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

Coppola, Paolo; Lago, Ugo Dal; Rocca, Simona Ronchi Della

doi:10.1007/11417170_11

“…Namely every well typed term β-reduces to normal form in a number of steps which depends in a polynomial or elementary way from its size, and moreover all functions with the corresponding complexity are representable by a well typed term. Examples of polynomial type assignment systems are in (Baillot and Terui 2004) and (Gaboardi and Ronchi Della Rocca 2007), based respectively on LAL ( an affine variant of LLL designed by Asperti and Roversi (Asperti and Roversi 2002)) and on SLL, and an example of an elementary type assignment system is in (Coppola et al 2005). …”

Section: Introductionmentioning

confidence: 99%

A logical account of pspace

Gaboardi

¹

,

Marion²,

Rocca

³

2008

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We propose a characterization of PSPACE by means of a type assignment for an extension of lambda calculus with a conditional construction. The type assignment STAB is an extension of STA, a type assignment for lambda-calculus inspired by Lafont's Soft Linear Logic. We extend STA by means of a ground type and terms for booleans.The key point is that the elimination rule for booleans is managed in an additive way. Thus, we are able to program polynomial time Alternating Turing Machines. Conversely, we introduce a call-byname evaluation machine in order to compute programs in polynomial space. As far as we know, this is the first characterization of PSPACE which is based on lambda calculus and light logics.

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“…Namely every well typed term β-reduces to normal form in a number of steps which depends in a polynomial or elementary way from its size, and moreover all functions with the corresponding complexity are representable by a well typed term. Examples of polynomial type assignment systems are in (Baillot and Terui 2004) and (Gaboardi and Ronchi Della Rocca 2007), based respectively on LAL ( an affine variant of LLL designed by Asperti and Roversi (Asperti and Roversi 2002)) and on SLL, and an example of an elementary type assignment system is in (Coppola et al 2005). …”

Section: Introductionmentioning

confidence: 99%

A logical account of pspace

Gaboardi

¹

,

Marion²,

Rocca

³

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Self Cite

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We propose a characterization of PSPACE by means of a type assignment for an extension of lambda calculus with a conditional construction. The type assignment STAB is an extension of STA, a type assignment for lambda-calculus inspired by Lafont's Soft Linear Logic. We extend STA by means of a ground type and terms for booleans.The key point is that the elimination rule for booleans is managed in an additive way. Thus, we are able to program polynomial time Alternating Turing Machines. Conversely, we introduce a call-byname evaluation machine in order to compute programs in polynomial space. As far as we know, this is the first characterization of PSPACE which is based on lambda calculus and light logics.

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“…she is using Linear Logic, and in particular Light Logic, for designing type assignment characterizing complexity classes. In [198,199] elementary computations are characterized, in [218] and [226] PTIME and PSPACE are characterized, respectively. In the recent years, from 2002, she is the leader of the italian group working in Linear Logic.…”

mentioning

confidence: 99%

Calculi, types and applications

Berardi

¹

,

de’Liguoro

²

2008

Theoretical Computer Science

0

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PrefaceThe 60th birthdays of Mario Coppo, Mariariangiola Dezani-Ciancaglini, and Simona Ronchi Della Rocca all fall between 2006 and 2007. These three researchers are widely known in the world community of theoretical computer scientists, and especially among the researchers in λ-calculus, type theory and semantics of programming languages. Owing to the significance of their contributions, the impact of their ideas and the large number of coworkers and students they have, we wish to honour them with the present collection of essays, covering most of their favourite topics, also showing how far the concepts and results originating from their works have gone.Our aim has been to illustrate both the past of the type assignment, the intersection types and the λ-calculus by presenting old results with new proofs in a new light; and to have a look at what is going on in these fields, since the original nucleus of the types for the λ-calculus has been widened encompassing object and process calculi, linear logic and implicit complexity.All of the present contributions have been invited, staring with a small group of coauthors of Coppo, Dezani and Ronchi. The number of papers has grown rapidly, as the news of our collection circulated, and other relevant themes were also suggested especially with regards to the most recent developments. The resulting collection is therefore the merit of the contributors, whose work has been submitted to a rigorous process of refereeing, and of the referees themselves, who provided criticism as well as suggestions to improve the papers. The absence of many researchers in the field is mostly casual, only due to the lack of space and to the poorness of our forces.Torino

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

Cited by 13 publications

References 9 publications

A logical account of pspace

A logical account of pspace

A logical account of pspace

Calculi, types and applications

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