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Characterisation of Strongly Normalising lambda-mu-Terms

Steffen van Bakel, Franco Barbanera, Ugo de'Liguoro
2013 Electronic Proceedings in Theoretical Computer Science  
We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types.  ...  The presence of the latter and a restricted use of the type omega enable us to represent the particular notion of continuation used in the literature for the definition of semantics for the lambda-mu-calculus  ...  The system we consider here does not include rules (∀I) and (∀E), since they have no effect on the subject in Parigot's first-order type assignment system.  ... 
doi:10.4204/eptcs.121.1 fatcat:tdwl3gn3tfgbvdubgezkgkquwe

Strong Normalization of Second Order Symmetric Lambda-mu Calculus [chapter]

Yoriyuki Yamagata
2001 Lecture Notes in Computer Science  
We prove strong normalization of second order λµ-calculus with these rules.  ...  Parigot suggested symmetric structural reduction rules for application to µ-abstraction in [9] to ensure unique representation of data type.  ...  I am grateful to Ken-etsu Fujita, Ryu Hasegawa and Charles Stewart for their helpful comments and discussion.  ... 
doi:10.1007/3-540-45500-0_23 fatcat:kjjhlecnczdk3jtg3zuvd4dbza

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
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.  ...  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.  ...  Finally, we introduce Parigot's lambda mu-calculus, which extends lambda calculus with two operators called mu and bracket, and then the extended calculus by De Groote, in which the operators mu and bracket  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

The λ μ T -calculus

Herman Geuvers, Robbert Krebbers, James McKinna
2013 Annals of Pure and Applied Logic  
As a first step in that direction, we introduce lambda-mu-T, a combination of Parigot's lambda-mu-calculus and G\"odel's T, to extend a calculus with control operators with a datatype of natural numbers  ...  We consider the problem of confluence on raw terms, and that of strong normalization for the well-typed terms.  ...  Acknowledgments We are grateful to the anonymous referees who spotted some mistakes in earlier versions of this paper and provided several helpful suggestions.  ... 
doi:10.1016/j.apal.2012.05.005 fatcat:3w7h5bjwdbh6fj5pgodlfxycai

Sound and Complete Typing for lambda-mu [article]

Steffen van Bakel
2011 arXiv   pre-print
In this paper we define intersection and union type assignment for Parigot's calculus lambda-mu.  ...  This implies that this notion of intersection-union type assignment is suitable to define a semantics.  ...  Conclusions We have seen that the calculus λµ is sufficiently limited to allow for the definition of a sound and complete notion of type assignment.  ... 
arXiv:1101.4425v1 fatcat:6ko4jvy4lbfz7n2lpzxxpwmphi

Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions [chapter]

Emmanuel Polonovski
2004 Lecture Notes in Computer Science  
Here we prove the strong normalization (SN) of simply typed λµμ-calculus with explicit substitutions.  ...  The λµμ-calculus, defined by Curien and Herbelin [7] , is a variant of the λµ-calculus that exhibits symmetries such as term/context and call-by-name/call-by-value.  ...  Introduction λµμ-Calculus and Explicit Substitutions The λµμ-calculus, defined by Curien and Herbelin [7] , is a symmetric variant of Parigot's λµ-calculus [11] that provides a term notation for classical  ... 
doi:10.1007/978-3-540-24727-2_30 fatcat:7zbsfvgh4ne3fbklq3er2cyiwi

Strong normalization results by translation [article]

René David
2009 arXiv   pre-print
We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed lambda-mu-calculus.  ...  In this paper, we study the typed λµ →∧∨ -calculus. This calculus, introduced by de Groote in [7] , is an extension of Parigot's λµ-calculus.  ...  whereas, using ϕ, the simulation is done with the usual rules of the λµ-calculus. • There is another way of coding ∧ and ∨ by using intuitionistic second order logic. - {A 1 ∧ A 2 } • = ∀X((A • 1 → (A  ... 
arXiv:0905.2892v1 fatcat:7kyierp6graqnpulalz675vpku

Strong normalization of lambda-Sym-Prop- and lambda-bar-mu-mu-tilde-star- calculi [article]

Peter Battyanyi, Karim Nour
2017 arXiv   pre-print
Then we give a translation between the lambda-Sym-Prop-calculus and the lambda-bar-mu-mu-tilde-star-calculus, which is the implicational part of the lambda-bar-mu-mu-tilde-calculus invented by Curien and  ...  In this paper we give an arithmetical proof of the strong normalization of lambda-Sym-Prop of Berardi and Barbanera [1], which can be considered as a formulae-as-types translation of classical propositional  ...  We wish to thank René David and the anonymous referees for helpful discussions and remarks.  ... 
arXiv:1706.07246v1 fatcat:irckjrv6mfedninho6kkivfagm

Intersection Types for the lambda-mu Calculus [article]

Steffen van Bakel, Franco Barbanera, Ugo de'Liguoro
2017 arXiv   pre-print
for the typed lambda-mu calculus.  ...  We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion.  ...  Following [52] , we define the interpretation of expressions of Parigot's λµ-calculus inductively via a set of equations.  ... 
arXiv:1704.00272v2 fatcat:lwx7666epbhkxd7woj4ng3bj2m

The stack calculus

Alberto Carraro, Thomas Ehrhard, Antonino Salibra
2013 Electronic Proceedings in Theoretical Computer Science  
Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic.  ...  We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded.  ...  We proved that the untyped stack calculus enjoys confluence, and that types enforce strong normalization. The typed fragment is a sound and complete system for full implicational Classical Logic.  ... 
doi:10.4204/eptcs.113.10 fatcat:kv2q2eb2w5chhhj345r6rlmpum

A fully-abstract semantics of lambda-mu in the pi-calculus

Steffen van Bakel, Maria Grazia Vigliotti
2014 Electronic Proceedings in Theoretical Computer Science  
We study the lambda-mu-calculus, extended with explicit substitution, and define a compositional output-based interpretation into a variant of the pi-calculus with pairing that preserves single-step explicit  ...  We define four notions of weak equivalence for lambda-mu -- one based on weak reduction, two modelling weak head-reduction and weak explicit head reduction (all considering terms without weak head-normal  ...  Conclusions and future work We have studied the output based, logic-inspired interpretation of untyped λµ with explicit substitution into the π-calculus and shown that this interpretation is fully abstract  ... 
doi:10.4204/eptcs.164.3 fatcat:ho2ne6x2obaqzcivrykulohdqi

Complexity Analysis in Presence of Control Operators and Higher-Order Functions (Long Version) [article]

Ugo Dal Lago, Giulio Pellitta
2013 arXiv   pre-print
This is the first example of a type system for the lambda-mu-calculus guaranteeing time complexity bounds for typable programs.  ...  Following Laurent, the logic naturally gives rise to a type system for the lambda-mu-calculus, whose derivations reveal bounds on the time complexity of the underlying term.  ...  An extension of de Groote's calculus named Λµ-calculus [29] satisfies a Böhm separation theorem that fails for Parigot's calculus [9] .  ... 
arXiv:1310.1763v1 fatcat:ws3ab46usvevlcezpj2hjpbbpa

A revised completeness result for the simply typed λμ-calculus using realizability semantics [article]

Karim Nour, Mohamad Ziadeh
2017 arXiv   pre-print
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type.  ...  This paper corrects some errors in [21] by the first author and Saber.  ...  We can now state and prove the completeness theorem. Theorem 3.1 (Completeness theorem) Let A be a type and t a term.  ... 
arXiv:1612.09223v3 fatcat:fndobp7qjff6peocyypxtys7vi

On Bar Recursion and Choice in a Classical Setting [chapter]

Valentin Blot, Colin Riba
2013 Lecture Notes in Computer Science  
We show how Modified Bar-Recursion, a variant of Spector's Bar-Recursion due to Berger and Oliva can be used to realize the Axiom of Countable Choice in Parigot's Lambda-Mu-calculus, a direct-style language  ...  for the representation and evaluation of classical proofs.  ...  Note that as with v • above, the amount to which an expression is curryfied/uncurryfied depends on the context, and moreover that in G, ( ) Lambda-Mu-Calculus We present here an extension of Parigot's  ... 
doi:10.1007/978-3-319-03542-0_25 fatcat:hrvceq7xsnhyjcbjdhqbqpipha

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

Jose Espirito Santo, Ralph Matthes, Luis Pinto, Simona Ronchi Della Rocca
2009 Logical Methods in Computer Science  
The results obtained extend to second and higher-order calculi.  ...  Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's λ_mu-calculus.  ...  The second author thanks for an invitation by that institution to Braga in October 2006 and in May 2007.  ... 
doi:10.2168/lmcs-5(2:11)2009 fatcat:33xfscvbnzgjtmvnzcioe4j3cm
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