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

Roberto Cosmo, Delia Kesner
1994 Lecture Notes in Computer Science  
It is well known that con uence 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  ... 
doi:10.1007/3-540-58201-0_90 fatcat:a3s3jyrjbrggzhu22f73vcz4ve

Call-by-name, call-by-value, call-by-need and the linear lambda calculus

J. Maraist, M. Odersky, D.N. Turner, P. Wadler
1999 Theoretical Computer Science  
The 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.  ... 
doi:10.1016/s0304-3975(98)00358-2 fatcat:wpm6kbycovabhlkibythzok3mu

Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus [chapter]

Masahito Hasegawa
2002 Lecture Notes in Computer Science  
We propose 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.  ... 
doi:10.1007/3-540-45788-7_10 fatcat:yci7e6djxfa43amh2mdd5373ty

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
Many students complete PhDs 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  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

Reduction in a Linear Lambda-Calculus with Applications to Operational Semantics [chapter]

Alex Simpson
2005 Lecture Notes in Computer Science  
We study beta-reduction 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.  ... 
doi:10.1007/978-3-540-32033-3_17 fatcat:4ueyxjhavbdmzks6mvxmkvkmc4

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.}  ... 

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  ... 

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  ... 

Call-by-name, Call-by-value, Call-by-need, and the Linear Lambda Calculus

John Maraist, Martin Odersky, David N. Turner, Philip Wadler
1995 Electronical Notes in Theoretical Computer Science  
The 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.  ... 
doi:10.1016/s1571-0661(04)00022-2 fatcat:at4imbsk3vcpxaotbrndpaxp3e

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

G.M. Bierman, A.M. Pitts, C.V. Russo
2001 Electronical Notes in Theoretical Computer Science  
Plotkin has advocated the combination of 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.  ... 
doi:10.1016/s1571-0661(04)80874-0 fatcat:tpou5kcubrawvldgy5m44dqsiy

Cumulative subject index

1988 Information and Computation  
, for determination of star height 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  ... 
doi:10.1016/0890-5401(88)90023-5 fatcat:xnrqpyeuefaepjhrbx4w5pqz4e

Combining algebraic rewriting, extensional lambda calculi, and fixpoints

Roberto Di Cosmo, Delia Kesner
1996 Theoretical Computer Science  
It is well known that confluence 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.  ... 
doi:10.1016/s0304-3975(96)00121-1 fatcat:3wj6hg4vobfxzoxumonlv3gvva

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.  ... 

The Limits of Computation

Andrew Powell
2021 Axiomathes  
Moreover, it is claimed that 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.  ... 
doi:10.1007/s10516-021-09561-8 fatcat:w6nlldlpxvblpjgxp37u6jejke
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