Papers by Lucius Meredith
Many term calculi, like lambda calculus or pi calculus, involve binders for names, and the mathem... more Many term calculi, like lambda calculus or pi calculus, involve binders for names, and the mathematics of bound variable names is subtle. Schoenfinkel introduced the SKI combinator calculus in 1924 to clarify the role of quantified variables in intuitionistic logic by eliminating them. 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. Recently, Meredith and Stay showed how to 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. Here we provide an alternative set of combinators built from SKI plus reflection that also eliminates all nominal phenomena, yet provides a faithful embedding of a reflective higher-order pi calculus. We show that with the nominal features effectively eliminated as...
W3C Working Draft, 2004
This document is a companion to the WSDL 2.0 specification (Web Services Description Language (WS... more This document is a companion to the WSDL 2.0 specification (Web Services Description Language (WSDL) Version 2.0 Part 1: Core Language [WSDL 2.0 Core], Web Services Description Language (WSDL) Version 2.0 Part 2: Adjuncts [WSDL 2.0 Adjuncts]). It is intended for readers who ...
Lecture Notes in Computer Science, 2005
We develop the static and dynamic semantics of PiDuce, a process calculus with XML values, schema... more We develop the static and dynamic semantics of PiDuce, a process calculus with XML values, schemas, and pattern matching. PiDuce values include channel names, therefore the structure of values may not reveal anything about their schemas. This is problematic in the pattern matching algorithm because it requires to verify whether a schema of a channel is a subschema of a pattern. Such a verification has exponential cost, in general. In order to reduce the computational complexity of the pattern matching, channel schemas are constrained to occur in tail positions of sequences and to be labelled-determined.
We present an approach to modeling computational calculi using higher category theory. Specifical... more 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.
Drossopoulou and Noble argue persuasively for the need for a means to express policy in object-ca... more Drossopoulou and Noble argue persuasively for the need for a means to express policy in object-capability-based systems. We investigate a practical means to realize their aim via the Curry-Howard isomorphism. Specifically, we investigate representing policy as types in a behavioral type system for the RHO-calculus, a reflective higher-order variant of the pi-calculus.
We present an algorithm for deriving a spatial-behavioral type system from a formal presentation ... more 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→ 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 ∘ Calc for subsets of terms. The interpretation of formulae is a natural transformation -: Form BoolAlg ∘ Calc defined by the units and multiplications of the monads and a distributive law transformation δ: Calc ∘ BoolAlg BoolAlg ∘ 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...
We present Synereo, a next-gen decentralized and distributed social network designed for an atten... more We present Synereo, a next-gen decentralized and distributed social network designed for an attention economy. Our presentation is given in two chapters. Chapter 1 presents our design philosophy. Our goal is to make our users more effective agents by presenting social content that is relevant and actionable based on the user’s own estimation of value. We discuss the relationship between attention, value, and social agency in order to motivate the central mechanisms for content flow on the network. Chapter 2 defines a network model showing the mechanics of the network interactions, as well as the compensation model enabling users to promote content on the network and receive compensation for attention given to the network. We discuss the high-level technical implementation of these concepts based on the π-calculus the most well known of a family of computational formalisms known as the mobile process calculi. 0.1 Prologue: This is not a manifesto The Internet is overflowing with soci...
We present an approach to modeling computational calculi using higher category theory. Specifical... more 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.
We give an interpretation of full classical linear logic, and linear proofs in terms of operation... more We give an interpretation of full classical linear logic, and linear proofs in terms of operations on the blockchain.
Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchr... more 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.
ArXiv, 2016
We present an algorithm for deriving a spatial-behavioral type system from a formal presentation ... more We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad $\Calc\maps \Cat \to \Cat$ 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 $\interp{-} \maps \Form \Rightarrow \BoolAlg \circ \Calc$ defined by the units and multiplications of the monads and a distributive law transformation $\delta\maps \Calc \circ \BoolAlg \Rightarrow \BoolAlg \circ \Calc.$ 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 $\...
Drossopoulou and Noble argue persuasively for the need for a means to express policy in object-ca... more Drossopoulou and Noble argue persuasively for the need for a means to express policy in object-capability-based systems. We investigate a practical means to realize their aim via the Curry-Howard isomorphism. Specifically, we investigate representing policy as types in a behavioral type system for the RHO-calculus, a reflective higher-order variant of the pi-calculus.
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Papers by Lucius Meredith