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Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree 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 higherorder program ..."
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Cited by 96 (12 self)
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The theory of cutfree 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 higherorder 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.
A MultipleConclusion MetaLogic
 In Proceedings of 9th Annual IEEE Symposium On Logic In Computer Science
, 1994
"... The theory of cutfree 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 [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic pro ..."
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Cited by 87 (7 self)
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The theory of cutfree 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 [12], provide data types, higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends the languages λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. As a metalanguage, Forum greatly extends the expressiveness of these other logic programming languages. To illustrate its expressive strength, we specify in Forum a sequent calculus proof system and the operational semantics of a functional programming language that incorporates such nonfunctional features as counters and references. 1
An Extension to ML to Handle Bound Variables in Data Structures
, 1990
"... Most conventional programming languages have direct methods for representing firstorder terms (say, via concrete datatypes in ML). If it is necessary to represent structures containing bound variables, such as λterms, formulas, types, or proofs, these must first be mapped into firstorder terms, a ..."
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Cited by 39 (2 self)
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Most conventional programming languages have direct methods for representing firstorder terms (say, via concrete datatypes in ML). If it is necessary to represent structures containing bound variables, such as λterms, formulas, types, or proofs, these must first be mapped into firstorder terms, and then a significant number of auxiliary procedures must be implemented to manage bound variable names, check for free occurrences, do substitution, test for equality modulo alphaconversion, etc. We shall show how the applicative core of the ML programming language can be enhanced so that λterms can be represented more directly and so that the enhanced language, called MLλ, provides a more elegant method of manipulating bound variables within data structures. In fact, the names of bound variables will not be accessible to the MLλ programmer. This extension to ML involves the following: introduction of the new type constructor ’a => ’b for the type of λterms formed by abstracting a parameter of type ’a out of a term of type ’b; a very restricted and simple form of higherorder pattern matching; a method for extending a given data structure with a new constructor; and, a method for extending function definitions to handle such new constructors. We present several examples of MLλ programs.
Encoding Transition Systems in Sequent Calculus
 Theoretical Computer Science
, 1996
"... Intuitionistic and linear logics can be used to specify the operational semantics of transition systems in various ways. We consider here two encodings: one uses linear logic and maps states of the transition system into formulas, and the other uses intuitionistic logic and maps states into terms. I ..."
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Cited by 38 (11 self)
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Intuitionistic and linear logics can be used to specify the operational semantics of transition systems in various ways. We consider here two encodings: one uses linear logic and maps states of the transition system into formulas, and the other uses intuitionistic logic and maps states into terms. In both cases, it is possible to relate transition paths to proofs in sequent calculus. In neither encoding, however, does it seem possible to capture properties, such as simulation and bisimulation, that need to consider all possible transitions or all possible computation paths. We consider augmenting both intuitionistic and linear logics with a proof theoretical treatment of definitions. In both cases, this addition allows proving various judgments concerning simulation and bisimulation (especially for noetherian transition systems). We also explore the use of infinite proofs to reason about infinite sequences of transitions. Finally, combining definitions and induction into sequent calculus proofs makes it possible to reason more richly about properties of transition systems completely within the formal setting of sequent calculus.
Deriving Mixed Evaluation from Standard Evaluation for a Simple Functional Language
, 1989
"... ..."
Understanding Programming Languages
 Minds and Machines 17(2
, 2007
"... We document the influence on programming language semantics of the Platonism/formalism divide in the philosophy of mathematics. 1 Semantic Requirements An implementation on a particular machine cannot serve as a definitional vehicle for a programming language. For one thing, there are too many extr ..."
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We document the influence on programming language semantics of the Platonism/formalism divide in the philosophy of mathematics. 1 Semantic Requirements An implementation on a particular machine cannot serve as a definitional vehicle for a programming language. For one thing, there are too many extraneous details that pertain to the target machine i.e., it is far too idiosyncratic to serve as a definition of a machine independent language. Indeed, it is not clear that all such implementation details are graspable. Certainly, someone trying to learn a language from studying an implementation would find it hard to distinguish the wood from the trees. And here the wood is the machine independent language, and a semantics is intended to define it. However, it is not that the semantic account will not involve a machine; at some level that is precisely what it does, but it is a formalisation of the underlying abstract machine of the language, an idealisation, a mathematical abstraction that is intended to guide the construction