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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
Coq in Coq
, 1997
"... . We formalize the definition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong normalization and decidability of type inference. From the latter proof, we extract a certified Objective Caml program which performs type inference in ..."
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. We formalize the definition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong normalization and decidability of type inference. From the latter proof, we extract a certified Objective Caml program which performs type inference
A Formalization of the Simply Typed Lambda Calculus in Coq
"... Abstract. In this paper we present a formalization of the simply typed lambda calculus with constants and with typing `a la Church. It has been accomplished using the theorem prover Coq. The formalization includes, among other results, definitions of typed terms over arbitrary manysorted signature, ..."
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Abstract. In this paper we present a formalization of the simply typed lambda calculus with constants and with typing `a la Church. It has been accomplished using the theorem prover Coq. The formalization includes, among other results, definitions of typed terms over arbitrary manysorted signature
A formalization of Γ ∞ in Coq
, 2010
"... In this paper we present a formalization of the type systems Γ ∞ in the proof assistant Coq. The family of type systems Γ∞, described in a recent article by Geuvers, McKinna and Wiedijk [9], presents type theory without the need for explicit contexts. A typing judgment in Γ ∞ is of the shape A: ∞ B ..."
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In this paper we present a formalization of the type systems Γ ∞ in the proof assistant Coq. The family of type systems Γ∞, described in a recent article by Geuvers, McKinna and Wiedijk [9], presents type theory without the need for explicit contexts. A typing judgment in Γ ∞ is of the shape A: ∞ B
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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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
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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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
of Calculus of Explicit Substitutions with Composition
"... Abstract. We develop a novel method for proving the strong normalizability of simply typed λx with a composition rule. Bloo and Geuvers [2] proved the strong normalizability of λx with a composition rule, but our composition rule is a new one: t〈y:=r〉〈x:=s 〉 → t〈x:=s〉〈y:=r〈x:=s〉 〉 if x ∈ FV(r). In ..."
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is finite. This implies that the metasubstitution is admissible in our calculus. 1
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