Simple Type Inference for Term Graph Rewriting Systems

a crude style rule basis Σ that is concrete (no polymorphism) and complete (each type has a rule). Build the final type-graph ∆, whose nodes are the concrete type symbols, and whose arcs are given by: for each ξ, if ξ ← ζ 1 …ζ n is the rule for ξ, then the k'th child of ξ is ζ k. If a system R is well typed acording to Σ and a suitable B, then for every execution graph G of the system, there is a node-symbol-forgetting homomorphism h : G → ∆. Readers should convince themselves that this property fails for the imperative discipline. To conclude then, we have discussed type inference for TGRSs and shown that credible type systems can be built using dataflow analysis and unification, even in the most general case where no particular nice structural properties are assumed for the system, fulfilling the promise in the conclusion of Banach (1989). We have also suggested that more powerful extensions of these systems can be contemplated. These extensions will be described elsewhere.