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Characterisation of Strongly Normalising lambda-mu-Terms

2013
*
Electronic Proceedings in Theoretical Computer Science
*

We provide a characterisation of strongly normalising terms of the

doi:10.4204/eptcs.121.1
fatcat:tdwl3gn3tfgbvdubgezkgkquwe
*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. ...##
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Strong Normalization of Second Order Symmetric Lambda-mu Calculus
[chapter]

2001
*
Lecture Notes in Computer Science
*

We prove strong normalization of

doi:10.1007/3-540-45500-0_23
fatcat:kjjhlecnczdk3jtg3zuvd4dbza
*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. ...##
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PhD Abstracts

2015
*
Journal of functional programming
*

We are delighted to publish 12 abstracts in this

doi:10.1017/s0956796815000040
fatcat:g7yt23qxivevte45fkiqv6xwna
*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 ...##
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The λ μ T -calculus

2013
*
Annals of Pure and Applied Logic
*

As a first step in that direction, we introduce

doi:10.1016/j.apal.2012.05.005
fatcat:3w7h5bjwdbh6fj5pgodlfxycai
*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. ...##
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Sound and Complete Typing for lambda-mu
[article]

2011
*
arXiv
*
pre-print

In this paper we define intersection

arXiv:1101.4425v1
fatcat:6ko4jvy4lbfz7n2lpzxxpwmphi
*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. ...##
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Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions
[chapter]

2004
*
Lecture Notes in Computer Science
*

Here we prove the strong normalization (SN) of simply

doi:10.1007/978-3-540-24727-2_30
fatcat:7zbsfvgh4ne3fbklq3er2cyiwi
*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 ...##
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Strong normalization results by translation
[article]

2009
*
arXiv
*
pre-print

We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction

arXiv:0905.2892v1
fatcat:7kyierp6graqnpulalz675vpku
*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 ...##
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Strong normalization of lambda-Sym-Prop- and lambda-bar-mu-mu-tilde-star- calculi
[article]

2017
*
arXiv
*
pre-print

Then we give a translation between the

arXiv:1706.07246v1
fatcat:irckjrv6mfedninho6kkivfagm
*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. ...##
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Intersection Types for the lambda-mu Calculus
[article]

2017
*
arXiv
*
pre-print

for the

arXiv:1704.00272v2
fatcat:lwx7666epbhkxd7woj4ng3bj2m
*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. ...##
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The stack calculus

2013
*
Electronic Proceedings in Theoretical Computer Science
*

Our

doi:10.4204/eptcs.113.10
fatcat:kv2q2eb2w5chhhj345r6rlmpum
*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. ...##
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A fully-abstract semantics of lambda-mu in the pi-calculus

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We study the

doi:10.4204/eptcs.164.3
fatcat:ho2ne6x2obaqzcivrykulohdqi
*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 ...##
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Complexity Analysis in Presence of Control Operators and Higher-Order Functions (Long Version)
[article]

2013
*
arXiv
*
pre-print

This is the first example of a

arXiv:1310.1763v1
fatcat:ws3ab46usvevlcezpj2hjpbbpa
*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] . ...##
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A revised completeness result for the simply typed λμ-calculus using realizability semantics
[article]

2017
*
arXiv
*
pre-print

In this paper, we define a new realizability semantics for the simply

arXiv:1612.09223v3
fatcat:fndobp7qjff6peocyypxtys7vi
*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. ...##
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On Bar Recursion and Choice in a Classical Setting
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show how Modified Bar-Recursion, a variant of Spector's Bar-Recursion due to Berger

doi:10.1007/978-3-319-03542-0_25
fatcat:hrvceq7xsnhyjcbjdhqbqpipha
*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*...##
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Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

2009
*
Logical Methods in Computer Science
*

The results obtained extend to

doi:10.2168/lmcs-5(2:11)2009
fatcat:33xfscvbnzgjtmvnzcioe4j3cm
*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. ...
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