Abstract
We explore an intuitionistic fragment of Artëmov’s Justification Logic as a type system for a programming language for mobile units. Such units consist of both a code and a certificate component. Our language, the Certifying Mobile Calculus, caters for code and certificate development in a unified theory. In the same way that mobile code is constructed out of code components and extant type systems track local resource usage to ensure the mobile nature of these components, our system additionally ensures correct certificate construction out of certificate components. We present proofs of type safety and strong normalization for a run-time system based on an abstract machine.
Highlights
We explore an intuitionistic fragment (IJL) of Artëmov’s Justification Logic (JL) as a type system for a programming language for mobile units
We present a Curry–de Bruijn–Howard analysis of an intuitionistic fragment (IJL) of Justification Logic JL
The modal type constructor [s]A is interpreted as the type of mobile units, expressions composed of a code and certificate component
Summary
We explore an intuitionistic fragment (IJL) of Artëmov’s Justification Logic (JL) as a type system for a programming language for mobile units. This language caters for both code and certificate development in a unified theory. JL may be regarded as refinement of modal logic S4 in which ✷A is replaced by [s]A, for s a proof term expression, and is read: ‘‘s is a proof of A’’. We provide an operational reading of expressions encoding proofs in this system in terms of global computation. Of the machine reduction semantics of together with updated proofs of subject reduction and strong normalization
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