Monadic concurrent linear logic programming

Abstract

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 Lolli's 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-byneed lambda-calculus, and several saturating algorithms presented in logical form.

Linear Logical Voting Protocols

“…To assign a logic programming interpretation, restrictions must be placed on the ways in which these connectives fit together so that proof search becomes more deterministic. Thus, in Celf [14] and its predecessor, LolliMon [13], the formulas of linear logic are polarized into positive and negative classes [1] and a monad is used to prevent interference between the two classes [16]. For the examples in this paper, only the following fragment of polarized monadic linear logic is needed:…”

“…4 The braces around B + denote a monad that is not found in conventional presentations of linear logic. It is used to give a committed-choice operational semantics for the logic programming interpretation [13] that is important to our work.…”

“…Linear logical specifications of these protocols can be transliterated, in a fully syntactic way, to source code of linear logic programming languages, such as LolliMon [13] and Celf [14]. To provide intuition about the operational behavior of specifications, Sect.…”

Distributed System Security via Logical Frameworks (SeLF)

“…In order to make this feasible, we restricted ourselves to a large fragment of CLF that is sufficient to express much of the proof-carrying authorization architecture of Grey. The design of this language [LPPW05] is a significant result of the work under this grant. The implementation is complete and publicly available.…”

ILC: A Foundation for Automated Reasoning About Pointer Programs

“…There are several reasons why we decided to focus on linear logic as opposed to bunched implications as a foundation for verifying programs. First, from a practical standpoint, there are a number of tools available for our use including logic programming engines Lolli [8] and Lollimon [9], theorem provers [10] and logical frameworks such as Forum [11], LLF [12], and CLF [13]. Second, since linear logic is older than BI, more is known about it.…”