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Graphic Lambda Calculus

Marius Buliga
2013 Complex Systems  
Graphs and Moves An oriented graph is a pair HV, EL, with V the set of nodes and E Õ V ä V the set of edges.  ...  I hope to convince the reader that graphic lambda calculus gives a rigorous answer to this question, being a formalism that contains, in a sense, lambda calculus, emergent algebras, and tangle diagrams  ...  Acknowledgments This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0383.  ... 
doi:10.25088/complexsystems.22.4.311 fatcat:5bocqjhennekrlnmuqmpp5lqbe

Graphic lambda calculus [article]

Marius Buliga
2013 arXiv   pre-print
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing  ...  Reidemeister moves of locally planar tangle diagrams.  ...  We may interpret the graph inside the green dotted rectangle as the currying of A, let's call him Curry(A). This graph has only one output and no inputs.  ... 
arXiv:1305.5786v2 fatcat:qpxxcqjq6zfk7olk6wot35g5nu

Demonstrating Lambda Calculus Reduction [chapter]

Peter Sestoft
2002 Lecture Notes in Computer Science  
We show how to simply and efficiently trace such reductions, and use this in a web-based lambda calculus reducer available at˜sestoft/lamreduce/ .  ...  We describe lambda calculus reduction strategies, such as call-by-value, call-by-name, normal order, and applicative order, using big-step operational semantics.  ...  Landin defined the semantics of programming languages in terms of the lambda calculus [11] , and gave a call-by-value interpreter for it: the secd-machine [10] .  ... 
doi:10.1007/3-540-36377-7_19 fatcat:lvhipzyr2nazjhkungdahil5fe

Demonstrating Lambda Calculus Reduction

Peter Sestoft
2001 Electronical Notes in Theoretical Computer Science  
We show how to simply and efficiently trace such reductions, and use this in a web-based lambda calculus reducer available at˜sestoft/lamreduce/ .  ...  We describe lambda calculus reduction strategies, such as call-by-value, call-by-name, normal order, and applicative order, using big-step operational semantics.  ...  Landin defined the semantics of programming languages in terms of the lambda calculus [11] , and gave a call-by-value interpreter for it: the secd-machine [10] .  ... 
doi:10.1016/s1571-0661(04)80973-3 fatcat:usjdjt53a5cbnkeh4g4n4qeit4

The Safe Lambda Calculus

William Blum, C.-H. Luke Ong, Simona Ronchi Della Rocca
2009 Logical Methods in Computer Science  
In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simply-typed lambda calculus.  ...  We also propose an adequate notion of beta-reduction that preserves safety.  ...  We thank Ugo dal Lago for the insightful discussions we had during his visit at the Oxford University Computing Laboratory in March 2008, and the anonymous referees for helpful comments.  ... 
doi:10.2168/lmcs-5(1:3)2009 fatcat:xo2amjpnyjewhoebjgdmrkjtpe

Continuity and Discontinuity in Lambda Calculus [chapter]

Paula Severi, Fer-Jan de Vries
2005 Lecture Notes in Computer Science  
As a first application, we prove that there is an injective embedding from the infinitary lambda calculus of the ∞η-Böhm trees in D∞.  ...  This paper studies continuity of the normal form and the context operators as functions in the infinitary lambda calculus.  ...  We thank Vincent van Oostrom and the referees for their useful comments, Mariangiola Dezani-Ciancaglini for her knowledge and inspiration, Simona Ronchi della Rocca for telling us the solution of a key  ... 
doi:10.1007/11417170_27 fatcat:wf5s5b6r2ndfhadzfgokgrktiu

Categorical completeness results for the simply-typed lambda-calculus [chapter]

Alex K. Simpson
1995 Lecture Notes in Computer Science  
We investigate, in a categorical setting, some completeness properties of beta-eta conversion between closed terms of the simplytyped lambda calculus.  ...  A cartesian-closed category is said to be complete if, for any two unconvertible terms, there is some interpretation of the calculus in the category that distinguishes them.  ...  Acknowledgements I thank Aurelio Carboni, Eugenio Moggi and Pino Rosolini for useful feedback when I presented this work in Genoa. This research was carried out under an EPSRC postdoctoral fellowship.  ... 
doi:10.1007/bfb0014068 fatcat:dbbegn55lrhsxgmxiilddv344e

Strict Ideal Completions of the Lambda Calculus

Patrick Bahr, Michael Wagner
2018 International Conference on Rewriting Techniques and Applications  
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions.  ...  In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion.  ...  the Lambda Calculus from Blom [9] , which will serve as mediator between metric completion and ideal completion. 1 A lambda tree is a (possibly infinite) labelled tree where a label λ indicates abstraction  ... 
doi:10.4230/lipics.fscd.2018.8 dblp:conf/rta/Bahr18 fatcat:krjoccbfcfbrjjk7b632j6trlm

On Constructor Rewrite Systems and the Lambda Calculus

Ugo Dal Lago, Simone Martini, Wolfgang Thomas
2012 Logical Methods in Computer Science  
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each  ...  In particular, weak call-by- value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps.  ...  Given a signature Σ, a labelled graph over Σ consists of a directed acyclic graph together with an ordering on the outgoing edges of each node and a (partial) labelling of nodes with symbols from Σ such  ... 
doi:10.2168/lmcs-8(3:12)2012 fatcat:b6jjp5g6nvcirmndn4i7iy3iru

An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

Damiano Mazza
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
This paper proposes a technical realization of this idea: an affine lambda-calculus is introduced, based on a fragment of intuitionistic multiplicative linear logic; the calculus is endowed with a notion  ...  of distance making the set of terms an incomplete metric space; the completion of this space is shown to yield an infinitary affine lambda-calculus, whose quotient under a suitable partial equivalence  ...  Acknowledgments We are thankful to Michele Pagani and Rune Bak for interesting discussions on the subject of this paper.  ... 
doi:10.1109/lics.2012.57 dblp:conf/lics/Mazza12 fatcat:ldqkg5sxyzb75lfgmanlhbwsl4

Polymorphic lambda calculus and subtyping

Adrian Fiech, David A. Schmidt
2002 Theoretical Computer Science  
We present a denotational model for F , the extension of second-order lambda calculus with subtyping deÿned in Cardelli and Wegner (ACM Comput. Surveys 17(4) (1985) 471-522.)  ...  Types are interpreted as arbitrary cpos and elements of types as natural transformations. We prove the soundness of our model with respect to the equational theory of F (Cardelli et al.  ...  is the at cpo of record labels.  ... 
doi:10.1016/s0304-3975(00)00333-9 fatcat:ubfrfxrhr5dudpgcutqaauhj2i

Normalization by Evaluation for Call-By-Push-Value and Polarized Lambda Calculus

Andreas Abel, Christian Sattler
2019 Proceedings of the 21st International Symposium on Principles and Practice of Programming Languages 2019 - PPDP '19  
We further discuss different implementations of the monad and their relation to existing normalization proofs for lambda-calculus with sums.  ...  We observe that normalization by evaluation for simply-typed lambda-calculus with weak coproducts can be carried out in a weak bi-cartesian closed category of presheaves equipped with a monad that allows  ...  Moggi's studies were continued by Levy [19] who designed the call-by-push-value (CBPV) lambda-calculus to embed both the CBN and CBV lambda calculus.  ... 
doi:10.1145/3354166.3354168 dblp:conf/ppdp/0001S19 fatcat:hyx7bh5jebgdrirboktvpxxoeu

A Calculus for Modeling Software Components [chapter]

Oscar Nierstrasz, Franz Achermann
2003 Lecture Notes in Computer Science  
We have identified a number of key features and mechanisms for expressing composable software, and propose a calculus for modeling components, based on the asynchronous π calculus extended with explicit  ...  This calculus serves as a semantic foundation and an executable abstract machine for Piccola, an experimental composition language.  ...  Acknowledgments We gratefully acknowledge the financial support of the Swiss National Science Foundation for projects No. 20-61655.00, "Meta-models and Tools for Evolution Towards Component Systems", and  ... 
doi:10.1007/978-3-540-39656-7_14 fatcat:tw7cbheuvnetrhe3eeytzxeifi

Algebras and coalgebras in the light affine Lambda calculus

Marco Gaboardi, Romain Péchoux
2015 SIGPLAN notices  
Their use permits to better structure the computations and also to enhance the expressivity of a language or of a proof system.  ...  Algebra and coalgebra are widely used to model data types in functional programming languages and proof assistants.  ...  The Light Affine Lambda Calculus The Light Affine Lambda Calculus is the affine version of the Light Linear Lambda Calculus [39] and provide a concrete syntax for Intuitionistic Light Affine Logic [  ... 
doi:10.1145/2858949.2784759 fatcat:ezlynnzdxrepfpxnj3qtddwj2q

The λ-calculus in the π-calculus

2011 Mathematical Structures in Computer Science  
The power of the approach is demonstrated by applying it to generate an encoding of the full lambda calculus in the π-calculus.  ...  -The intensional equalities of source models are interpreted by the observational equivalence of the π-calculus. The quality of an interpretation is judged by a full abstraction property.  ...  We are also grateful to the two anonymous referees for their detailed comments on a previous version of this paper.  ... 
doi:10.1017/s0960129511000260 fatcat:2awxblpejfaubfqtjqpgl7mv7i
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