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290
Formalizing a Named Explicit Substitutions Calculus in Coq
"... Abstract. Explicit Substitutions (ES) calculi are extensions of the λcalculus that internalize the substitution operation, which is a metaoperation, by taking it as an ordinary operation belonging to the grammar of the ES calculus. As a formal system, ES are closer to implementations of function ..."
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Abstract. Explicit Substitutions (ES) calculi are extensions of the λcalculus that internalize the substitution operation, which is a metaoperation, by taking it as an ordinary operation belonging to the grammar of the ES calculus. As a formal system, ES are closer to imple
Formalization of a λCalculus with Explicit Substitutions in Coq
"... We present a formalization of the λσ⇑calculus[9] in the Coq V5.8 system[6]. The principal axiomatized result is the confluence of this calculus. Furthermore we propose a uniform encoding for manysorted first order term rewriting systems, on which we study the local confluence by critical pairs ana ..."
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We present a formalization of the λσ⇑calculus[9] in the Coq V5.8 system[6]. The principal axiomatized result is the confluence of this calculus. Furthermore we propose a uniform encoding for manysorted first order term rewriting systems, on which we study the local confluence by critical pairs
Formalizing Real Calculus in Coq
, 2002
"... We have finished a constructive formalization in the theorem prover Coq of the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes. This formalization is built upon the library of constructive algebra created in the FTA (Fundamental Theorem of Alg ..."
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We have finished a constructive formalization in the theorem prover Coq of the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse processes. This formalization is built upon the library of constructive algebra created in the FTA (Fundamental Theorem
Handling Substitutions Explicitely in the piCalculus
"... . We present two calculi aimed at describing the mechanism of name manipulation in the {calculus. Following the ideas underlying the introduction of the s and calculi, we dene s and . The former calculus includes operators on De Bruijn indices, and is rst introduced to give an intuitive description ..."
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description of the De Bruijn representation of { calculus terms. The latter is a calculus of explicit substitutions, where the computations pertaining to name manipulation are described by a Term Rewrite System. We introduce the two corresponding notions of bisimulation, and show that they can be put
The Calculus of Explicit Substitutions
, 1994
"... AEcalculus is a new simple calculus of explicit substitutions. In this paper we explore its properties, namely we prove that it correctly implements fi reduction, it is confluent, its simply typed version is strongly normalizing. We associate with AE an abstract machine called the Umachine and we ..."
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Cited by 4 (1 self)
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AEcalculus is a new simple calculus of explicit substitutions. In this paper we explore its properties, namely we prove that it correctly implements fi reduction, it is confluent, its simply typed version is strongly normalizing. We associate with AE an abstract machine called the Umachine and we
The πcalculus with explicit substitutions
, 1996
"... Abstract. The aim of this work is to describe the prototypical mobility expressed by the πcalculus within a CCSlike approach to process algebras. Many versions of πcalculus bisimulation equivalence are found in the literature: late – both strong and weak – bisimilarity and full congruence, early ..."
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ogous characterizations do hold for branching and progressing – both late and early – bisimulations. The goal is achieved by introducing suitable constructors for both the explicit handling of name substitutions and the explicit instantiation of names. The operational interpretation of those operators ensures that input
Explicit substitutions for the calculus
"... Abstract. The calculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong normalisa ..."
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Abstract. The calculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong
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 ..."
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Cited by 129 (7 self)
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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
On Explicit Substitutions and Names
 In Proc. ICALP
, 1997
"... Calculi with explicit substitutions have found widespread acceptance as a basis for abstract machines for functional languages. In this paper we investigate the relations between variants with de Bruijnnumbers, with variable names, with reduction based on raw expressions and calculi with equational ..."
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Cited by 2 (1 self)
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Calculi with explicit substitutions have found widespread acceptance as a basis for abstract machines for functional languages. In this paper we investigate the relations between variants with de Bruijnnumbers, with variable names, with reduction based on raw expressions and calculi
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
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