Forum: A multiple-conclusion specification logic

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Forum: A multiple-conclusion specification logic (1996)

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by Dale Miller

Venue:	Theoretical Computer Science
Citations:	96 - 12 self

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@ARTICLE{Miller96forum:a,
    author = {Dale Miller},
    title = {Forum: A multiple-conclusion specification logic},
    journal = {Theoretical Computer Science},
    year = {1996},
    volume = {165}
}

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Abstract

The theory of cut-free sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higher-order programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.

Keyphrases

multiple-conclusion specification logic linear logic logic programming language abstract data type sequent calculus proof system present forum meta theory new expressive strength abstraction mechanism linear logic refinement linear object operational semantics higher-order programming logic programming presentation cut-free sequent proof programming language various form

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