Filters








2,575 Hits in 3.6 sec

The Minimal Graph Model of Lambda Calculus [chapter]

Antonio Bucciarelli, Antonino Salibra
2003 Lecture Notes in Computer Science  
A longstanding open problem in lambda-calculus, raised by G.Plotkin, is whether there exists a continuous model of the untyped lambda-calculus whose theory is exactly the beta-theory or the beta-eta-theory  ...  In particular, we build a graph model the equational theory of which is exactly the set of equations satisfied in any graph model. ¾ ¼ models in each of them inducing pairwise distinct lambda theories  ...  A lambda theory Ì is the minimal lambda theory of the class of graph models if there exists a graph model´ Ôµ such that Ì Ì ´ Ôµ and Ì Ì ´ µ for all other graph modelś µ.  ... 
doi:10.1007/978-3-540-45138-9_24 fatcat:dpc7xdg6qze7fj3ewmpinj5sky

The sensible graph theories of lambda calculus

A. Bucciarelli, A. Salibra
2004 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.  
In this paper we give a positive answer to this question for the semantics of lambda calculus given in terms of graph models.  ...  non-existence of a graph model whose equational theory is exactly the minimal lambda theory § ¦ (this result negatively answers Question 1 in [7, Section 6.2] for the restricted class of graph models).  ...  With regard to the lambda calculus we follow the notation and terminology of [4] . Lambda calculus Graph models The class of graph models belongs to Scott's continuous semantics.  ... 
doi:10.1109/lics.2004.1319622 dblp:conf/lics/BucciarelliS04 fatcat:u6hslqrpgfftjontp6wtlxsk3y

Topological incompleteness and order incompleteness of the lambda calculus

Antonino Salibra
2003 ACM Transactions on Computational Logic  
A model of the untyped lambda calculus univocally induces a lambda theory (i.e., a congruence relation on λ-terms closed under α-and β-conversion) through the kernel congruence relation of the interpretation  ...  A semantics of lambda calculus is (equationally) incomplete if there exists a lambda theory which is not induced by any model in the semantics.  ...  ACKNOWLEDGMENTS The author wishes to thank Gordon Plotkin and the referees for helpful comments and suggestions.  ... 
doi:10.1145/772062.772067 fatcat:ptvuocqvcbe5nawqmtj2ztltyu

Graph lambda theories

ANTONIO BUCCIARELLI, ANTONINO SALIBRA
2008 Mathematical Structures in Computer Science  
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the λβ or the the least sensible λ-theory H (generated by  ...  Berline, is whether, given a class of lambda models, there are a minimal λ-theory and a minimal sensible λ-theory represented by it.  ...  Then one recasts classical recursion theory results in the framework of graph models, and this seems particularly compelling since those are models of the λ-calculus.  ... 
doi:10.1017/s0960129508006683 fatcat:an6ar3j6w5efzbqodnw7fxjdli

Anagopos: A Reduction Graph Visualizer for Term Rewriting and Lambda Calculus

Niels Bjørn Bugge Grathwohl, Jeroen Ketema, Jens Duelund Pallesen, Jakob Grue Simonsen, Marc Herbstritt
2011 International Conference on Rewriting Techniques and Applications  
We present Anagopos, an open source tool for visualizing reduction graphs of terms in lambda calculus and term rewriting.  ...  Anagopos allows step-by-step generation of reduction graphs under six different graph drawing algorithms. We provide ample examples of graphs drawn with the tool.  ...  Acknowledgments The authors thank Jan Willem Klop, Peter Sestoft, and the anonymous referees for useful feedback.  ... 
doi:10.4230/lipics.rta.2011.61 dblp:conf/rta/GrathwohlKPS11 fatcat:wjr3phbg6ne4zavrklslj37f4a

Molecular computers [article]

Marius Buliga
2018 arXiv   pre-print
We propose the chemlambda artificial chemistry, whose behavior strongly suggests that real molecules which embed Interaction Nets patterns and real chemical reactions which resemble Interaction Nets graph  ...  rewrites could be a realistic path towards molecular computers, in the sense explained in the article.  ...  There is a github repository [15] where this model is implemented and various demos are available [9] , which show some features of the model: classical examples of lambda calculus computations, demos  ... 
arXiv:1811.04960v1 fatcat:2spmzxhmpnaudibbuvie4jiloa

Molecular computers

Marius Buliga
2018 Figshare  
rewrites could be a realistic path towards molecular computers, in the sense explained in the article.This is a text version of the article [7].  ...  We propose the chemlambda artificial chemistry, whose behavior strongly suggests that real molecules which embed Interaction Nets patterns and real chemical reactions which resemble Interaction Nets graph  ...  There is a github repository [15] where this model is implemented and various demos are available [9] , which show some features of the model: classical examples of lambda calculus computations, demos  ... 
doi:10.6084/m9.figshare.7339103 fatcat:6t2whbifsjdzrp2vo26cf5qsaa

Easiness in graph models

C. Berline, A. Salibra
2006 Theoretical Computer Science  
In this paper we concentrate on the semantics G of lambda calculus given in terms of graph models, graph semantics for short.  ...  of lambda calculus.  ...  model of lambda calculus.  ... 
doi:10.1016/j.tcs.2005.11.005 fatcat:367kbdjdh5cerfzoybtblycmvi

Foreword

Corrado Böhm, Irène Guessarian
1999 Theoretical Computer Science  
Spreen is a fundamental study on enrichments and refinements of dI-domains and related classes of models. Lambda Calculus of Objects by V. Bono and M.  ...  On Functions Preserving Levels of Approximations: a Refined Model Construction for Various Lambda Calculi by D.  ... 
doi:10.1016/s0304-3975(98)00133-9 fatcat:ea62itnvanbttcep6sq5qojv5y

Lambda calculus as a workflow model

Peter M. Kelly, Paul D. Coddington, Andrew L. Wendelborn
2009 Concurrency and Computation  
We discuss how these can be modeled using lambda calculus, and how ideas from functional programming are applicable in the design of workflows.  ...  This paper explains why lambda calculus is an appropriate model for workflow representation, and how a suitably efficient implementation can provide a wide range of capabilities to developers.  ...  Lambda calculus Lambda calculus [2] is an abstract model of computation which is the theoretical foundation of functional programming.  ... 
doi:10.1002/cpe.1448 fatcat:446xuff7lfei3aa2co6kw25hwi

Lambda Calculus as a Workflow Model

Peter M. Kelly, Paul D. Coddington, Andrew L. Wendelborn
2008 2008 The 3rd International Conference on Grid and Pervasive Computing - Workshops  
We discuss how these can be modeled using lambda calculus, and how ideas from functional programming are applicable in the design of workflows.  ...  This paper explains why lambda calculus is an appropriate model for workflow representation, and how a suitably efficient implementation can provide a wide range of capabilities to developers.  ...  Lambda calculus Lambda calculus [2] is an abstract model of computation which is the theoretical foundation of functional programming.  ... 
doi:10.1109/gpc.workshops.2008.38 dblp:conf/gpc/KellyCW08 fatcat:usih6kyd6bhqjdsz3b5bbewcna

Page 3623 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
It combines the communication mechanism of chi calculus and the recursion mechanism of full lambda calculus, and therefore extends both.”  ...  It is shown that chi calulus is capable of modeling sequential computation in that it captures the operational semantics of call-by-name lambda calculus.  ... 

Page 459 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
In Chapter 18 we get the construction of the projective model D,, and the graph model Pw.  ...  To be sure, models are not the only kind of reality to be considered; the computations encoded in lambda calculus terms are also a reality, perhaps more fundamental than that of the set-theoretic models  ... 

Page 016 of Mathematical Reviews Vol. , Issue 81I [page]

1981 Mathematical Reviews  
The representation of the lambda calculus which we give faithfully models reduction to normal form of terms of the classical lambda calculus which have normal forms; we prove for this representation that  ...  Roman Murawski (Heidelberg) Staples, John 81i1:03017 A graph-like lambda calculus for which leftmost-outermost reduction is optimal.  ... 

Graph easy sets of mute lambda terms

A. Bucciarelli, A. Carraro, G. Favro, A. Salibra
2016 Theoretical Computer Science  
In this paper, we define for each natural number n, an infinite and recursive set M n of mute terms, and show that it is graph-easy: for any closed term t of the lambda calculus there exists a graph model  ...  Among the unsolvable terms of the lambda calculus, the mute ones are those having the highest degree of undefinedness.  ...  Graph models are arguably the simplest models of the lambda calculus. There are two known methods for building graph models, namely: by forcing or by canonical completion.  ... 
doi:10.1016/j.tcs.2015.12.024 fatcat:4ronvkej6vfw7lpptda55gql4q
« Previous Showing results 1 — 15 out of 2,575 results