Relevant bibliographies by topics / Lambda calculi

Academic literature on the topic 'Lambda calculi'

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Published: 11 March 2023

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Journal articles on the topic "Lambda calculi"

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Zamdzhiev, Vladimir. "Computational Adequacy for Substructural Lambda Calculi." Electronic Proceedings in Theoretical Computer Science 333 (February 8, 2021): 322–34. http://dx.doi.org/10.4204/eptcs.333.22.

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KAMAREDDINE, FAIROUZ. "Typed $\lambda$-calculi with one binder." Journal of Functional Programming 15, no. 05 (June 8, 2005): 771. http://dx.doi.org/10.1017/s095679680500554x.

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Boudol, G. "Lambda-Calculi for (Strict) Parallel Functions." Information and Computation 108, no. 1 (January 1994): 51–127. http://dx.doi.org/10.1006/inco.1994.1003.

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Staples, John. "Delaying unification algorithms for lambda calculi." Theoretical Computer Science 56, no. 3 (March 1988): 277–88. http://dx.doi.org/10.1016/0304-3975(88)90135-1.

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BOUDOL, GÉRARD, PIERRE-LOUIS CURIEN, and CAROLINA LAVATELLI. "A semantics for lambda calculi with resources." Mathematical Structures in Computer Science 9, no. 4 (August 1999): 437–82. http://dx.doi.org/10.1017/s0960129599002893.

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We present the λ-calculus with resources λr, and two variants of it: a deterministic restriction λm and an extension λcr with a convergence testing operator. These calculi provide a control on the substitution process – deadlocks may arise if not enough resources are available to carry out all the substitutions needed to pursue a computation. The design of these calculi was motivated by Milner's encoding of the λ-calculus in the π-calculus. As Boudol and Laneve have shown elsewhere, the discriminating power of λm (given by the contextual observational equivalence) over λ-terms coincides with that induced by Milner's π-encoding, and coincides also with that provided by the lazy algebraic semantics (Lévy–Longo trees). The main contribution of this paper is model-theoretic. We define and solve an appropriate domain equation, and show that the model thus obtained is fully abstract with respect to λcr. The techniques used are in the line of those used by Abramsky for the lazy λ-calculus, the main departure being that the resource-consciousness of our calculi leads us to introduce a non-idempotent form of intersection types.
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Katayama, Susumu. "Computable Variants of AIXI which are More Powerful than AIXItl." Journal of Artificial General Intelligence 10, no. 1 (January 1, 2019): 1–23. http://dx.doi.org/10.2478/jagi-2019-0001.

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Abstract This paper presents Unlimited Computable AI, or UCAI, that is a family of computable variants of AIXI. UCAI is more powerful than AIXItl, which is a conventional family of computable variants of AIXI, in the following ways: 1) UCAI supports models of terminating computation, including typed lambda calculi, while AIXItl only supports Turing machine with timeout ˜t, which can be simulated by typed lambda calculi for any ˜t; 2) unlike UCAI, AIXItl limits the program length to some ˜l .
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ZORZI, MARGHERITA. "On quantum lambda calculi: a foundational perspective." Mathematical Structures in Computer Science 26, no. 7 (November 17, 2014): 1107–95. http://dx.doi.org/10.1017/s0960129514000425.

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In this paper, we propose an approach to quantum λ-calculi. The ‘quantum data-classical control’ paradigm is considered. Starting from a measurement-free untyped quantum λ-calculus calledQ, we will study standard properties such as confluence and subject reduction, and some good quantum properties. We will focus on the expressive power, analysing the relationship with other quantum computational models. Successively, we will add an explicit measurement operator toQ. On the resulting calculus, calledQ*, we will propose a complete study of reduction sequences regardless of their finiteness, proving confluence results. Moreover, since the stronger motivation behind quantum computing is the research of new results in computational complexity, we will also propose a calculus which captures the three classes of quantum polytime complexity, showing an ICC-like approach in the quantum setting.
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Mulmuley, Ketan. "Fully abstract submodels of typed lambda calculi." Journal of Computer and System Sciences 33, no. 1 (August 1986): 2–46. http://dx.doi.org/10.1016/0022-0000(86)90041-3.

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Nielson, Flemming, and Hanne Riis Nielson. "Prescriptive Frameworks for Multi-Level Lambda-Calculi." ACM SIGPLAN Notices 32, no. 12 (December 1997): 193–202. http://dx.doi.org/10.1145/258994.259018.

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Joy, M. "Lambda Calculi: A Guide For Computer Scientists." Computer Journal 38, no. 1 (January 1, 1995): 78–79. http://dx.doi.org/10.1093/comjnl/38.1.78-a.

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Dissertations / Theses on the topic "Lambda calculi"

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Yang, Liqun. "Logical relation categories and lambda calculi." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/9876.

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An aspect of programming languages is the study of the operational semantics, which, in the case of a lambda calculus, is based on a directed form of equational reasoning called reduction. In computer science terminology, reduction may be regarded as a form of symbolic evaluation. It models a sequential computation process step by step. The crucial properties for a rewriting system are confluence, also called the Church-Rosser property and termination, the (Strong) normalization property, respectively. These are studied in depth in Chapter 2 and 6. The problem whether all $\lambda$-terms satisfy termination corresponds to the halting problem. From a different point of view, studying the problem of both Church-Rosser and strong normalization corresponds to, in a particular field, studying the word problem. The notion of categories is familiar to mathematicians as a branch of algebra. It has been developed quite rapidly in less than 40 years. In particular, recently more and more computer scientists are using categories for their own purposes. It is the connection between categories and $\lambda$-calculi that interests computer scientists. This connection is a thread that goes through the whole thesis. (Abstract shortened by UMI.)
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Madiot, Jean-Marie. "Higher-order languages : dualities and bisimulation enhancements." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL0988/document.

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Les comportements des processus concurrents peuvent être exprimés en utilisant des calculs de processus, des langages formels simples qui permettent de démontrer des résultats mathématiques précis sur les interactions entre processus. Un exemple très simple est CCS, un autre exemple est le pi-calcul, plus expressif grâce à un mécanisme de communication de canaux. Dans ce dernier, on peut instaurer un système de types (pour raffiner l'analyse aux environnements plus contraints) et encoder le lambda-calcul (qui représente les calculs séquentiels).Certains de ces calculs, comme CCS ou des variantes du pi-calcul comme les calculs de fusions, ont une certaine propriété de symétrie. On utilise dans un premier temps cette symétrie comme un outil, pour prouver que deux encodages du lambda-calcul dans le pi-calcul sont en fait équivalents.Cette preuve nécessitant un système de types et une forme de symétrie, on se pose la question de l'existence d'un système de types pour les autres calculs symétriques, notamment les calculs de fusion, à laquelle on répond par la négative avec un théorème d'impossibilité.En analysant ce théorème, on découvre un contrainte fondamentale de ces calculs qui empêche l'utilisation des types, à savoir la présence d'une notion de relation d'équivalence entre les canaux de communication. Le relâchement de cette contrainte pour obtenir une relation de pré-ordre engendre un calcul intéressant qui recouvre des notions importantes du pi-calcul, absentes dans les calculs de fusion : les types et les noms privés. La première partie de la thèse se concentre sur l'étude de ce calcul.La deuxième partie de la thèse se concentre sur la bisimulation, une méthode pour établir l'équivalence de deux agents dans des langages d'ordre supérieur, par exemple le pi-calcul ou le lambda-calcul. Une amélioration de cette méthode est la théorie des techniques modulo, très puissante, mais qui malheureusement s'applique uniquement aux systèmes de premier ordre, comme les automates ou CCS.Cette thèse s'applique alors à décrire les langages d'ordre supérieur en tant que systèmes du premier ordre. On récupère ainsi la théorie générale des techniques modulo pour ces langages, en prouvant correctes la correspondance induite et les techniques spécifiques à chaque langage. On détaille les tenants et aboutissants de cette approche, pour fournir les outils nécessaires à son utilisation pour d'autres langages d'ordre supérieur
The behaviours of concurrent processes can be expressed using process calculi, which are simple formal languages that let us establish precise mathematical results on the behaviours and interactions between processes. A very simple example is CCS, another one is the pi-calculus, which is more expressive thanks to a name-passing mechanism. The pi-calculus supports the addition of type systems (to refine the analysis to more subtle environments) and the encoding of the lambda-calculus (which represents sequential computations).Some of these calculi, like CCS or variants of the pi-calculus such as fusion calculi, enjoy a property of symmetry. First, we use this symmetry as a tool to prove that two encodings of the lambda-calculus in the pi-calculus are in fact equivalent.This proof using a type system and a form of symmetry, we wonder if other existing symmetric calculi can support the addition of type systems. We answer negatively to this question with an impossibility theorem.Investigating this theorem leads us to a fundamental constraint of these calculi that forbids types: they induce an equivalence relation on names. Relaxing this constraint to make it a preorder relation yields another calculus that recovers important notions of the pi-calculus, that fusion calculi do not satisfy: the notions of types and of privacy of names. The first part of this thesis focuses on the study of this calculus, a pi-calculus with preorders on names.The second part of this thesis focuses on bisimulation, a proof method for equivalence of agents in higher-order languages, like the pi- or the lambda-calculi. An enhancement of this method is the powerful theory of bisimulations up to, which unfortunately only applies for first-order systems, like automata or CCS.We then proceed to describe higher-order languages as first-order systems. This way, we inherit the general theory of up-to techniques for these languages, by proving correct the translations and up-to techniques that are specific to each language. We give details on the approach, to provide the necessary tools for future applications of this method to other higher-order languages
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ZORZI, Margherita. "Lambda calculi and logics for quantum computing." Doctoral thesis, Università degli Studi di Verona, 2009. http://hdl.handle.net/11562/337380.

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In questa tesi proponiamo diversi risultati originali riguardo i lambda calcoli e le logiche per le computazioni quantistiche. Il lavoro `e diviso in tre parti. Nella prima parte richiamiamo alcune nozioni fondamentali di algebra lineare, logica e computazione quantistica. La seconda parte volge l’attenzione ai lambda calcoli quantistici. Introdurremo dapprima Q, un lambda calcolo quantistico con controllo classico. Studieremo le sue proprie`a classiche, come la confluenza e la Subject Reduction, proseguendo poi con un’importante propriet`a quantistica, chiamata standardizzazione. In seguito sar`a studiato il potere espressivo di Q, attraverso la provata equivalenza con il formalismo delle famiglie di circuiti quantistici. A partire da Q, sar`a poi definito e studiato il sottolinguaggio SQ, ispirato alla Soft Linear Logic ed intrinsecamente polytime. Sia Q sia SQ non hanno nella sintassi un operatore di misurazione, e quindi un’implicita misurazione viene assunta alla fine delle computazioni. I problemi relativi alla misura sono studiati in un terzo lambda calcolo chiamato Q*, che estende Q con un operatore di misura. Partendo dall’osservazione che un esplicito operatore di misura interrompe l’evoluzione altrimenti deterministica del calcolo, importando un comportamento probabilistico, sono stati definiti dei nuovi strumenti tecnici quali le computazioni probabilistiche e gli stati misti. Proveremo un forte teorema di confluenza, valido anche nell’importante caso delle computazioni infinite. Nella terza parte della tesi studieremo invece due sistemi modali etichettati, chiamati rispettivamente MSQS e MSpQS, che permettono di ragionare qualitativamente sulle computazioni quantistiche. I due sistemi rappresentano un possibile punto di partenza verso un nuovo modello per ragionare qualitativamente sulle trasformazioni computazionali degli stati quantistici, viste come modelli di Kripke. 1
In this thesis we propose several original results about lambda calculi and logics for quantum computing. The work is divided into three parts. The first one is devoted to recall the main notions about linear algebra, logics and quantum computing. The second and main part focalizes on quantum lambda calculi. We start with Q, a quantum lambda calculus with classical control. We study its classical properties, such as confluence and Subject Reduction. We go on with an important quantum property of Q, called standardization, and successively, we study the expressive power of the proposed calculus, by proving the equivalence with the computational model of quantum circuit families. From the calculus Q, subsequently a sublanguage of Q called SQ is defined and studied: SQ is inspired to the Soft Linear Logic and it is a quantum lambda calculus intrinsically poly-time. Since Q and SQ have not an explicit measurement operator in the syntax, an implicit measurement at the end of the computations is assumed. Measurement problems are explicitly studied in a third quantum lambda calculus called Q*, an extension of Q with a measurement operator. Starting from the observation that an explicit measurement operator breaks the deterministic evolution of the computation by importing a probabilistic behavior, new technical instruments, such as the probabilistic computations and the mixed states are defined. We prove a confluence result for the calculus, also for the relevant case of infinite computations. In the last part of the thesis, we propose two labeled modal deduction systems able to describe quantum computations from a qualitative point of view. The two systems, called respectively MSQS and MSpQS, represent a starting point toward a new model to deal (in a qualitative way) with computational quantum structures, seen as Kripke models. 1
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Barral, Freiric. "Decidability for Non-Standard Conversions in Typed Lambda-Calculi." Diss., lmu, 2008. http://nbn-resolving.de/urn:nbn:de:bvb:19-97617.

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Ritter, Eike. "Categorical abstract machines for higher-order typed lambda calculi." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.281971.

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Carraro, Alberto <1983&gt. "Models and theories of pure and resource lambda calculi." Doctoral thesis, Università Ca' Foscari Venezia, 2011. http://hdl.handle.net/10579/1089.

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Parte I: Un problema aperto da lungo tempo è se esiste un modello del lambda calcolo non tipato nella categoria CPO degli ordinamenti parziali completi e funzioni Scott-continue, la cui teoria equazionale è esattamente la minima lambda-teoria λβ o la minima lambda-teoria estensionale λβη: è il Problema 22 nella lista dei problemi aperti TLCA (http://tlca.di.unito.it/opltlca/problem22.pdf). In questa tesi si analizza la classe dei dominii di Scott riflessivi, i modelli del lambda calcolo che vivono nella categoria dei dominii di Scott (una sottocategoria piena di CPO). Noi isoliamo, tra i domini riflessivi di Scott, una classe di modelli a trama derivanti dai sistemi informativi di Scott, che noi chiamiamo i-modelli. La classe degli i-modelli comprende, ad esempio, tutti i modelli preordinati coerenti, tutti i modelli a filtro che vivono in CPO e tutti i dominii di Scott estensionali riflessivi. Effettuando uno studio a dettagliato, di una versione "effettiva" dei sistemi informativi di Scott degli i-modelli si ottengono i seguenti risultati principali: c'è un'importante classe di i-modelli che non è completa per il lambda calcolo estensionale e tale nessun suo membro ha una teoria dell'ordine ricorsivamente enumerabile. Un lambda-termine chiuso M è facile se, per qualsiasi altro termine chiuso N, la lambda-teoria generata dall'equazione M=N è consistente, mentre è facile semplice se, dato un tipo intersezione τ arbitrario, si può trovare un pre-ordine adeguato sui tipi che permette di derivare τ per M. La facilità semplice implica la facilità. La questione se la facilità implichi o meno la facilità semplice costituisce il Problema 19 nella lista dei problemi aperti TLCA (http://tlca.di.unito.it/opltlca/problem19.pdf). Come sottoprodotto del nostro lavoro sugli i-modelli, siamo in grado di risolvere questo problema: diamo una risposta negativa, fornendo un insieme non vuoto di lambda-termini facili ma non facili semplici. Parte II: Dato un semi-anello con unità che soddisfi alcune condizioni, si definisce un funtore esponenziale della categoria degli insiemi e relazioni che consente di definire un modello denotazionale della Logica Lineare Differenziale e del lambda calcolo con risorse . Si dimostra che, quando il semi-anello è un elemento che è "infinitario", questo modello non convalida la formula di Taylor e che è possibile costruire, nella categoria Cartesiana chiusa di Kleisli associata, un modello del lambda calcolo puro che non è sensibile. Questo è un analogo quantitativo della costruzione del grafo modello di Park nella categoria dei dominii di Scott. Abbiamo avviato uno studio puramente algebrico del lambda calcolo con risorse di Ehrhard e Regnier, introducendo tre varietà algebriche: algebre combinatorie con risorse, lambda-algebre con risorse e algebre di lambda-astrazione con risorse. Stabiliamo le relazioni tra di esse, e gettiamo le basi per una teoria dei modelli del lambda calcolo con risorse. Mostriamo anche che il completamento ideale di un'algebra combinatoria (resp. lambda-algebra, algebra di lambda-astrazione) con risorse induce un'algebra combinatoria (resp. lambda-algebra, algebra di lambda-astrazione) "classica'', e che qualsiasi modello del lambda calcolo classico proveniente da una lambda-algebra con risorse determina una lambda-teoria che identifica tutti i termini che hanno lo stesso albero di Bohm.
Part I: A longstanding open problem is whether there exists a model of the untyped lambda calculus in the category CPO of complete partial orderings and Scott continuous functions, whose theory is exactly the least lambda-theory λβ or the least extensional lambda-theory λβη: it is Problem 22 in the TLCA list of open problems (http://tlca.di.unito.it/opltlca/problem22.pdf). In this thesis we analyze the class of reflexive Scott domains, the models of lambda calculus living in the category of Scott domains (a full subcategory of CPO). We isolate, among the reflexive Scott domains, a class of webbed models arising from Scott's information systems, that we call i-models. The class of i-models includes, for example, all preordered coherent models, all filter models living in CPO and all extensional reflexive Scott domains. By performing a fine-grained study of an ''effective'' version of Scott's information systems and i-models we obtain the following main results: there is an important class of i-models which is not complete for the extensional calculus and whose members never have a recursively enumerable order theory. A closed lambda-term M is easy if, for any other closed term N, the lambda-theory generated by the equation M = N is consistent, while it is simple easy if, given an arbitrary intersection type τ, one can find a suitable pre-order on types which allows to derive τ for M. Simple easiness implies easiness. The question whether easiness implies simple easiness constitutes Problem 19 in the TLCA list of open problems (http://tlca.di.unito.it/opltlca/problem19.pdf). As a byproduct of our work on i-models, we are in the position of solving this problem: we answer negatively, providing a nonempty set of easy, but non simple easy, lambda-terms. Part II: Given a semi-ring with unit which satisfies some conditions, we define an exponential functor on the category of sets and relations which allows to define a denotational model of Differential Linear Logic and of the lambda-calculus with resources. We show that, when the semi-ring has an element which is ''infinitary", this model does not validate the Taylor formula and that it is possible to build, in the associated Kleisli cartesian closed category, a model of the pure lambda-calculus which is not sensible. This is a quantitative analogue of the Park's graph model construction in the category of Scott domains. We initiate a purely algebraic study of Ehrhard and Regnier's resource lambda-calculus, by introducing three algebraic varieties: resource combinatory algebras, resource lambda-algebras and resource lambda-abstraction algebras. We establish the relations between them, laying down foundations for a model theory of resource lambda calculus. We also show that the ideal completion of a resource combinatory algebra (resp. lambda-algebra, lambda-abstraction algebra) induces a ''classical'' combinatory algebra (resp. lambda-algebra, lambda-abstraction algebra), and that any model of the pure lambda calculus raising from a resource lambda-algebra determines a lambda-theory which equates all terms having the same Bohm tree.
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Loader, Ralph. "Models of lambda calculi and linear logic : structural, equational and proof-theoretic characterisations." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282167.

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Kuc̆an, Jakov. "Metatheorems about convertibility in typed lambda calculi : applications to CPS transform and "free theorems"." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42606.

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Solieri, Marco. "Sharing, Superposition and Epansion : Geometrical Studies on the semantics and Implementation of lambda-calculi and proof-nets." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCD015/document.

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Des sémantiques élégantes et des implémentations efficaces des langages de programmation fonctionnels peuvent être décrits par les mêmes structures mathématiques, notamment dans la correspondance Curry-Howard, où le programmes, les types et l’exécution, coïncident aux preuves, formules et normalisation. Une telle flexibilité est aiguisé par l’approche déconstructive et géométrique de la logique linéaire (LL) et les réseaux de preuve, et de la réduction optimale et les graphes de partage (SG).En adaptent la géométrie de l’interaction de Girard, cette thèse propose une géométrie de l’interaction des ressources (GoRI), une sémantique dynamique et dénotationnelle, qui décrit algébriquement par leurs chemins, les termes du calcul des ressources (RC), une variation linéaire et non-déterministe du lambda calcul (LC). Les séries infinis dans RC sont aussi le domaine du développement de Taylor-Ehrhard-Regnier, une linéarisation du LC. La thèse explique la relation entre ce dernier et la réduction démontrant qu’ils commutent, et présente une version développé de la formule d’exécution pour calculer les chemins du LC typé.Les SG sont un modèle d’implémentation du LC, dont les pas sont locales et asynchrones, et le partage implique et les termes et les contextes. Bien que les tests ont montré des accélérations exceptionnelles, jusqu à exponentielles, par rapport aux implémentations traditionnelles, les SG n’ont pas que des avantages. La thèse montre que, dans le cas restreint des réseaux élémentaires, où seule le cœur des SG est requis, les désavantages sont au plus quadratique, donc inoffensifs
Elegant semantics and efficient implementations of functional programming languages can both be described by the very same mathematical structures, most prominently with in the Curry-Howard correspondence, where programs, types and execution respectively coincide with proofs, formulæ and normalisation. Such a flexibility is sharpened by the deconstructive and geometrical approach pioneered by linear logic (LL) and proof-nets, and by Lévy-optimal reduction and sharing graphs (SG).Adapting Girard’s geometry of interaction, this thesis introduces the geometry of resource interaction (GoRI), a dynamic and denotational semantics, which describes, algebra-ically by their paths, terms of the resource calculus (RC), a linear and non-deterministic variation of the ordinary lambda calculus. Infinite series of RC-terms are also the domain of the Taylor-Ehrhard-Regnier expansion, a linearisation of LC. The thesis explains the relation between the former and the reduction by proving that they commute, and provides an expanded version of the execution formula to compute paths for the typed LC. SG are an abstract implementation of LC and proof-nets whose steps are local and asynchronous, and sharing involves both terms and contexts. Whilst experimental tests on SG show outstanding speedups, up to exponential, with respect to traditional implementations, sharing comes at price. The thesis proves that, in the restricted case of elementary proof-nets, where only the core of SG is needed, such a price is at most quadratic, hence harmless
Semantiche eleganti ed implementazioni efficienti di linguaggi di programmazione funzionale possono entrambe essere descritte dalle stesse strutture matematiche, più notevolmente nella corrispondenza Curry-Howard, dove i programmi, i tipi e l’esecuzione coincidono, nell’ordine, con le dimostrazioni, le formule e la normalizzazione. Tale flsesibilità è acuita dall’approccio decostruttivo e geometrico della logica lineare (LL) e le reti di dimostrazione, e della riduzione ottimale e i grafi di condivisione (SG).Adattando la geometria dell’interazione di Girard, questa tesi introduce la geometria dell’interazione delle risorse (GoRI), una semantica dinamica e denotazionale che descrive, algebricamente tramite i loro per-corsi, i termini del calcolo delle risorse (RC), una variante lineare e non-deterministica del lambda calcolo ordinario. Le serie infinite di termini del RC sono inoltre il dominio dell’espansione di Taylor-Ehrhard-Regnier, una linearizzazione del LC. La tesi spiega la relazione tra quest’ultima e la riduzione dimostrando che esse commutano, e fornisce una versione espansa della for-mula di esecuzione per calcolare i percorsi del LC tipato. I SG sono un modello d’implementazione del LC, i cui passi sono loc-ali e asincroni, e la cui condivisione riguarda sia termini che contesti. Sebbene le prove sperimentali sui SG mostrino accellerazioni eccezionali, persino esponenziali, rispetto alle implementazioni tradizionali, la condivisione ha un costo. La tesi dimostra che, nel caso ristretto delle reti elementari, dove è necessario solo il cuore dei SG, tale costo è al più quad-ratico, e quindi innocuo
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Taylor, Amelia V. "A unifying framework for Lambda Calculi and their extensions with explicit substitution operators that is useful for verifying confluence." Thesis, Heriot-Watt University, 2006. http://hdl.handle.net/10399/119.

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Books on the topic "Lambda calculi"

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Amadio, Roberto M. Domains and lambda-calculi. Cambridge, U.K: Cambridge University Press, 1998.

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Hasegawa, Masahito, ed. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38946-7.

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Hofmann, Martin, ed. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44904-3.

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Della Rocca, Simona Ronchi, ed. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73228-0.

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Groote, Philippe, and J. Roger Hindley, eds. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-62688-3.

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Dezani-Ciancaglini, Mariangiola, and Gordon Plotkin, eds. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0014040.

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Bezem, Marc, and Jan Friso Groote, eds. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0037093.

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Ong, Luke, ed. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21691-6.

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Dowek, Gilles, ed. Rewriting and Typed Lambda Calculi. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08918-8.

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Abramsky, Samson, ed. Typed Lambda Calculi and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45413-6.

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Book chapters on the topic "Lambda calculi"

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Hölzl, Matthias, and John N. Crossley. "Constraint-Lambda Calculi." In Frontiers of Combining Systems, 207–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45988-x_17.

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Ariola, Zena M., and Stefan Blom. "Cyclic lambda calculi." In Lecture Notes in Computer Science, 77–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0014548.

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Dal Lago, Ugo, Giulio Guerrieri, and Willem Heijltjes. "Decomposing Probabilistic Lambda-Calculi." In Lecture Notes in Computer Science, 136–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_8.

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AbstractA notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one of the main advantages of lambda-calculus: confluence, which means results are independent from the choice of strategy. We present a probabilistic lambda-calculus where the probabilistic operator is decomposed into two syntactic constructs: a generator, which represents a probabilistic event; and a consumer, which acts on the term depending on a given event. The resulting calculus, the Probabilistic Event Lambda-Calculus, is confluent, and interprets the call-by-name and call-by-value strategies through different interpretations of the probabilistic operator into our generator and consumer constructs. We present two notions of reduction, one via fine-grained local rewrite steps, and one by generation and consumption of probabilistic events. Simple types for the calculus are essentially standard, and they convey strong normalization. We demonstrate how we can encode call-by-name and call-by-value probabilistic evaluation.
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Hankin, Chris. "Lambda Calculi: A Guide." In Handbook of Philosophical Logic, 1–66. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0485-5_1.

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Hölzl, Matthias M., and John N. Crossley. "Disjunctive Constraint Lambda Calculi." In Logic for Programming, Artificial Intelligence, and Reasoning, 64–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11591191_6.

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Ghilezan, Silvia. "Application of typed lambda calculi in the untyped lambda calculus." In Logical Foundations of Computer Science, 129–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58140-5_13.

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Faggian, Claudia, and Giulio Guerrieri. "Factorization in Call-by-Name and Call-by-Value Calculi via Linear Logic." In Lecture Notes in Computer Science, 205–25. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_11.

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AbstractIn each variant of the $$\lambda $$ λ -calculus, factorization and normalization are two key properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants separately, we prove them only once, for the bang calculus (an extension of the $$\lambda $$ λ -calculus inspired by linear logic and subsuming CbN and CbV), and then we transfer the result via translations, obtaining factorization/normalization for CbN and CbV.The approach is robust: it still holds when extending the calculi with operators and extra rules to model some additional computational features.
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Sands, David, Jörgen Gustavsson, and Andrew Moran. "Lambda Calculi and Linear Speedups." In Lecture Notes in Computer Science, 60–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36377-7_4.

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Clouston, Ranald. "Fitch-Style Modal Lambda Calculi." In Lecture Notes in Computer Science, 258–75. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89366-2_14.

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Santo, José Espírito, Delia Kesner, and Loïc Peyrot. "A Faithful and Quantitative Notion of Distant Reduction for Generalized Applications." In Lecture Notes in Computer Science, 285–304. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99253-8_15.

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AbstractWe introduce a call-by-name lambda-calculus $$\lambda J$$ λ J with generalized applications which integrates a notion of distant reduction that allows to unblock $$\beta $$ β -redexes without resorting to the permutative conversions of generalized applications. We show strong normalization of simply typed terms, and we then fully characterize strong normalization by means of a quantitative typing system. This characterization uses a non-trivial inductive definition of strong normalization –that we relate to others in the literature–, which is based on a weak-head normalizing strategy. Our calculus relates to explicit substitution calculi by means of a translation between the two formalisms which is faithful, in the sense that it preserves strong normalization. We show that our calculus $$\lambda J$$ λ J and the well-know calculus $$\varLambda J$$ Λ J determine equivalent notions of strong normalization. As a consequence, $$\varLambda J$$ Λ J inherits a faithful translation into explicit substitutions, and its strong normalization can be characterized by the quantitative typing system designed for $$\lambda J$$ λ J , despite the fact that quantitative subject reduction fails for permutative conversions.
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Conference papers on the topic "Lambda calculi"

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Deng, Yuxin, and Yuan Feng. "Bisimulations for probabilistic linear lambda calculi." In 2017 International Symposium on Theoretical Aspects of Software Engineering (TASE). IEEE, 2017. http://dx.doi.org/10.1109/tase.2017.8285625.

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Nielson, Flemming, and Hanne Riis Nielson. "Prescriptive frameworks for multi-level lambda-calculi." In the 1997 ACM SIGPLAN symposium. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/258993.259018.

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Laird, Jim, Giulio Manzonetto, Guy McCusker, and Michele Pagani. "Weighted Relational Models of Typed Lambda-Calculi." In 2013 Twenty-Eighth Annual IEEE/ACM Symposium on Logic in Computer Science (LICS 2013). IEEE, 2013. http://dx.doi.org/10.1109/lics.2013.36.

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Breuvart, Flavien, and Ugo Dal Lago. "On Intersection Types and Probabilistic Lambda Calculi." In PPDP '18: The 20th International Symposium on Principles and Practice of Declarative Programming. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3236950.3236968.

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Lago, Ugo Dal. "Infinitary Lambda Calculi from a Linear Perspective." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2934505.

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Henglein, Fritz, and Harry G. Mairson. "The complexity of type inference for higher-order lambda calculi." In the 18th ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/99583.99602.

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Bloom, Bard. "CHOCOLATE: Calculi of Higher Order COmmunication and LAmbda TErms (preliminary report)." In the 21st ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/174675.177948.

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Maranget, Luc. "Optimal derivations in weak lambda-calculi and in orthogonal term rewriting systems." In the 18th ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/99583.99618.

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Hillebrand, Gerd G., and Paris C. Kanellakis. "Functional database query languages as typed lambda calculi of fixed order (extended abstract)." In the thirteenth ACM SIGACT-SIGMOD-SIGART symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/182591.182615.

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Goyet, Alexis. "The Lambda Lambda-Bar calculus." In the 40th annual ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2429069.2429089.

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Reports on the topic "Lambda calculi"

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Durfee, Glenn. A Model for a List-Oriented Extension of the Lambda Calculus,. Fort Belvoir, VA: Defense Technical Information Center, May 1997. http://dx.doi.org/10.21236/ada327564.

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