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Expansion: the Crucial Mechanism for Type Inference with Intersection Types: Survey and Explanation
 In: (ITRS ’04
, 2005
"... The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying ..."
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Cited by 17 (7 self)
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The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying out compositional type inference. The fundamental idea of expansion is to be able to calculate the effect on the final judgement of a typing derivation of inserting a use of the intersectionintroduction typing rule at some (possibly deeply nested) position, without actually needing to build the new derivation.
The Implicit Calculus of Constructions  Extending Pure Type Systems with an Intersection Type Binder and Subtyping
 Proc. of 5th Int. Conf. on Typed Lambda Calculi and Applications, TLCA'01, Krakow
, 2001
"... In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Currystyle variant of the Calculus of Constructions that we extend by adding an intersection type binder called the implicit dependent product. Unlike the usual approach of Type Assignment Systems ..."
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Cited by 13 (0 self)
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In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Currystyle variant of the Calculus of Constructions that we extend by adding an intersection type binder called the implicit dependent product. Unlike the usual approach of Type Assignment Systems, the implicit product can be used at every place in the universe hierarchy. We study syntactical properties of this calculus such as the subject reduction property, and we show that the implicit product induces a rich subtyping relation over the type system in a natural way. We also illustrate the specicities of this calculus by revisitting the impredicative encodings of the Calculus of Constructions, and we show that their translation into the implicit calculus helps to reect the computational meaning of the underlying terms in a more accurate way.
Comparing cubes of typed and type assignment systems
 Annals of Pure and Applied Logic
, 1997
"... We study the cube of type assignment systems, as introduced in [13], and confront it with Barendregt’s typed λcube [4]. The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address th ..."
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Cited by 7 (3 self)
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We study the cube of type assignment systems, as introduced in [13], and confront it with Barendregt’s typed λcube [4]. The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address the question whether a judgement, derivable in a type assignment system, is always an erasure of a derivable judgement in a corresponding typed system; we show that this property holds only for the systems without polymorphism. The type assignment systems we consider satisfy the properties ‘subject reduction’ and ‘strong normalization’. Moreover, we define a new type assignment cube that is isomorphic to the typed one.
Polymorphic type inference of the relational algebra
 Journal of Computer and System Sciences
"... ..."
Type Inference in the Polymorphic Relational Algebra
, 1999
"... We give a polymorphic account of the relational algebra. We introduce a formalism of "type formulas" specifically tuned for relational algebra expressions, and present an algorithm that computes the "principal" type for a given expression. The principal type of an expression is a ..."
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Cited by 4 (0 self)
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We give a polymorphic account of the relational algebra. We introduce a formalism of "type formulas" specifically tuned for relational algebra expressions, and present an algorithm that computes the "principal" type for a given expression. The principal type of an expression is a formula that specifies, in a clear and concise manner, all assignments of types (sets of attributes) to relation names, under which a given relational algebra expression is welltyped, as well as the output type that expression will have under each of these assignments. Topics discussed include complexity, the relationship with monadic logic, and polymorphic expressive power. 1 Introduction The operators of the relational algebra (the basis of all relational query languages) are polymorphic. We can take the natural join of any two relations, regardless of their sets of attributes. We can take the union of any two relations over the same set of attributes. We can take the cartesian product of any two relation...
Comparing Cubes of Typed and Type Assignment Systems
"... We study the cube of type assignment systems, as introduced in [13], and confront it with Barendregt’s typedcube [4]. The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address the ..."
Abstract
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We study the cube of type assignment systems, as introduced in [13], and confront it with Barendregt’s typedcube [4]. The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address the question whether a judgement, derivable in a type assignment system, is always an erasure of a derivable judgement in a corresponding typed system; we show that this property holds only for the systems without polymorphism. The type assignment systems we consider satisfy the properties ‘subject reduction ’ and ‘strong normalization’. Moreover, we define a new type assignment cube that is isomorphic to the typed one.
WRLA 2004 Preliminary Version The Polymorphic Rewritingcalculus [Type Checking vs. Type Inference]
"... The Rewritingcalculus (Rhocalculus), is a minimal framework embedding Lambdacalculus and Term Rewriting Systems, by allowing abstraction on variables and patterns. The Rhocalculus features higherorder functions (from Lambdacalculus) and patternmatching (from Term Rewriting Systems). In this ..."
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The Rewritingcalculus (Rhocalculus), is a minimal framework embedding Lambdacalculus and Term Rewriting Systems, by allowing abstraction on variables and patterns. The Rhocalculus features higherorder functions (from Lambdacalculus) and patternmatching (from Term Rewriting Systems). In this paper, we study extensively a secondorder Rhocalculus a ̀ la Church (RhoF) that enjoys subject reduction, type uniqueness, and decidability of typing. We then apply a classical typeerasing function to RhoF obtaining an untyped Rhocalculus a ̀ la Curry (uRhoF). The related type inference system is isomorphic to RhoF and enjoys subject reduction. Both RhoF and uRhoF systems can be considered as minimal calculi for polymorphic rewritingbased programming languages. We discuss the possibility of a logic existing underneath the type systems via a CurryHoward Isomorphism.