Safety of Strictness Analysis via Term Graph Rewriting

A safe abstraction is presented for a restricted form of term graph rewriting. This abstraction can be seen as a formalisation of the rewrite system employed by the strictness analyser in the Concurrent Clean compiler. Programs written in a core functional language are interpreted as graph rewriting systems using a form of equational term graph rewriting due to Ariola and Arvind. Abstract graphs are defined by extending the signature of ordinary graphs and it is shown how to extend a rewriting system on ordinary graphs to one on abstract graphs. An abstraction relation between abstract graphs is used to define a notion of safety with respect to a variant of Ariola and Arvind’s direct approximation semantics, and this notion of safety is shown to be adequate for strictness analysis. Abstract reduction is defined as the union of the extended rewrite system with additional ‘heuristic’ reductions and shown to be safe.

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