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Compilation and Equivalence of Imperative Objects
, 1998
"... We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics fo ..."
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Cited by 36 (4 self)
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We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics for the calculus. Our rst two results are theorems asserting the equivalence of our substitutionbased semantics with a closurebased semantics like that given by Abadi and Cardelli. Our third result is a direct proof of the correctness of compilation to a stackbased abstract machine via a smallstep decompilation algorithm. Our fourth result is that contextual equivalence of objects coincides with a form of Mason and Talcott's CIU equivalence; the latter provides a tractable means of establishing operational equivalences. Finally, we prove correct an algorithm, used in our prototype compiler, for statically resolving method osets. This is the rst study of correctness of an objectoriented abstract machine, and of operational equivalence for the imperative object calculus.
lambdacalculi with explicit substitutions and composition which preserve beta strong normalization (Extended Abstract)
, 1996
"... ) Maria C. F. Ferreira 1 and Delia Kesner 2 and Laurence Puel 2 1 Dep. de Inform'atica, Fac. de Ciencias e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre, 2825 Monte de Caparica, Portugal, cf@fct.unl.pt. 2 CNRS & Lab. de Rech. en Informatique, Bat 490, Univ. de ParisSud, 91405 O ..."
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Cited by 29 (4 self)
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) Maria C. F. Ferreira 1 and Delia Kesner 2 and Laurence Puel 2 1 Dep. de Inform'atica, Fac. de Ciencias e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre, 2825 Monte de Caparica, Portugal, cf@fct.unl.pt. 2 CNRS & Lab. de Rech. en Informatique, Bat 490, Univ. de ParisSud, 91405 Orsay Cedex, France, fkesner,puelg@lri.fr. Abstract. We study preservation of fistrong normalization by d and dn , two confluent calculi with explicit substitutions defined in [10]; the particularity of these calculi is that both have a composition operator for substitutions. We develop an abstract simulation technique allowing to reduce preservation of fistrong normalization of one calculus to that of another one, and apply said technique to reduce preservation of fistrong normalization of d and dn to that of f , another calculus having no composition operator. Then, preservation of fistrong normalization of f is shown using the same technique as in [2]. As a consequence, d and dn become the fir...
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
, 1996
"... Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. In that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. The oe calculus of explicit s ..."
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Cited by 24 (6 self)
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Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. In that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. The oe calculus of explicit substitutions, proposed by Abadi, Cardelli, Curien andL evy, is a firstorder rewriting system that implements substitution and renaming mechanism of calculus. However, oe does not preserve strong normalisation of calculus and it is not a confluent system. Typed variants of oe without composition are strongly normalising but not confluent, while variants with composition are confluent but do not preserve strong normalisation. Neither of them enjoys both properties. In this paper we propose the i calculus. This is, as far as we know, the first confluent calculus of explicit substitutions that preserves strong normalisation. 1. Explicit substitutions The calculus is a higherorder theor...
Confluence of Extensional and NonExtensional λcalculi with Explicit Substitutions
 Theoretical Computer Science
"... This paper studies confluence of extensional and nonextensional calculi with explicit substitutions, where extensionality is interpreted by jexpansion. For that, we propose a scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. O ..."
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Cited by 12 (2 self)
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This paper studies confluence of extensional and nonextensional calculi with explicit substitutions, where extensionality is interpreted by jexpansion. For that, we propose a scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our method makes it possible to treat at the same time many wellknown calculi such as oe , oe * , OE , s , AE , f , d and dn . Keywords: functional programming, calculi, explicit substitutions, confluence, extensionality. 1 Introduction The calculus is a convenient framework to study functional programming, where the evaluation process is modeled by fireduction. The main mechanism used to perform fireduction is substitution, which consists of the replacement of formal parameters by actual arguments. The correctness of substitution is guaranteed by a systematic renaming of bound variables, inconvenient which can be simply avoided in the calculus `a la de Bruijn by using natur...
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
, 1995
"... Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. Thus, in that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. This feature is useful, f ..."
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Cited by 10 (0 self)
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Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. Thus, in that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. This feature is useful, for instance, to represent incomplete proofs in type based proof systems. The oe calculus of explicit substitutions proposed by Abadi, Cardelli, Curien and L'evy gives an elegant way to deal with management of variable names and substitutions of calculus. However, oe does not preserve strong normalisation of calculus and it is not a confluent system. Typed variants of oe without composition are strongly normalising but not confluent, while variants with composition are confluent but do not preserve strong normalisation. Neither of them enjoys both properties. In this paper we propose the i  calculus an we present the full proofs of its main properties. This is, as far as we know, the...
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 characteris ..."
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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.
A Leftlinear Variant of λσ
, 1997
"... In this paper we consider calculi of explicit substitutions that admit open expressions, i.e. expressions with metavariables. In particular, we propose a variant of the oecalculus that we call L . For this calculus and its simplytyped version, we study its metatheoretical properties. The Lcal ..."
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In this paper we consider calculi of explicit substitutions that admit open expressions, i.e. expressions with metavariables. In particular, we propose a variant of the oecalculus that we call L . For this calculus and its simplytyped version, we study its metatheoretical properties. The Lcalculus enjoys the same general characteristics as oe, i.e. a simple and finitary firstorder presentation, confluent on expressions with metavariables of terms and weakly normalizing on typed expressions. Moreover, L does not have the nonleftlinear surjective pairing rule of oe which raises technical problems in some frameworks.