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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
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  . 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
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
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
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
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  where this model is implemented and various demos are available  , which show some features of the model: classical examples of lambda calculus computations, demos ...arXiv:1811.04960v1 fatcat:2spmzxhmpnaudibbuvie4jiloa
rewrites could be a realistic path towards molecular computers, in the sense explained in the article.This is a text version of the article . ... 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  where this model is implemented and various demos are available  , which show some features of the model: classical examples of lambda calculus computations, demos ...doi:10.6084/m9.figshare.7339103 fatcat:6t2whbifsjdzrp2vo26cf5qsaa
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
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
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  is an abstract model of computation which is the theoretical foundation of functional programming. ...doi:10.1002/cpe.1448 fatcat:446xuff7lfei3aa2co6kw25hwi
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  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
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. ...
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 ...
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. ...
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
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