Typing Lambda Terms in Elementary Logic with Linear Constraints

Coppola, Paolo; Martini, Simone

doi:10.1007/3-540-45413-6_10

Cited by 21 publications

(29 citation statements)

References 7 publications

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“…We use a natural deduction presentation of the type-assignment system in the lines of [7,8] (it can also be presented in a sequent calculus style as in [1,3]). This formulation is not as well adapted as that of proof-nets [2,14] to the study of reduction, but it is easier to understand for typing.…”

Section: Type Systemmentioning

confidence: 99%

“…Coppola and Martini studied in [8] type inference in Elementary Affine Logic (EAL), a system corresponding to Kalmar elementary complexity (see also [10]), for which they showed decidability of type inference. Their algorithm was based on the idea of first proposing a simple type derivation for the term and then interpolating this derivation with modality rules in order to find a suitable EAL derivation (in the line of the works on linear decorations as [11]).…”

Section: Introductionmentioning

confidence: 99%

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Type inference for light affine logic via constraints on words

Baillot

2004

Theoretical Computer Science

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Light Affine Logic (LAL) is a system due to Girard and Asperti capturing the complexity class P in a proof-theoretical approach based on Linear Logic. LAL provides a typing for lambda-calculus which guarantees that a well-typed program is executable in polynomial time on any input. We prove that the LAL type inference problem for lambda-calculus is decidable (for propositional LAL). To establish this result we reformulate the type-assignment system into an equivalent one which makes use of subtyping and is more flexible. We then use a reduction to a satisfiability problem for a system of inequations on words over a binary alphabet, for which we provide a decision procedure.

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Section: Type Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Type inference for light affine logic via constraints on words

Baillot

2004

Theoretical Computer Science

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“…A notion of typability for lambda calculus has been defined in [10,11,7] for EAL, and in [4] for LAL. Type inference has been proved to be decidable.…”

Section: Introductionmentioning

confidence: 99%

Light Logics and the Call-by-Value Lambda Calculus

Coppola¹,

Lago²,

Rocca³

2008

Log.Meth.Comput.Sci.

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Abstract. The so-called light logics [13,1,2] have been introduced as logical systems enjoying quite remarkable normalization properties. Designing a type assignment system for pure lambda calculus from these logics, however, is problematic, as discussed in [6]. In this paper we show that shifting from usual call-by-name to call-by-value lambda calculus allows regaining strong connections with the underlying logic. This will be done in the context of Elementary Affine Logic (EAL), designing a type system in natural deduction style assigning EAL formulae to lambda terms.

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“…After their introduction, they have been shown to be relevant for optimal reduction [5,6], programming language design [4,7] and set theory [8]. However, proof languages for these logics, designed through the Curry-Howard Correspondence, are syntactically quite complex and can hardly be proposed as programming languages.…”

Section: Introductionmentioning

confidence: 99%

Elementary Affine Logic and the Call-by-Value Lambda Calculus

Coppola

Lago

Rocca

2005

Lecture Notes in Computer Science

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Abstract. Light and elementary linear logics have been introduced as logical systems enjoying quite remarkable normalization properties. Designing a type assignment system for pure lambda calculus from these logics, however, is problematic, as discussed in [1]. In this paper, we show that shifting from usual call-by-name to call-by-value lambda calculus allows to regain strong connections with the underlying logic. We will do this in the context of Elementary Affine Logic (EAL), designing a type system in natural deduction style assigning EAL formulae to lambda terms.

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Typing Lambda Terms in Elementary Logic with Linear Constraints

Cited by 21 publications

References 7 publications

Type inference for light affine logic via constraints on words

Type inference for light affine logic via constraints on words

Light Logics and the Call-by-Value Lambda Calculus

Elementary Affine Logic and the Call-by-Value Lambda Calculus

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