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Communication Dans Un Congrès Année : 2023

Extensional and Non-extensional Functions as Processes

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Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure λ-calculus, the process representations yield (at best) non-extensional λ-theories (i.e., β rule holds, whereas η does not). In the paper, we study how to obtain extensional representations, and how to move between extensional and non-extensional representations. Using Internal π, Iπ (a subset of the π-calculus in which all outputs are bound), we develop a refinement of Milner's original encoding of functions as processes that is parametric on certain abstract components called wires. These are, intuitively, processes whose task is to connect two end-point channels. We show that when a few algebraic properties of wires hold, the encoding yields a λ-theory. Exploiting the symmetries and dualities of Iπ, we isolate three main classes of wires. The first two have a sequential behaviour and are dual of each other; the third has a parallel behaviour and is the dual of itself. We show the adoption of the parallel wires yields an extensional λ-theory; in fact, it yields an equality that coincides with that of Böhm trees with infinite η. In contrast, the other two classes of wires yield nonextensional λ-theories whose equalities are those of the Lévy-Longo and Böhm trees.
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hal-04081885 , version 1 (26-04-2023)

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Ken Sakayori, Davide Sangiorgi. Extensional and Non-extensional Functions as Processes. 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Jun 2023, Boston, United States. ⟨10.1109/LICS56636.2023.10175686⟩. ⟨hal-04081885⟩
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