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Parametricity as a Notion of Uniformity in Reflexive Graphs
, 2002
"... data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information. ..."
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data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information.
Constructed Product Result Analysis for Haskell
"... Compilers for ML and Haskell typically go to a good deal of trouble to arrange that multiple arguments can be passed eciently to a procedure. For some reason, less effort seems to be invested in ensuring that multiple results can also be returned efficiently. In the context ..."
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Cited by 7 (1 self)
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Compilers for ML and Haskell typically go to a good deal of trouble to arrange that multiple arguments can be passed eciently to a procedure. For some reason, less effort seems to be invested in ensuring that multiple results can also be returned efficiently. In the context
System ST  Toward A Type System for Extraction AND Proof of Programs
, 2001
"... We introduce a new type system called \System ST" (ST stands for SubTyping), based on subtyping, and prove the basic property of the system. We show the extraordinary expressive power of the system which leads us to think that it could be a good candidate for doing both proof and extraction ..."
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We introduce a new type system called \System ST" (ST stands for SubTyping), based on subtyping, and prove the basic property of the system. We show the extraordinary expressive power of the system which leads us to think that it could be a good candidate for doing both proof and extraction of programs.
Building continuous webbed models for System F
, 2000
"... We present here a large family of concrete models for Girard and Reynolds polymorphism (System F ), in a non categorical setting. The family generalizes the construction of the model of Barbanera and Berardi [2], hence it contains complete models for F [5] and we conjecture that it contains models w ..."
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We present here a large family of concrete models for Girard and Reynolds polymorphism (System F ), in a non categorical setting. The family generalizes the construction of the model of Barbanera and Berardi [2], hence it contains complete models for F [5] and we conjecture that it contains models which are complete for F . It also contains simpler models, the simplest of them, E 2 ; being a second order variant of the EngelerPlotkin model E . All the models here belong to the continuous semantics and have underlying prime algebraic domains, all have the maximum number of polymorphic maps. The class contains models which can be viewed as two intertwined compatible webbed models of untyped calculus (in the sense of [8]), but it is much larger than this. Finally many of its models might be read as two intertwined strict intersection type systems. Contents 1
On Phase Semantics and Denotational Semantics: The SecondOrder
, 2002
"... In this paper, we extend the nonuniform denotational semantics de ned by Bucciarelli and Ehrhard in [BuEh,00] to secondorder linear logic. ..."
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In this paper, we extend the nonuniform denotational semantics de ned by Bucciarelli and Ehrhard in [BuEh,00] to secondorder linear logic.
QPC 2 : A Constructive Calculus with Parameterized Specifications
, 1995
"... A second order constructive calculus is presented in this paper. The idea is not to give a yet another system but to restrict higher order calculi such as the Calculus of Constructions (CoC) [2, 3] and MartinLöf's Intuitionistic Type Theory (ITT) with the hierarchy of universes [10]. One of th ..."
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A second order constructive calculus is presented in this paper. The idea is not to give a yet another system but to restrict higher order calculi such as the Calculus of Constructions (CoC) [2, 3] and MartinLöf's Intuitionistic Type Theory (ITT) with the hierarchy of universes [10]. One of the aims of the restriction is to provide a program synthesis system which directly generates functional programs with the program constructs such as ifthenelse and pairing. Unlike CoC, F [5], and F ! [4], we do not use Prawitz coding of logical connectives [15] because, if we use the coding, the constructs such as ifthenelse and pairing are not primitives but the functionals dened in higher order lambda terms. Another aim of the restriction is to nd a subset of existing higher order systems which is necessary and su cient for parameterized specications. The obtained system, which is called QPC 2 , roughly corresponds to a subset of ITT with the universes U 1 and U 2 , but has a few die...
Type Checking in System . . .
"... The main contribution of this paper is a partial typechecking algorithm for the system F and its use in a programming language like ML. We dene this system as an extension of the secondorder calculus (system F) verifying the preservation of type during computation (subjectreduction) for red ..."
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The main contribution of this paper is a partial typechecking algorithm for the system F and its use in a programming language like ML. We dene this system as an extension of the secondorder calculus (system F) verifying the preservation of type during computation (subjectreduction) for reduction (this result fails for reduction in system F). Our presentation is based on an original notion of subtyping which includes all the handling of quantication rules. 1 Introduction. Motivation. Type systems have proved to be useful for many modern functional programming languages such as ML, Miranda, Haskell, . . . . In most cases, the basis of the type system is Milner's algorithm [12]. The main characteristic of these type systems is polymorphism which allows the programmer to write generic functions that can work on arguments of dierent types. However it is often insucient: polymorphic recursion, existential types or the state monad of Haskell are treated using specic exte...
A kappadenotational semantics for Map Theory in ZFC + SI
 in ZFC+SI, Theoretical Computer Science 179
, 1997
"... Map theory, or MT for short, has been designed as an \integrated" foundation for mathematics, logic and computer science. By this we mean that most primitives and tools are designed from the beginning to bear the three intended meanings: logical, computational, and settheoretic. MT was ori ..."
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Map theory, or MT for short, has been designed as an \integrated" foundation for mathematics, logic and computer science. By this we mean that most primitives and tools are designed from the beginning to bear the three intended meanings: logical, computational, and settheoretic. MT was originally introduced in [17]. It is based on calculus instead of logic and sets, and it fullls Church's original aim of introducing calculus. In particular, it embodies all of ZFC set theory, including classical propositional and classical rst order predicate calculus. MT also embodies the unrestricted, untyped lambda calculus including unrestricted abstraction and unrestricted use of the xed point operator. MT is an equational theory. We present here a semantic proof of the consistency of map theory within ZFC + SI, where SI asserts the existence of an inaccessible cardinal. The proof is in the spirit of denotational semantics and relies on mathematical tools which reect faithful...