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Polymorphism and Type Inference in Database Programming
"... In order to find a static type system that adequately supports database languages, we need to express the most general type of a program that involves database operations. This can be achieved through an extension to the type system of ML that captures the polymorphic nature of field selection, toge ..."
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Cited by 38 (10 self)
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In order to find a static type system that adequately supports database languages, we need to express the most general type of a program that involves database operations. This can be achieved through an extension to the type system of ML that captures the polymorphic nature of field selection, together with a technique that generalizes relational operators to arbitrary data structures. The combination provides a statically typed language in which generalized relational databases may be cleanly represented as typed structures. As in ML types are inferred, which relieves the programmer of making the type assertions that may be required in a complex database environment. These extensions may also be used to provide static polymorphic typechecking in objectoriented languages and databases. A problem that arises with objectoriented databases is the apparent need for dynamic typechecking when dealing with queries on heterogeneous collections of objects. An extension of the type system needed for generalized relational operations can also be used for manipulating collections of dynamically typed values in a statically typed language. A prototype language based on these ideas has been implemented. While it lacks a proper treatment of persistent data, it demonstrates that a wide variety of database structures can be cleanly represented in a polymorphic programming language.
Types as abstract interpretations, invited paper
 In 24 th POPL
, 1997
"... Starting from a denotational semantics of the eager untyped lambdacalculus with explicit runtime errors, the standard collecting semantics is defined as specifying the strongest program properties. By a first abstraction, a new sound type collecting semantics is derived in compositional fixpoint fo ..."
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Cited by 38 (11 self)
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Starting from a denotational semantics of the eager untyped lambdacalculus with explicit runtime errors, the standard collecting semantics is defined as specifying the strongest program properties. By a first abstraction, a new sound type collecting semantics is derived in compositional fixpoint form. Then by successive (semidual) Galois connection based abstractions, type systems and/or type inference algorithms are designed as abstract semantics or abstract interpreters approximating the type collecting semantics. This leads to a hierarchy of type systems, which is part of the lattice of abstract interpretations of the untyped lambdacalculus. This hierarchy includes two new à la Church/Curry polytype systems. Abstractions of this polytype semantics lead to classical Milner/Mycroft and Damas/Milner polymorphic type schemes, Church/Curry monotypes and Hindley principal typing algorithm. This shows that types are abstract interpretations. 1
Monads and Composable Continuations
, 1993
"... . Moggi's use of monads to factor semantics is used to model the composable continuations of Danvy and Filinski. This yields some insights into the type systems proposed by Murthy and by Danvy and Filinski. Interestingly, modelling some aspects of composable continuations requires a structure that i ..."
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Cited by 35 (1 self)
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. Moggi's use of monads to factor semantics is used to model the composable continuations of Danvy and Filinski. This yields some insights into the type systems proposed by Murthy and by Danvy and Filinski. Interestingly, modelling some aspects of composable continuations requires a structure that is almost, but not quite, a monad. 1. Introduction Continuationpassing style was introduced to model one feature of programming languages  the jump  and to explicate the execution order of programs [14, 12]. Recently, Moggi has shown how monads, a notion from category theory, generalise the continuationpassing style transformation [9]. Monads can model a wide variety of features, including continuations, state, exceptions, inputoutput, nondeterminism, and parallellism. Monads have also been applied both as a way of structuring functional programs [16, 17] and as a way of introducing new features into functional languages [11]. It begins to seem as if any feature of a programming lang...
Abstract interpretation based formal methods and future challenges, invited paper
 Informatics — 10 Years Back, 10 Years Ahead, volume 2000 of Lecture Notes in Computer Science
, 2001
"... Abstract. In order to contribute to the solution of the software reliability problem, tools have been designed to analyze statically the runtime behavior of programs. Because the correctness problem is undecidable, some form of approximation is needed. The purpose of abstract interpretation is to f ..."
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Cited by 28 (6 self)
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Abstract. In order to contribute to the solution of the software reliability problem, tools have been designed to analyze statically the runtime behavior of programs. Because the correctness problem is undecidable, some form of approximation is needed. The purpose of abstract interpretation is to formalize this idea of approximation. We illustrate informally the application of abstraction to the semantics of programming languages as well as to static program analysis. The main point is that in order to reason or compute about a complex system, some information must be lost, that is the observation of executions must be either partial or at a high level of abstraction. In the second part of the paper, we compare static program analysis with deductive methods, modelchecking and type inference. Their foundational ideas are briefly reviewed, and the shortcomings of these four methods are discussed, including when they should be combined. Alternatively, since program debugging is still the main program verification
Viewing A Program Transformation System At Work
 Joint 6th International Conference on Programming Language Implementation and Logic Programming (PLILP) and 4th International conference on Algebraic and Logic Programming (ALP), volume 844 of Lecture Notes in Computer Science
, 1994
"... How to decrease labor and improve reliability in the development of efficient implementations of nonnumerical algorithms and labor intensive software is an increasingly important problem as the demand for computer technology shifts from easier applications to more complex algorithmic ones; e.g., opt ..."
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Cited by 27 (2 self)
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How to decrease labor and improve reliability in the development of efficient implementations of nonnumerical algorithms and labor intensive software is an increasingly important problem as the demand for computer technology shifts from easier applications to more complex algorithmic ones; e.g., optimizing compilers for supercomputers, intricate data structures to implement efficient solutions to operations research problems, search and analysis algorithms in genetic engineering, complex software tools for workstations, design automation, etc. It is also a difficult problem that is not solved by current CASE tools and software management disciplines, which are oriented towards data processing and other applications, where the implementation and a prediction of its resource utilization follow more directly from the specification. Recently, Cai and Paige reported experiments suggesting a way to implement nonnumerical algorithms in C at a programming rate (i.e., source lines per second) t...
On the undecidability of partial polymorphic type reconstruction
 FUNDAMENTA INFORMATICAE
, 1992
"... We prove that partial type reconstruction for the pure polymorphic *calculus is undecidable by a reduction from the secondorder unification problem, extending a previous result by H.J. Boehm. We show further that partial type reconstruction remains undecidable even in a very small predicative f ..."
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Cited by 27 (0 self)
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We prove that partial type reconstruction for the pure polymorphic *calculus is undecidable by a reduction from the secondorder unification problem, extending a previous result by H.J. Boehm. We show further that partial type reconstruction remains undecidable even in a very small predicative fragment of the polymorphic *calculus, which implies undecidability of partial type reconstruction for * ML as introduced by Harper, Mitchell, and Moggi.
Typing References by Effect Inference
 4th European Symposium on Programming
, 1992
"... Hindley/Milnerstyle polymorphism is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. We present a new technique for typing references in the presence of polymorphism by inferring a concise summary of each expression's al ..."
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Cited by 26 (5 self)
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Hindley/Milnerstyle polymorphism is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. We present a new technique for typing references in the presence of polymorphism by inferring a concise summary of each expression's allocation behaviora type effect. A simple technique for proving soundness with respect to a reduction semantics demonstrates that the type system prevents type errors. By establishing that the system corresponds to an alternate system better suited to implementation, we obtain an algorithm to perform type and effect inference. 1 Polymorphism and References Hindley/Milnerstyle polymorphism [8, 12] is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. While a number of systems for typing reference cells exist [3, 10, 16, 17, 18], we have devised a more direct approach based on inferring a concise summary of each ...
Type inference and semiunification
 In Proceedings of the ACM Conference on LISP and Functional Programming (LFP ) (Snowbird
, 1988
"... In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically type ..."
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Cited by 25 (6 self)
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In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically typed languages (Algol68, Pascal). These polymorphic languages can be type checked at compile time, yet allow functions whose arguments range over a variety of types. We investigate several polymorphic type systems, the most powerful of which, termed MilnerMycroft Calculus, extends the socalled letpolymorphism found in, e.g., ML with a polymorphic typing rule for recursive definitions. We show that semiunification, the problem of solving inequalities over firstorder terms, characterizes type checking in the MilnerMycroft Calculus to polynomial time, even in the restricted case where nested definitions are disallowed. This permits us to extend some infeasibility results for related combinatorial problems to type inference and to correct several claims and statements in the literature. We prove the existence of unique most general solutions of term inequalities, called most general semiunifiers, and present an algorithm for computing them that terminates for all known inputs due to a novel “extended occurs check”. We conjecture this algorithm to be
ConstraintBased Type Inference for Guarded Algebraic Data Types
, 2003
"... Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch ..."
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Cited by 25 (3 self)
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Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch must be checked under di#erent typing assumptions. This mechanism allows exploiting the presence of dynamic tests in the code to produce extra static type information.
A constraintbased approach to guarded algebraic data types
 ACM Trans. Prog. Languages Systems
, 2007
"... We study HMG(X), an extension of the constraintbased type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (firstcla ..."
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Cited by 24 (0 self)
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We study HMG(X), an extension of the constraintbased type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (firstclass) phantom types, and equality qualified types, and are closely related to inductive types. Their characteristic property is to allow every branch of a case construct to be typechecked under different assumptions about the type variables in scope. We prove that HMG(X) is sound and that, provided recursive definitions carry a type annotation, type inference can be reduced to constraint solving. Constraint solving is decidable, at least for some instances of X, but prohibitively expensive. Effective type inference for guarded algebraic data types is left as an issue for future research.