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Lucius Gregory Meredith

Publications and source records attributed to Lucius Gregory Meredith.

5 recordsLinked to original sources
arXiv2019

Name-free combinators for concurrency

Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchronous pi calculus, but her combinators still depend on the "new" operator to bind names. We modify Yoshida's combinators by replacing "new" and replication with reflective operators to provide the first combinator calculus with no bound names into which the asynchronous pi calculus has a faithful embedding. We also show that multisorted Lawvere theories enriched over graphs suffice to capture the operational semantics of the calculus.

cs.LO↗
arXiv2016

Logic as a distributive law

We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad BoolAlg for the free Boolean algebra on a category, we get a 2-monad Form = BoolAlg + Calc for the free category of formulae and proofs. We also get the 2-monad BoolAlg $\circ$ Calc for subsets of terms. The interpretation of formulae is a natural transformation $\interp{-}$: Form $\Rightarrow$ BoolAlg $\circ$ Calc defined by the units and multiplications of the monads and a distributive law transformation $δ$: Calc $\circ$ BoolAlg $\Rightarrow$ BoolAlg $\circ$ Calc. This interpretation is consistent both with the Curry-Howard isomorphism and with realizability. We give an implementation of the "possibly" modal operator parametrized by a two-hole term context and show that, surprisingly, the arrow type constructor in the $λ$-calculus is a specific case. We also exhibit nontrivial formulae encoding confinement and liveness properties for a reflective higher-order variant of the $π$-calculus.

cs.LO↗
arXiv2015

Higher category models of the pi-calculus

We present an approach to modeling computational calculi using higher category theory. Specifically we present a fully abstract semantics for the pi-calculus. The interpretation is consistent with Curry-Howard, interpreting terms as typed morphisms, while simultaneously providing an explicit interpretation of the rewrite rules of standard operational presentations as 2-morphisms. One of the key contributions, inspired by catalysis in chemical reactions, is a method of restricting the application of 2-morphisms interpreting rewrites to specific contexts.

cs.LO↗