of a program. We show that it may be expressed directly in terms of the standard semantics without the need for instrumentation at the expression level and, in doing so, bring out a connection with strictness. This also makes it possible to prove a stronger theorem of correctness for the minimal function graph semantics. Commonly, in abstract interpretation, we start with a standard semantics in denotational style, modify this to make an instrumented semantics which includes further operational detail (for example by adding timing information) and nally abstract this to form a decidable abstract semantics. Much work has gone into the theory of the abstraction process, but relatively little into the instrumentation process. We note that choices (or errors) in the instrumentation can lead to very diierent conclusions about execution. For example, if we instrument a semantics by replacing values v with pairs (v; n) where n is the number of steps required to reduce an expression e to v then we have possible sensible representations for the instrumented The minimal function graph semantics was deened by Jones and Mycroft 5] and in part represents a special case of the Cousots' work 3] on analysing recursive procedures by predicate transformers. It is speciied as an instrumented semantics leaving to intuition questions about whether A fuller version of this paper appears as 7].