Local reasoning about programs exploits the natural local behaviour common in
programs by focussing on the footprint - that part of the resource accessed by
the program. We address the problem of formally characterising and analysing
the footprint notion for abstract local functions introduced by Calcagno, O
Hearn and Yang. With our definition, we prove that the footprints are the only
essential elements required for a complete specification of a local function.
We formalise the notion of small specifications in local reasoning and show
that for well-founded resource models, a smallest specification always exists
that only includes the footprints, and also present results for the
non-well-founded case. Finally, we use this theory of footprints to investigate
the conditions under which the footprints correspond to the smallest safe
states. We present a new model of RAM in which, unlike the standard model, the
footprints of every program correspond to the smallest safe states, and we also
identify a general condition on the primitive commands of a programming
language which guarantees this property for arbitrary models.Comment: LMCS 2009 (FOSSACS 2008 special issue