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From Proof-Nets to Linear Logic Type Systems for Polynomial Time Computing [chapter]

Patrick Baillot
2007 Lecture Notes in Computer Science  
We stress the importance of proof-nets from Light linear logic for the design of this type system and for a result establishing that typable lambda-terms can be evaluated efficiently with optimal reduction  ...  In this presentation we give an overview of Dual Light Affine Logic (DLAL), a polymorphic type system for lambda calculus ensuring that typable lambda terms are executable in polynomial time.  ...  Any solution of the constraints system gives a valid DLAL type derivation.  ... 
doi:10.1007/978-3-540-73228-0_2 fatcat:7axovijfpfbbxhxe5umqljqnku

A Feasible Algorithm for Typing in Elementary Affine Logic [chapter]

Patrick Baillot, Kazushige Terui
2005 Lecture Notes in Computer Science  
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction.  ...  Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL type inference in polynomial  ...  We have shown that the set of constraints needed in our algorithm is polynomial in the size of the term and its simple type assignment.  ... 
doi:10.1007/11417170_6 fatcat:ataltroq2zcxxc6x6ozgpykk34

A feasible algorithm for typing in Elementary Affine Logic [article]

Patrick Baillot, Kazushige Terui
2004 arXiv   pre-print
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction.  ...  Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL* type inference in polynomial  ...  We have shown that the set of constraints needed in our algorithm is polynomial in the size of the term and its simple type assignment.  ... 
arXiv:cs/0412028v1 fatcat:s4qaxtdd6zebbhcgp7lowpzbgq

Checking Polynomial Time Complexity with Types [chapter]

Patrick Baillot
2002 Foundations of Information Technology in the Era of Network and Mobile Computing  
such that the term admits the corresponding type?  ...  It can be used as a type system for lambda-calculus, ensuring a well-typed program has a polynomial time bound on any input. Types use modalities meant to control duplication.  ...  The results in this paper were first presented at the 'Linear' TMR network meeting held in Bertinoro in april 2001 and we wish to thank the organizers.  ... 
doi:10.1007/978-0-387-35608-2_31 dblp:conf/ifipTCS/Baillot02 fatcat:7x4rxh4mb5agzdpfxryxtipkg4

Elementary Affine Logic and the Call-by-Value Lambda Calculus [chapter]

Paolo Coppola, Ugo Dal Lago, Simona Ronchi Della Rocca
2005 Lecture Notes in Computer Science  
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.  ...  Light and elementary linear logics have been introduced as logical systems enjoying quite remarkable normalization properties.  ...  The Elementary Type Assignment System In this section we will define a type assignment system typing lambda-terms with EAL formulae.  ... 
doi:10.1007/11417170_11 fatcat:yj7f7zel6jcenoiamfhxga7po4

Page 7328 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
We define here a second-order lambda calculus in which type abstraction is stratified to levels up to w”, an ordinal that permits highly uniform (and finite) type in- ference rules.  ...  the super-elementary functions (level &, in the Grzegorczyk hierarchy).  ... 

About the efficient reduction of lambda terms [article]

Andrea Asperti
2017 arXiv   pre-print
There is still a lot of confusion about "optimal" sharing in the lambda calculus, and its actual efficiency. In this article, we shall try to clarify some of these issues.  ...  ACKNOWLEDGMENTS This short note was mostly motivated by a recent Haskell discussion thread debating why isn't anyone talking about optimal lambda calculus implementations? 4 .  ...  The sharing graph reduction of lambda terms typable in elementary linear logic can be done without the use of brackets, and hence without bookkeeping.  ... 
arXiv:1701.04240v1 fatcat:e7wndrc5qjcgrgqsryjcf2xbz4

Light Logics and the Call-by-Value Lambda Calculus

Paolo Coppola, Ugo Dal Lago, Simona Ronchi Della Rocca, Harry Mairson
2008 Logical Methods in Computer Science  
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.  ...  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.  ...  The Elementary Type Assignment System In this section we will define a type assignment system typing lambda-terms with EAL formulae.  ... 
doi:10.2168/lmcs-4(4:5)2008 fatcat:li2b2uivfrc23lxtselbo6eszi

Optimizing optimal reduction

Paolo Coppola, Simone Martini
2006 ACM Transactions on Computational Logic  
We propose a type inference algorithm for lambda terms in Elementary Affine Logic (EAL).  ...  The algorithm decorates the syntax tree of a simple typed lambda term and collects a set of linear constraints.  ...  There is large class of (typed) terms, however, for which this decision is trivial, namely those λ-terms whose sharing graph is a proof-net of Elementary Logic, both in the Linear [Gir98] (ELL) and the  ... 
doi:10.1145/1131313.1131315 fatcat:m4t7rsfwdzh2jlkygbanavcwum

Page 8491 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Gordon, Logical properties of name restriction (46-60); Juliusz Chroboczek, Subtyping recursive games (61-75); Paolo Coppola and Simone Martini, Typing lambda terms in elementary logic with linear constraints  ...  Ibarra, Jianwen Su and Constantinos Bartzis, Counter machines and the safety and disjointness problems for database queries with linear constraints (127-137); Martin Kutrib, Au- tomata arrays and context-free  ... 

Light types for polynomial time computation in lambda-calculus

P. Baillot, K. Terui
2004 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.  
DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL).  ...  We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL).  ...  By contrast Elementary affine logic (EAL) (corresponding to elementary complexity) has only one modality and its type inference can be performed using linear constraints, that is to say integer programming  ... 
doi:10.1109/lics.2004.1319621 dblp:conf/lics/BaillotT04 fatcat:vgv6qbozbffv7axhycotxzsjpa

Optimizing Optimal Reduction: A Type Inference Algorithm for Elementary Affine Logic [article]

Paolo Coppola, Simone Martini
2003 arXiv   pre-print
We present a type inference algorithm for lambda-terms in Elementary Affine Logic using linear constraints. We prove that the algorithm is correct and complete.  ...  There is large class of (typed) terms, however, for which this decision is very simple, namely those λ-terms whose sharing graph is a proof-net of Elementary Logic, both in the Linear [Gir98] (ELL) and  ...  Baillot [Bai02] gives a type-checking algorithm for Light Affine Logic, but it applies only to lambda terms in normal form.  ... 
arXiv:cs/0305011v1 fatcat:h3ih2qebr5hybj7n4bxwbfy32a

Light types for polynomial time computation in lambda-calculus [article]

Patrick Baillot, Kazushige Terui
2004 arXiv   pre-print
DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL).  ...  We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL).  ...  By contrast Elementary affine logic (EAL) (corresponding to elementary complexity) has only one modality !  ... 
arXiv:cs/0402059v2 fatcat:q2ricscan5giboyeygjk3j5pba

Verification of Ptime reducibility for system F terms via Dual Light Affine Logic [article]

Vincent Atassi
2006 arXiv   pre-print
In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable  ...  In the present work we address the problem of typing lambda-terms in second-order DLAL.  ...  Elementary linear logic (EAL) in particular is another variant of Linear logic which characterizes Kalmar elementary time and has applications to optimal reduction.  ... 
arXiv:cs/0603104v1 fatcat:vprhuepk4ffm3liazicqjzq2u4

Verification of Ptime Reducibility for System F Terms Via Dual Light Affine Logic [chapter]

Vincent Atassi, Patrick Baillot, Kazushige Terui
2006 Lecture Notes in Computer Science  
In a previous work we introduced Dual Light Affine Logic (DLAL) ([BT04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can  ...  In the present work we address the problem of typing lambda-terms in second-order DLAL.  ...  Elementary linear logic (EAL) in particular is another variant of Linear logic which characterizes Kalmar elementary time and has applications to optimal reduction.  ... 
doi:10.1007/11874683_10 fatcat:gd5st3xswzdlxp7nrdblcfzdya
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