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

Patrick Baillot, Kazushige Terui
2004 arXiv   pre-print
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).  ...  We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy.  ...  We are grateful to Paolo Coppola, Simone Martini and Ugo Dal Lago for their accurate reading and important suggestions.  ... 
arXiv:cs/0402059v2 fatcat:q2ricscan5giboyeygjk3j5pba

Light types for polynomial time computation in lambda calculus

Patrick Baillot, Kazushige Terui
2009 Information and Computation  
We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial time: dual light affine logic (DLAL).  ...  We also give a translation of LAL into DLAL and deduce from it that all polynomial time functions can be represented in DLAL.  ...  Light affine logic is a logic for polynomial time computation in the proofs-as-programs approach to computing.  ... 
doi:10.1016/j.ic.2008.08.005 fatcat:vtr4yo6kz5dsfp6qzoqe3szxte

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.  
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).  ...  We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy.  ...  We are grateful to Paolo Coppola, Simone Martini and Ugo Dal Lago for their accurate reading and important suggestions.  ... 
doi:10.1109/lics.2004.1319621 dblp:conf/lics/BaillotT04 fatcat:vgv6qbozbffv7axhycotxzsjpa

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

Patrick Baillot
2007 Lecture Notes in Computer Science  
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.  ...  We also discuss the issue of DLAL type inference, which can be performed in polynomial time for system F terms.  ...  This resolution procedure is correct and complete and it can be performed in polynomial time w.r.t. the size of the original system F term.  ... 
doi:10.1007/978-3-540-73228-0_2 fatcat:7axovijfpfbbxhxe5umqljqnku

An Embedding of the BSS Model of Computation in Light Affine Lambda-Calculus [article]

Patrick Baillot, Marco Pedicini
2006 arXiv   pre-print
Given a fixed ring structure K we define an extension of Terui's light affine lambda-calculus typed in LAL (Light Affine Logic) with a basic type for K.  ...  We show that this calculus captures the polynomial time function class FP(K): every typed term can be evaluated in polynomial time and conversely every polynomial time BSS machine over K can be simulated  ...  In section 4, we define our extension λ LA K of light affine lambda-calculus to a structure K; then we show that the terms can be reduced in polynomial time (section 5) and conversely that all ptime BSS  ... 
arXiv:cs/0608040v1 fatcat:zpyjpm7iafd6zfpvbytnuz3xqu

Page 562 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
Kok, Infinite intersection and union types for the lazy lambda calculus (448- 458); Yoriyuki Yamagata, Strong normalization of second order symmetric lambda-mu calculus (459-467); Philip Wadler, The Girard-Reynolds  ...  Cog (362-377); Freek Wiedijk, Mizar light for HOL light (378-393).  ... 

Soft lambda-Calculus: A Language for Polynomial Time Computation [chapter]

Patrick Baillot, Virgile Mogbil
2004 Lecture Notes in Computer Science  
We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time.  ...  It is possible to consider variants of LL with alternative, stricter rules for modalities, for which all proofs-programs can be run in polynomial time.  ...  We wish to thank Marcel Masseron for the stimulating discussions we had together on Soft linear logic and which led to the present paper.  ... 
doi:10.1007/978-3-540-24727-2_4 fatcat:xi3sw7bcd5dnrgqrm2x7pwkdda

Soft lambda-calculus: a language for polynomial time computation [article]

Patrick Baillot, Virgile Mogbil
2003 arXiv   pre-print
We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time.  ...  We then extend the type system of Soft logic with recursive types. This allows us to consider non-standard types for representing lists.  ...  Our Soft lambda-calculus is inspired from Terui's Light affine lambda-calculus ([Ter01]), which is a calculus with a polynomial bound on reduction sequences that can be typed in Light affine logic.  ... 
arXiv:cs/0312015v1 fatcat:kyrtagxsybfe3gy27u4jayh7sm

Algebras and coalgebras in the light affine Lambda calculus

Marco Gaboardi, Romain Péchoux
2015 SIGPLAN notices  
Algebra and coalgebra are widely used to model data types in functional programming languages and proof assistants.  ...  Their use permits to better structure the computations and also to enhance the expressivity of a language or of a proof system.  ...  For this reason, their principles have been used to design a lambda calculus [39] , a type system [5] and an extended language [6] for polynomial time computations.  ... 
doi:10.1145/2858949.2784759 fatcat:ezlynnzdxrepfpxnj3qtddwj2q

Intersection Types for Light Affine Lambda Calculus

Daniel de Carvalho
2005 Electronical Notes in Theoretical Computer Science  
Light Affine Lambda Calculus is a term calculus for polynomial time computation ([12]). Some of the terms of Light Affine Lambda Calculus must however be regarded as errors.  ...  We introduce two type assignment systems with intersection types : in the first one, typable pseudo-terms are exactly the terms without errors ; in the second one, they are exactly those that reduce to  ...  Acknowledgement We have to thank Patrick Baillot for all his comments, remarks and suggestions ; we do it here warmly.  ... 
doi:10.1016/j.entcs.2005.06.011 fatcat:6gzxljsqcfd7rcnad4eyhsf5uu

Deciding ML typability is complete for deterministic exponential time

Harry G. Mairson
1990 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '90  
A well known but incorrect piece of functional programming folklore is that ML expressions can be efficiently typed in polynomial time.  ...  The simulation of the transition function 6 of the Turing Machine is realized uniquely through terms in the lambda calculus zoilhovl the use of the polymorphic let construct.  ...  For any type tree variable V, we can compute x(V) in polynomial space.  ... 
doi:10.1145/96709.96748 dblp:conf/popl/Mairson90 fatcat:3liiwezldndofnbf5msy6jxtn4

Checking Polynomial Time Complexity with Types [chapter]

Patrick Baillot
2002 Foundations of Information Technology in the Era of Network and Mobile Computing  
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.  ...  Light Affine Logic (LAL) is a logical system due to Girard and Asperti offering a polynomial time cut-elimination procedure.  ...  Acknowledgments The author wishes to thank Roberto Amadio and Laurent Rgnier for suggestions and encouragements, as well as Kazushige Terui for useful discussions.  ... 
doi:10.1007/978-0-387-35608-2_31 dblp:conf/ifipTCS/Baillot02 fatcat:7x4rxh4mb5agzdpfxryxtipkg4

Light logics and higher-order processes

UGO DAL LAGO, SIMONE MARTINI, DAVIDE SANGIORGI
2014 Mathematical Structures in Computer Science  
In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time.  ...  We show that the techniques for resource control that have been developed by the so-calledlight logicscan be fruitfully applied also to process algebras.  ...  In the sequential case several achievements have been obtained via the so-called light logics (Girard 1998 , Asperti & Roversi 2002 , Lafont 2004 , which allow for type systems for λ-calculus exactly  ... 
doi:10.1017/s0960129514000310 fatcat:y6nytejct5hfjeq7qqcu4lcs5e

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

Light Logics and Higher-Order Processes

Ugo Dal Lago, Simone Martini, Davide Sangiorgi
2010 Electronic Proceedings in Theoretical Computer Science  
In the sequential case several achievements have been obtained via the so-called light logics (Girard 1998 , Asperti & Roversi 2002 , Lafont 2004 , which allow for type systems for λ-calculus exactly  ...  For smaller classes (e.g., polynomial time) one also forbids that a duplicating computation could drive another duplication.  ...  As pointed out earlier, we are mainly interested in techniques capable of ensuring polynomial bounds  ... 
doi:10.4204/eptcs.41.4 fatcat:6qaoolewtzam5ftl766gbzvymu
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