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48
The Relevance of Semantic Subtyping
 In IEEE Symposium on Logic in Computer Science (LICS
, 2002
"... We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, ..."
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Cited by 52 (9 self)
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We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, which is defined in purely settheoretical terms, coincides with the relevant entailment of the logic B+ . 1
From Polyvariant Flow Information to Intersection and Union Types
 J. FUNCT. PROGRAMMING
, 1998
"... Many polyvariant program analyses have been studied in the 1990s, including kCFA, polymorphic splitting, and the cartesian product algorithm. The idea of polyvariance is to analyze functions more than once and thereby obtain better precision for each call site. In this paper we present an equivalen ..."
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Cited by 41 (7 self)
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Many polyvariant program analyses have been studied in the 1990s, including kCFA, polymorphic splitting, and the cartesian product algorithm. The idea of polyvariance is to analyze functions more than once and thereby obtain better precision for each call site. In this paper we present an equivalence theorem which relates a coinductively defined family of polyvariant ow analyses and a standard type system. The proof embodies a way of understanding polyvariant flow information in terms of union and intersection types, and, conversely, a way of understanding union and intersection types in terms of polyvariant flow information. We use the theorem as basis for a new flowtype system in the spirit of the CIL calculus of Wells, Dimock, Muller, and Turbak, in which types are annotated with flow information. A flowtype system is useful as an interface between a owanalysis algorithm and a program optimizer. Derived systematically via our equivalence theorem, our flowtype system should be a g...
Intersection Types and Bounded Polymorphism
, 1996
"... this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism ..."
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Cited by 37 (0 self)
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this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism and dependent types have been studied by Pfenning (Pfenning, 1993). Following a more detailed discussion of the pure systems of intersections and bounded quantification (Section 2), we describe, in Section 3, a typed calculus called F ("Fmeet ") integrating the features of both. Section 4 gives some examples illustrating this system's expressive power. Section 5 presents the main results of the paper: a prooftheoretic analysis of F 's subtyping and typechecking relations leading to algorithms for checking subtyping and for synthesizing minimal types for terms. Section 6 discusses semantic aspects of the calculus, obtaining a simple soundness proof for the typing rules by interpreting types as partial equivalence relations; however, another prooftheoretic result, the nonexistence of least upper bounds for arbitrary pairs of types, implies that typed models may be more difficult to construct. Section 7 offers concluding remarks. 2. Background
Tridirectional Typechecking
, 2004
"... In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. In this paper ..."
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Cited by 36 (8 self)
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In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. In this paper
Union Types for Semistructured Data
 University of Pennsylvania Dept. of CIS
, 1999
"... Semistructured databases are treated as dynamically typed: they come equipped with no independent schema or type system to constrain the data. Query languages that are designed for semistructured data, even when used with structured data, typically ignore any type information that may be present. ..."
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Cited by 34 (4 self)
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Semistructured databases are treated as dynamically typed: they come equipped with no independent schema or type system to constrain the data. Query languages that are designed for semistructured data, even when used with structured data, typically ignore any type information that may be present. The consequences of this are what one would expect from using a dynamic type system with complex data: fewer guarantees on the correctness of applications. For example, a query that would cause a type error in a statically typed query language will return the empty set when applied to a semistructured representation of the same data. Much semistructured data originates in structured data. A semistructured representation is useful when one wants to add data that does not conform to the original type or when one wants to combine sources of different types. However, the deviations from the prescribed types are often minor, and we believe that a better strategy than throwing away all typ...
Strongly Typed FlowDirected Representation Transformations (Extended Abstract)
 In ICFP ’97 [ICFP97
, 1997
"... We present a new framework for transforming data representations in a strongly typed intermediate language. Our method allows both value producers (sources) and value consumers (sinks) to support multiple representations, automatically inserting any required code. Specialized representations can be ..."
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Cited by 29 (13 self)
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We present a new framework for transforming data representations in a strongly typed intermediate language. Our method allows both value producers (sources) and value consumers (sinks) to support multiple representations, automatically inserting any required code. Specialized representations can be easily chosen for particular source/sink pairs. The framework is based on these techniques: 1. Flow annotated types encode the "flowsfrom" (source) and "flowsto" (sink) information of a flow graph. 2. Intersection and union types support (a) encoding precise flow information, (b) separating flow information so that transformations can be well typed, (c) automatically reorganizing flow paths to enable multiple representations. As an instance of our framework, we provide a function representation transformation that encompasses both closure conversion and inlining. Our framework is adaptable to data other than functions.
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 28 (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.
A Compositional Logic for Polymorphic HigherOrder Functions
 PPDP'04
, 2004
"... This paper introduces a compositional program logic for higherorder polymorphic functions and standard data types. The logic enables us to reason about observable properties of polymorphic programs starting from those of their constituents. Just as types attached to programs offer information on the ..."
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Cited by 26 (11 self)
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This paper introduces a compositional program logic for higherorder polymorphic functions and standard data types. The logic enables us to reason about observable properties of polymorphic programs starting from those of their constituents. Just as types attached to programs offer information on their composability so as to guarantee basic safety of composite programs, formulae of the proposed logic attached to programs offer information on their composability so as to guarantee finegrained behavioural properties of polymorphic programs. The central feature of the logic is a systematic usage of names and operations on them, whose origin is in the logics for typed πcalculi. The paper introduces the program logic and its proof rules and illustrates their usage by nontrivial reasoning examples, taking a prototypical callbyvalue functional language with impredicative polymorphism and recursive types as a target language.
Typed Generic Traversal With Term Rewriting Strategies
 Journal of Logic and Algebraic Programming
, 2002
"... A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy t ..."
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Cited by 26 (8 self)
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A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of typepreserving and typeunifying strategies. S ′ γ offers traversal combinators to construct traversals or schemes thereof from manysorted and generic strategies. The traversal combinators model different forms of onestep traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a manysorted strategy s to a generic type γ. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be typedependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program
A Typed Intermediate Language for FlowDirected Compilation
, 1997
"... We present a typed intermediate language # CIL for optimizing compilers for functionoriented and polymorphically typed programming languages (e.g., ML). The language # CIL is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow label ..."
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Cited by 22 (13 self)
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We present a typed intermediate language # CIL for optimizing compilers for functionoriented and polymorphically typed programming languages (e.g., ML). The language # CIL is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow labels. A novel formulation of intersection and union types supports encoding flow information in the typed program representation. This flow information can direct optimization.