Kevin Watkins

A Concurrent Logical Framework: The Propositional Fragment

We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations differing only in the order of execution of independent steps. From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic. An encoding of a small Petri net exemplifies the representation methodology, which can be summarized as “concurrent computations as monadic expressions”.

Monadic concurrent linear logic programming

Lolli is a logic programming language based on the asynchronous propositions of intuitionistic linear logic. It uses a backward chaining, backtracking operational semantics. In this paper we extend Lolli with the remaining connectives of intuitionistic linear logic restricted to occur inside a monad, an idea taken from the concurrent logical framework (CLF). The resulting language, called LolliMon, has a natural forward chaining, committed choice operational semantics inside the monad, while retaining Lollis semantics outside the monad. LolliMon thereby cleanly integrates both concurrency and saturation with logic programming search. We illustrate its expressive power through several examples including an implementation of the pi-calculus, a call-by-need lambda-calculus, and several saturating algorithms presented in logical form.

On regions and linear types (extended abstract)

We explore how two different mechanisms for reasoning about state,linear typing and the type, region and effect discipline,complement one another in the design of a strongly typed functionalprogramming language. The basis for our language is a simple lambdacalculus containing first-class memory regions, which areexplicitly passed as arguments to functions, returned as resultsand stored in user-defined data structures. In order to ensureappropriate memory safety properties, we draw upon the literatureon linear type systems to help control access to and deallocationof regions. In fact, we use two different interpretations of lineartypes, one in which multiple-use values are freely copied anddiscarded and one in which multiple-use values are explicitlyreference-counted, and show that both interpretations give rise tointeresting invariants for manipulating regions. We also explorenew programming paradigms that arise by mixing first-class regionsand conventional linear data structures.

Specifying Properties of Concurrent Computations in CLF

CLF (the Concurrent Logical Framework) is a language for specifying and reasoning about concurrent systems. Its most significant feature is the first-class representation of concurrent executions as monadic expressions. We illustrate the representation techniques available within CLF by applying them to an asynchronous pi-calculus with correspondence assertions, including its dynamic semantics, safety criterion, and a type system with latent effects due to Gordon and Jeffrey.

Fault-tolerant multicast routing in the mesh with no virtual channels

This paper addresses the problem of fault-tolerant multicast routing in wormhole-routed multicomputers. We present a new pseudo-Hamiltonian path-based routing methodology for constructing deadlock-free multicast routing algorithms requiring no virtual channels. This technique is applied to construct the first fault-tolerant multicast routing algorithm for the mesh that requires no virtual channels. Simulation results indicate that this technique results in minimal performance degradation in the presence of a large number of node and channel faults.