7 research outputs found
An Elementary Affine λ-Calculus with Multithreading and Side Effects
International audienceLinear 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
An Elementary affine λ-calculus with multithreading and side effects (extended version)
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 provide a new combinatorial proof of termination in elementary time for the functional case. Second, we develop an extension of the approach to a call-by-value -calculus with multithreading and side effects. 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
Indexed realizability for bounded-time programming with references and type fixpoints
The field of implicit complexity has recently produced several
bounded-complexity programming languages. This kind of language allows to
implement exactly the functions belonging to a certain complexity class. We
here present a realizability semantics for a higher-order functional language
based on a fragment of linear logic called LAL which characterizes the
complexity class PTIME. This language features recursive types and higher-order
store. Our realizability is based on biorthogonality, step-indexing and is
moreover quantitative. This last feature enables us not only to derive a
semantical proof of termination, but also to give bounds on the number of
computational steps needed by typed programs to terminate
On paths-based criteria for polynomial time complexity in proof-nets
Girard's Light linear logic (LLL) characterized polynomial time in the
proof-as-program paradigm with a bound on cut elimination. This logic relied on
a stratification principle and a "one-door" principle which were generalized
later respectively in the systems L^4 and L^3a. Each system was brought with
its own complex proof of Ptime soundness.
In this paper we propose a broad sufficient criterion for Ptime soundness for
linear logic subsystems, based on the study of paths inside the proof-nets,
which factorizes proofs of soundness of existing systems and may be used for
future systems. As an additional gain, our bound stands for any reduction
strategy whereas most bounds in the literature only stand for a particular
strategy.Comment: Long version of a conference pape