Dyna 2: Towards a General Weighted Logic Language
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Date
2017-10-27
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Johns Hopkins University
Abstract
We investigate the design of an expressive, purely-declarative, weighted logic programming language, Dyna. Dyna is a decade-plus effort in pushing the boundaries of declarative programming and “executable mathematics;” it instantiates an unusual point in the design space, as it is both Turing-complete (unlike Datalog) and devoid of a specified execution order (unlike Prolog). That is, it is designed to be, at once, both highly expressive and rich in opportunities for automated optimization. This thesis contains two major thrusts. We first consider both the denotational (§2.1.2 and §3.1.4) and operational aspects (§2.2 to §2.5, §3.2 to §3.6, and §4) of Dyna. In particular, for operational semantics, we introduce (§2.2) and extend (through §2.5) our EarthBound solver for finite circuits; §3 considers the generalization to logic programs proper. We then turn our attention to the static analysis of this language, considering mechanisms for reasoning both about abstract notions of well-formedness of programs (§5.2) as well as more mundane concerns of realizability of programs in actual computation (§5.3 and §5.4). Along the way we endeavour to place our work in the context of the larger field of logic programming languages and present our current thoughts on future avenues of exploration.
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Logic programming