Non-Deterministic Abstract Machines

We present a generic design of abstract machines for non-deterministic programming languages, such as process calculi or concurrent lambda calculi, that provides a simple way to implement them. Such a machine traverses a term in the search for a redex, making non-deterministic choices when several paths are possible and backtracking when it reaches a dead end, i.e., an irreducible subterm. The search is guaranteed to terminate thanks to term annotations the machine introduces along the way. We show how to automatically derive a non-deterministic abstract machine from a zipper semantics - a form of structural operational semantics in which the decomposition process of a term into a context and a redex is made explicit. The derivation method ensures the soundness and completeness of the machines w.r.t. the zipper semantics

The Zoo of Lambda-Calculus Reduction Strategies, And Coq

We present a generic framework for the specification and reasoning about reduction strategies in the lambda calculus, representable as sets of term decompositions. It is provided as a Coq formalization that features a novel format of phased strategies. It facilitates concise description and algebraic reasoning about properties of reduction strategies. The formalization accommodates many well-known strategies, both weak and strong, such as call by name, call by value, head reduction, normal order, full ?-reduction, etc. We illustrate the use of the framework as a tool to inspect and categorize the "zoo" of existing strategies, as well as to discover and study new ones with particular properties