Call-by-Value Non-determinism in a Linear Logic Type Discipline
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- Díaz-Caro A., Manzonetto G., Pagani M. (2013) Call-by-Value Non-determinism in a Linear Logic Type Discipline. In: Artemov S., Nerode A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg
We consider the call-by-value λ-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard’s second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction.
Keywordsλ-calculus linear logic non-determinism call-by-value
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