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Standard ML Type Generativity as Existential Quantification
, 1996
"... One of the distinguishing features of Standard ML is the use of type generativity. Each declaration of a datatype binds a globally fresh type name to the type identifier introduced. Type generativity has been regarded as an extralogical device which, though desirable in a programming language to ..."
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One of the distinguishing features of Standard ML is the use of type generativity. Each declaration of a datatype binds a globally fresh type name to the type identifier introduced. Type generativity has been regarded as an extralogical device which, though desirable in a programming language to ensure data abstraction, bears no close resemblance to type theoretic constructs. We show that it corresponds precisely to existential quantification over types, and use the observation to suggest proper extensions to the current static semantics of Standard ML.
Proof of the subject reduction property for a πcalculus in COQ
, 1999
"... This paper presents a method for coding picalculus in the COQ proof assistant, in order to use this environment to formalize properties of the picalculus. This method consists in making a syntactic discrimination between free names (then called parameters) and bound names (then called variables) o ..."
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This paper presents a method for coding picalculus in the COQ proof assistant, in order to use this environment to formalize properties of the picalculus. This method consists in making a syntactic discrimination between free names (then called parameters) and bound names (then called variables) of the processes, so that implicit renamings of bound names are avoided in the substitution operation. This technique has been used by J.McKinna and R.Pollack in an extensive study of PTS [5]. We use this coding here to prove subject reduction property for a type system of a monadic picalculus.
Formalization of a Concurrent Object Calculus Up to AlphaConversion
, 1999
"... We present a formalization of a concurrent object calculus in the Calculus of Inductive Constructions. We use de Bruijn technique in an intermediate syntax, but de Bruijn indices do not appear in the final formalization of the terms of the calculus, which are still dened up to ffconversion. We deri ..."
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We present a formalization of a concurrent object calculus in the Calculus of Inductive Constructions. We use de Bruijn technique in an intermediate syntax, but de Bruijn indices do not appear in the final formalization of the terms of the calculus, which are still dened up to ffconversion. We derive substitution rewriting rules and an inductive principle on the subset of the terms which formalize the calculus. Once a certain amount of preliminary work has been done on the intermediate syntax this induction theorem makes possible natural proofs which do not deal with de Bruijn number.