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

2004
*
arXiv
*
pre-print

We propose a new

arXiv:cs/0402059v2
fatcat:q2ricscan5giboyeygjk3j5pba
*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. ...##
###
Light types for polynomial time computation in lambda calculus

2009
*
Information and Computation
*

We present a polymorphic

doi:10.1016/j.ic.2008.08.005
fatcat:vtr4yo6kz5dsfp6qzoqe3szxte
*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*. ...##
###
Light types for polynomial time computation in lambda-calculus

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

We propose a new

doi:10.1109/lics.2004.1319621
dblp:conf/lics/BaillotT04
fatcat:vgv6qbozbffv7axhycotxzsjpa
*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. ...##
###
From Proof-Nets to Linear Logic Type Systems for Polynomial Time Computing
[chapter]

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. ...

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

2006
*
arXiv
*
pre-print

Given a fixed ring structure K we define an extension of Terui's

arXiv:cs/0608040v1
fatcat:zpyjpm7iafd6zfpvbytnuz3xqu
*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 ...##
###
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]

2004
*
Lecture Notes in Computer Science
*

We introduce Soft

doi:10.1007/978-3-540-24727-2_4
fatcat:xi3sw7bcd5dnrgqrm2x7pwkdda
*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. ...##
###
Soft lambda-calculus: a language for polynomial time computation
[article]

2003
*
arXiv
*
pre-print

We introduce Soft

arXiv:cs/0312015v1
fatcat:kyrtagxsybfe3gy27u4jayh7sm
*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. ...##
###
Algebras and coalgebras in the light affine Lambda calculus

2015
*
SIGPLAN notices
*

Algebra and coalgebra are widely used to model data

doi:10.1145/2858949.2784759
fatcat:ezlynnzdxrepfpxnj3qtddwj2q
*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*. ...##
###
Intersection Types for Light Affine Lambda Calculus

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. ...

##
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Deciding ML typability is complete for deterministic exponential time

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

doi:10.1145/96709.96748
dblp:conf/popl/Mairson90
fatcat:3liiwezldndofnbf5msy6jxtn4
*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. ...##
###
Checking Polynomial Time Complexity with Types
[chapter]

2002
*
Foundations of Information Technology in the Era of Network and Mobile Computing
*

It can be used as a

doi:10.1007/978-0-387-35608-2_31
dblp:conf/ifipTCS/Baillot02
fatcat:7x4rxh4mb5agzdpfxryxtipkg4
*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. ...##
###
Light logics and higher-order processes

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 ...

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

2005
*
Lecture Notes in Computer Science
*

We give a new

doi:10.1007/11417170_6
fatcat:ataltroq2zcxxc6x6ozgpykk34
*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. ...##
###
Light Logics and Higher-Order Processes

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 ...

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