Showing papers by "Jean-Yves Girard published in 1989"
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TL;DR: In this paper, the Curry-Howard isomorphism and the normalisation theorem of a natural deduction system T coherence spaces have been studied in the context of linear logic and linear logic semantics.
Abstract: Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system F coherence semantics of the sum cut elimination (Hauptsatz) strong normalisation for F representation theorem semantics of System F what is linear logic?
1,771 citations
TL;DR: In this paper, the fall of Hilbert's program is discussed, and the first Incompleteness Theorem is shown to be equivalent to the cut-free rules of the Calculus of Sequents.
401 citations
TL;DR: The chapter describes the development of a semantics of computation free from the twin drawbacks of reductionism and subjectivism and that a representative class of algorithms can be modelized by means of standard mathematics.
Abstract: Publisher Summary This chapter describes the development of a semantics of computation free from the twin drawbacks of reductionism (that leads to static modification) and subjectivism (that leads to syntactical abuses, in other terms, bureaucracy). The new approach initiated in this chapter rests on the use of a specific C*-algebra Λ* that has the distinguished property of bearing a (non associative) inner tensor product. The chapter describes that a representative class of algorithms can be modelized by means of standard mathematics.
321 citations