Abstract
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main contributions are as follows. First, we introduce a modal call-by-value λ-calculus with multithreading and side effects. Second, we provide a combinatorial proof of termination in elementary time for the language. Third, we introduce an elementary affine type system that guarantees the standard subject reduction and progress properties. Finally, we illustrate the programming of iterative functions with side effects in the presented formalism.
Work partially supported by project ANR-08-BLANC-0211-01 “COMPLICE” and the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number: 243881 (project CerCo).
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Madet, A., Amadio, R.M. (2011). An Elementary Affine λ-Calculus with Multithreading and Side Effects. In: Ong, L. (eds) Typed Lambda Calculi and Applications. TLCA 2011. Lecture Notes in Computer Science, vol 6690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21691-6_13
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