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Combining first order algebraic rewriting systems, recursion and extensional lambda calculi
[chapter]

1994
*
Lecture Notes in Computer Science
*

It is well known that con uence

doi:10.1007/3-540-58201-0_90
fatcat:a3s3jyrjbrggzhu22f73vcz4ve
*and*strong normalization are preserved when combining left-*linear*algebraic rewriting systems with the simply*typed**lambda**calculus*. ... We show that con uence*and*normalization are modular properties for the combination of left-*linear*algebraic rewriting systems with*typed**lambda*calculi enriched with expansive extensional rules for*and*... This fact is stated*in**a*weaker form*in*Dou93]: there it is noticed that an equivalent of theorem 4.5 used*in*conjunction with L evy's trick rules out any left-*linear*con uent*and*strongly normalizing ...##
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Call-by-name, call-by-value, call-by-need and the linear lambda calculus

1999
*
Theoretical Computer Science
*

The

doi:10.1016/s0304-3975(98)00358-2
fatcat:wpm6kbycovabhlkibythzok3mu
*linear**lambda**calculus*used*in*this paper is*a*minor reÿnement of one previously presented by Wadler [41, 42], which is based on Girard's successor to*linear*logic, the Logic of Unity [15]. ... Our translations are into*a**linear**lambda**calculus*, corresponding to intuitionistic*linear*logic, while Mackie's translation is into proof nets, corresponding to classical*linear*logic. ...*lambda**calculus**and*for & introduction*and*elimination*in*the*linear**lambda**calculus*. ...##
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Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus
[chapter]

2002
*
Lecture Notes in Computer Science
*

We propose

doi:10.1007/3-540-45788-7_10
fatcat:yci7e6djxfa43amh2mdd5373ty
*a*semantic*and*syntactic framework for modelling linearly used effects, by giving the monadic transforms of the computational*lambda**calculus*(considered as the core*calculus*of*typed*call-by-value ... s work on linearly used continuations can be put*in*this general picture. As*a*technical result we show the full completeness of the CPS transform into the*linear**lambda**calculus*. ... Acknowledgements I thank Josh Berdine, Peter O'Hearn, Uday Reddy, Hayo Thielecke*and*Hongseok Yang for helpful discussions,*and*Jacques Garrigue*and*Susumu Nishimura for comments on an early version. ...##
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PhD Abstracts

2015
*
Journal of functional programming
*

Many students complete PhDs

doi:10.1017/s0956796815000040
fatcat:g7yt23qxivevte45fkiqv6xwna
*in*functional programming each year, but there is currently no common location*in*which to promote*and*advertise the resulting work. ... We are delighted to publish 12 abstracts*in*this second round,*and*hope that JFP readers will find many interesting dissertations*in*this collection that they may not otherwise have seen. ... Among various*type*systems for*lambda**calculus*inspired by variants of*linear*logic with restricted rules, we focus on Girard's BLL,*a**type*systems for terms that can be run*in*polynomial time w.r.t. input ...##
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Reduction in a Linear Lambda-Calculus with Applications to Operational Semantics
[chapter]

2005
*
Lecture Notes in Computer Science
*

We study beta-reduction

doi:10.1007/978-3-540-32033-3_17
fatcat:4ueyxjhavbdmzks6mvxmkvkmc4
*in**a**linear**lambda*-*calculus*derived from Abramsky's*linear*combinatory algebras. ... Simpson,*A*. (2005). Reduction*in**a**linear**lambda*-*calculus*with applications to operational semantics. ... Introduction The language Lily was introduced by Bierman, Pitts*and*Russo*in*[3] . It is*a**typed**lambda*-*calculus*based on*a*second-order intuitionistic*linear**type*theory with*recursion*. ...##
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Page 4081 of Mathematical Reviews Vol. , Issue 98G
[page]

1998
*
Mathematical Reviews
*

This result is

*in*sharp contrast to what happens*in**typed*/-*calculus*for the standard continuous, stable*and*strongly stable models of PCF,*and**in*pure /-*calculus*for Park’s model*and*the analogous stable ... Our cyclic*lambda**calculus*serves as*a*uniform language for this wider range of models of*recursive*computation.” {For the entire collection see MR 98f:68017.} ...##
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Page 5288 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Summary: “This paper introduces

*a*simply*typed**lambda**calculus*with both modal*and**linear*function*types*. ... {For the entire collection see MR 2000g:03005. } 2000h:03030 03B40 03D15 68N18 68Q15 Hofmann, Martin (D-DARM; Darmstadt)*A*mixed modal/*linear**lambda**calculus*with applications to Bellantoni-Cook safe*recursion*...##
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Page 6076 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

If t is

*a*simple*type**and*@+ M:r° is derivable*in**linear**lambda**calculus*then there is*a*term N*in*the simply-*typed**lambda**calculus*such that @+ M = N°:r° holds*in*the*linear**lambda**calculus*. ...*In**a*nutshell the idea of the proof is as follows: For each*type*t*in*the*linear**lambda**calculus**and*simple*typing*context I’*a*subset For the web version of Mathematical Reviews, see http: //www.ams.org ...##
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Call-by-name, Call-by-value, Call-by-need, and the Linear Lambda Calculus

1995
*
Electronical Notes in Theoretical Computer Science
*

The

doi:10.1016/s1571-0661(04)00022-2
fatcat:at4imbsk3vcpxaotbrndpaxp3e
*linear**lambda**calculus*used*in*this paper is*a*minor re nement of one previously presented by W adler 36,37], which is based on Girard's successor to*linear*logic, the Logic of Unity 12]. ... Our translations are into*a**linear**lambda**calculus*, corresponding to intuitionistic*linear*logic, while Mackie's translation is into proof nets, corresponding to classical*linear*logic. ... ,*and*for & introduction*and*elimination*in*the*linear**lambda**calculus*. ...##
###
Page 2745 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

There is

*a*remarkable difference between usability*and*solvability:*in*the untyped*lambda**calculus*the solvable terms are precisely the terms with*a*head normal form, whereas*in**typed**lambda**calculus*the ... Coquand’s “*calculus*of constructions” is*a*system of*typed*4-*calculus**in*which the second-order polymorphic*typed**A*-*calculus*can be interpreted. ...##
###
Operational Properties of Lily, a Polymorphic Linear Lambda Calculus with Recursion

2001
*
Electronical Notes in Theoretical Computer Science
*

Plotkin has advocated the combination of

doi:10.1016/s1571-0661(04)80874-0
fatcat:tpou5kcubrawvldgy5m44dqsiy
*linear**lambda**calculus*, polymorphism*and*fixed point*recursion*as an expressive semantic metalanguage. ... We show that the naturally call-by-value operators of*linear**lambda**calculus*can be given*a*call-by-name semantics without affecting termination at exponential*types**and*hence without affecting ground ... -*types**in*Lily. to*linear**lambda**calculus*, as we now explain. ...##
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Cumulative subject index

1988
*
Information and Computation
*

, for determination of star height

doi:10.1016/0890-5401(88)90023-5
fatcat:xnrqpyeuefaepjhrbx4w5pqz4e
*and*description, 77, 1 relative star height, 78, 124 C*Calculus*constructions, basic theory, 76, 95*lambda*strictness analysis*and*denotationa] abstract interpretation ... , 76, 29*typed*, reducibility of*types**in*, 77, 131 non-clausal propositional, algorithm for satisliability testing, 79, 1 Categories for multi-tree approach to reliability*in*distributed networks, 79, 43 ... , expressions over untyped*lambda**calculus*models, semantics, inference*and*containment rules, 76, 211 reducibility*in**typed**lambda**calculus*, 77, 131 w Well-foundedness*and*markings*and*infinite ...##
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Combining algebraic rewriting, extensional lambda calculi, and fixpoints

1996
*
Theoretical Computer Science
*

It is well known that confluence

doi:10.1016/s0304-3975(96)00121-1
fatcat:3wj6hg4vobfxzoxumonlv3gvva
*and*strong normalization are preserved when combining algebraic rewriting systems with the simply*typed**lambda**calculus*. ... We show that confluence*and*strong normalization are modular properties for the combination of algebraic rewriting systems with*typed**lambda*calculi enriched with expansive extensional rules for q*and*... the*recursion*-free fragment. ...##
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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. ... (English summary) Inform.*and*Comput. 153 (1999), no.2, 173-237. System F-bounded is*a*second-order*typed**lambda**calculus*used to model the basic features of object-oriented programming lan- guages. ...##
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The Limits of Computation

2021
*
Axiomathes
*

Moreover, it is claimed that

doi:10.1007/s10516-021-09561-8
fatcat:w6nlldlpxvblpjgxp37u6jejke
*typed*systems of the*lambda**calculus*give rise naturally to*a*functional interpretation of rich systems of*types**and*to*a*hierarchy of ordinal*recursive*functionals of arbitrary ... It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable*in**type*-theoretic translations of subsystems of second-order Zermelo Fraenkel set ... There is*a*focus*in*this paper on*typed*systems of*lambda**calculus*. To informally introduce the*typed**lambda**calculus*,*a**type*is*a*property of*a*set of objects. ...
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