Results 1 
6 of
6
Explicit substitutions
, 1996
"... The λσcalculus is a refinement of the λcalculus where substitutions are manipulated explicitly. The λσcalculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λcalculus and concrete implementatio ..."
Abstract

Cited by 390 (11 self)
 Add to MetaCart
The λσcalculus is a refinement of the λcalculus where substitutions are manipulated explicitly. The λσcalculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λcalculus and concrete implementations.
Confluence properties of Weak and Strong Calculi of Explicit Substitutions
 JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence prope ..."
Abstract

Cited by 120 (7 self)
 Add to MetaCart
Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. [12, 21, 1, 23] are the following: 1. We present a confluent weak calculus of substitutions, where no variable clashes can be feared. 2. We solve a conjecture raised in [1]: oecalculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of oecalculus, named the Envcalculus in [23], called here the confluent oecalculus.
Confluence Properties of Extensional and NonExtensional lambdaCalculi with Explicit Substitutions (Extended Abstract)
 in Proceedings of the Seventh International Conference on Rewriting Techniques and Applications
, 1996
"... ) Delia Kesner CNRS and LRI, B at 490, Universit e ParisSud  91405 Orsay Cedex, France. email:Delia.Kesner@lri.fr Abstract. This paper studies confluence properties of extensional and nonextensional #calculi with explicit substitutions, where extensionality is interpreted by #expansion. For ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
) Delia Kesner CNRS and LRI, B at 490, Universit e ParisSud  91405 Orsay Cedex, France. email:Delia.Kesner@lri.fr Abstract. This paper studies confluence properties of extensional and nonextensional #calculi with explicit substitutions, where extensionality is interpreted by #expansion. For that, we propose a general scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our general scheme makes it possible to treat at the same time many wellknown calculi such as ## , ## # and ## , or some other new calculi that we propose in this paper. We also show for those calculi not fitting in the general scheme that can be translated to another one fitting the scheme, such as #s , how to reason about confluence properties of their extensional and nonextensional versions. 1 Introduction The #calculus is a convenient framework to study functional programming, where the evaluation process is modeled by #reduction. The...
Normalization for Typed Lambda Calculi with Explicit Substitution
 University of Cambridge, Computer Laboratory, Technical Report
, 1994
"... This paper shows that the strong normalization property holds for a restricted class of reductions: those which push a substitution under a abstraction only if this is the outermost constructor. All standard implementations of the typed calculus, like those using a lazy or eager strategy, have th ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
This paper shows that the strong normalization property holds for a restricted class of reductions: those which push a substitution under a abstraction only if this is the outermost constructor. All standard implementations of the typed calculus, like those using a lazy or eager strategy, have this property, hence we can conclude that they terminate. Furthermore, this result means that an implementation of a typed 
Metatheoretical properties of ...: A leftlinear variant of ...
, 1997
"... : In this paper we consider explicit substitutions calculi that allow open terms. In particular, we propose a variant of the oe calculus, that we call OE . For this calculus and its simplytyped version, we study its metatheoretical properties. The OE calculus enjoys the same general character ..."
Abstract
 Add to MetaCart
: In this paper we consider explicit substitutions calculi that allow open terms. In particular, we propose a variant of the oe calculus, that we call OE . For this calculus and its simplytyped version, we study its metatheoretical properties. The OE calculus enjoys the same general characteristics as oe , i.e. a simple and finitary firstorder presentation, confluent on terms with metavariables, with a composition operator and with simultaneous substitutions. However, OE does not have the nonleftlinear surjective pairing rule of oe which raises technical problems in some frameworks. (R'esum'e : tsvp) Cesar.Munoz@inria.fr Unit'e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T'el'ephone : (33 1) 39 63 55 11  T'el'ecopie : (33 1) 39 63 53 30 Propri'et'es m'etath'eoriques de OE : Une variante lin'eaire `a gauche de oe R'esum'e : Dans cet article, on s'int'eresse aux calculs avec substitutions explicites q...
Typedcalculi with explicit substitutions may not terminate
, 1995
"... . We present a simply typed term whose computation in the oecalculus does not always terminate. 1 The oecalculus, introduction Any effective implementation of the calculus requires some control on the substitution to benefit from graph sharing [1] and avoid immediate size explosion. The origin ..."
Abstract
 Add to MetaCart
. We present a simply typed term whose computation in the oecalculus does not always terminate. 1 The oecalculus, introduction Any effective implementation of the calculus requires some control on the substitution to benefit from graph sharing [1] and avoid immediate size explosion. The original calculus cannot describe these controls an easy way. The oe calculus was introduced in [2] as a bridge between the classical calculus and its concrete implementations. Substitutions become explicit, they can be delayed and stored. The calculus provides a pleasant setting to study substitutions and check implementations. The syntax of the oecalculus contains two classes of objects: terms and substitutions. Terms are written in the De Brujn notation [3]. Terms a ::= 1jabjaja[s] Substitutions s ::= idj"ja \Delta sjs ffi t The rule Beta is equivalent to the usual firule of the calculus. The other rules, called oerules, expose how substitutions are pushed inside the terms and perform...