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53
The Essence of Principal Typings
 In Proc. 29th Int’l Coll. Automata, Languages, and Programming, volume 2380 of LNCS
, 2002
"... Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A M : # meanin ..."
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Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A M : # meaning that M has result type # when assuming the types of free variables are given by A. Then (A, #) is a typing for M .
A Calculus with Polymorphic and Polyvariant Flow Types
"... We present # CIL , a typed #calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higherorder polymorphic programming languages. The key innovation of # CIL is a novel formulation of intersection and union types and flow labels on both terms and ..."
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Cited by 29 (11 self)
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We present # CIL , a typed #calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higherorder polymorphic programming languages. The key innovation of # CIL is a novel formulation of intersection and union types and flow labels on both terms and types. These flow types can encode polyvariant control and data flow information within a polymorphically typed program representation. Flow types can guide a compiler in generating customized data representations in a strongly typed setting. Since # CIL enjoys confluence, standardization, and subject reduction properties, it is a valuable tool for reasoning about programs and program transformations.
Principality and Type Inference for Intersection Types Using Expansion Variables
, 2003
"... Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typ ..."
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Cited by 26 (12 self)
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Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typings and types exactly the strongly normalizable #terms. More interestingly, every finiterank restriction of this system (using Leivant's first notion of rank) has principal typings and also has decidable type inference.
System E: Expansion variables for flexible typing with linear and nonlinear types and intersection types
 IN PROGRAMMING LANGUAGES & SYSTEMS, 13TH EUROPEAN SYMP. PROGRAMMING
, 2004
"... Types are often used to control and analyze computer programs. ..."
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Cited by 25 (15 self)
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Types are often used to control and analyze computer programs.
Relating Typability and Expressiveness in FiniteRank Intersection Type Systems (Extended Abstract)
 In Proc. 1999 Int’l Conf. Functional Programming
, 1999
"... We investigate finiterank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type T1 /\ T2 to be used in some places at type T1 and in other places ..."
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Cited by 22 (9 self)
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We investigate finiterank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type T1 /\ T2 to be used in some places at type T1 and in other places at type T2 . A finiterank intersection type system bounds how deeply the /\ can appear in type expressions. Such type systems enjoy strong normalization, subject reduction, and computable type inference, and they support a pragmatics for implementing parametric polymorphism. As a consequence, they provide a conceptually simple and tractable alternative to the impredicative polymorphism of System F and its extensions, while typing many more programs than the HindleyMilner type system found in ML and Haskell. While type inference is computable at every rank, we show that its complexity grows exponentially as rank increases. Let K(0, n) = n and K(t + 1, n) = 2^K(t,n); we prove that recognizing the pure lambdaterms of size n that are typable at rank k is complete for dtime[K(k1, n)]. We then consider the problem of deciding whether two lambdaterms typable at rank k have the same normal form, Generalizing a wellknown result of Statman from simple types to finiterank intersection types. ...
A calculus for linktime compilation
, 2000
"... Abstract. We present a module calculus for studying a simple model of linktime compilation. The calculus is stratified into a term calculus, a core module calculus, and a linking calculus. At each level, we show that the calculus enjoys a computational soundness property: iftwo terms are equivalent ..."
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Cited by 21 (4 self)
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Abstract. We present a module calculus for studying a simple model of linktime compilation. The calculus is stratified into a term calculus, a core module calculus, and a linking calculus. At each level, we show that the calculus enjoys a computational soundness property: iftwo terms are equivalent in the calculus, then they have the same outcome in a smallstep operational semantics. This implies that any module transformation justified by the calculus is meaning preserving. This result is interesting because recursive module bindings thwart confluence at two levels ofour calculus, and prohibit application ofthe traditional technique for showing computational soundness, which requires confluence. We introduce a new technique, based on properties we call lift and project, thatusesa weaker notion of confluence with respect to evaluation to establish computational soundness for our module calculus. We also introduce the weak distributivity property for a transformation T operating on modules D1 and D2 linked by ⊕: T (D1 ⊕ D2) =T (T (D1) ⊕ T (D2)). We argue that this property finds promising candidates for linktime optimizations. 1
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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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.
Branching Types
, 2002
"... Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type ..."
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Cited by 14 (5 self)
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Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type selection parameters. The new system # an explicitly typed system with the same expressiveness as a system with intersection types. Typing derivations in # use branching types to squash together what would be separate parallel derivations in earlier systems with intersection types.
ML^F  Raising ML to the Power of System F
 In ICFP ’03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
, 2003
"... We propose a type system ML F that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, ..."
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Cited by 14 (0 self)
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We propose a type system ML F that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, with a possibly more general type than in ML, without any need for type annotation. Only arguments of functions that are used polymorphically must be annotated, which allows to type all expressions of System F as well.
Type Inference with Expansion Variables and Intersection Types in System E and an Exact Correspondence with βReduction
 In Proc. 6th Int’l Conf. Principles & Practice Declarative Programming
"... System E is a recently designed type system for the # calculus with intersection types and expansion variables. During automatic type inference, expansion variables allow postponing decisions about which nonsyntaxdriven typing rules to use until the right information is available and allow imple ..."
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System E is a recently designed type system for the # calculus with intersection types and expansion variables. During automatic type inference, expansion variables allow postponing decisions about which nonsyntaxdriven typing rules to use until the right information is available and allow implementing the choices via substitution.