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HMF: Simple type inference for firstclass polymorphism
, 2008
"... HMF is a conservative extension of HindleyMilner type inference with firstclass polymorphism. In contrast to other proposals, HML uses regular System F types and has a simple type inference algorithm that is just a small extension of the usual DamasMilner algorithm W. Given the relative simplicit ..."
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Cited by 14 (0 self)
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HMF is a conservative extension of HindleyMilner type inference with firstclass polymorphism. In contrast to other proposals, HML uses regular System F types and has a simple type inference algorithm that is just a small extension of the usual DamasMilner algorithm W. Given the relative simplicity and expressive power, we feel that HMF can be an attractive type system in practice. There is a reference implementation of the type system available online together with
Flexible types: robust type inference for firstclass polymorphism
 In Proceedings of the 36th ACM Symposium on Principles of Programming Languages (POPL’09
, 2009
"... We present HML, a type inference system that supports full firstclass polymorphism where few annotations are needed: only function parameters with a polymorphic type need to be annotated. HML is a simplification of MLF where only flexibly quantified types are used. This makes the types easier to wor ..."
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Cited by 12 (1 self)
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We present HML, a type inference system that supports full firstclass polymorphism where few annotations are needed: only function parameters with a polymorphic type need to be annotated. HML is a simplification of MLF where only flexibly quantified types are used. This makes the types easier to work with from a programmers perspective, and simplifies the implementation of the type inference algorithm. Still, HML retains much of the expressiveness of MLF, it is robust with respect to small program transformations, and has a simple specification of the type rules with an effective type inference algorithm that infers principal types. A small reference implementation with many examples is
From ML to MLF: Graphic Type Constraints with Efficient Type Inference
"... MLF is a type system that seamlessly merges MLstyle type inference with SystemF polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or MLF. We show that this constraint system is a small extension of the formalism of graphic types, ..."
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Cited by 6 (2 self)
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MLF is a type system that seamlessly merges MLstyle type inference with SystemF polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or MLF. We show that this constraint system is a small extension of the formalism of graphic types, originally introduced to represent MLF types. We give a few semantic preserving transformations on constraints and propose a strategy for applying them to solve constraints. We show that the resulting algorithm has optimal complexity for MLF type inference, and argue that, as for ML, this complexity is linear under reasonable assumptions. Categories and Subject Descriptors D.3.3 [Programming Languages]: Language Constructs and Features—Constraints; Polymorphism;
Types for UnitsofMeasure: Theory and Practice
"... Unitsofmeasure are to science what types are to programming. In science and engineering, dimensional and unit consistency provides a first check on the correctness of an equation or formula, just as in programming the validation of a program by the typechecker eliminates one possible reason for f ..."
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Cited by 2 (1 self)
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Unitsofmeasure are to science what types are to programming. In science and engineering, dimensional and unit consistency provides a first check on the correctness of an equation or formula, just as in programming the validation of a program by the typechecker eliminates one possible reason for failure.
QML: Explicit FirstClass Polymorphism for ML
"... Recent years have seen a revival of interest in extending ML’s predicative type inference system with impredicative quantification in the style of System F, for which type inference is undecidable. This paper suggests a modest extension of ML with System F types: the heart of the idea is to extend t ..."
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Recent years have seen a revival of interest in extending ML’s predicative type inference system with impredicative quantification in the style of System F, for which type inference is undecidable. This paper suggests a modest extension of ML with System F types: the heart of the idea is to extend the language of types with unary universal and existential quantifiers. The introduction and elimination of a quantified type is never inferred but indicated explicitly by the programmer by supplying the quantified type itself. Quantified types coexist with ordinary ML schemes, which are in turn implicitly introduced and eliminated at letbindings and use sites, respectively. The resulting language, QML, does not impose any restriction on instantiating quantified variables with quantified types; neither let nor λbound variables ever require a type annotation, even if the variable’s inferred scheme or type involves quantified types. This proposal, albeit more verbose in terms of annotations than others, is simple to specify, implement, understand, and formalize.
Complete and Easy Bidirectional Typechecking for HigherRank Polymorphism
"... Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike DamasMilner type inference, bidirectional typing remains decidable even for very expressive type systems), its error reporting, and its relative ea ..."
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Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike DamasMilner type inference, bidirectional typing remains decidable even for very expressive type systems), its error reporting, and its relative ease of implementation. Following design principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to polymorphism, however, are less obvious. We give a declarative, bidirectional account of higherrank polymorphism, grounded in proof theory; this calculus enjoys many properties such as ηreduction and predictability of annotations. We give an algorithm for implementing the declarative system; our algorithm is remarkably simple and wellbehaved, despite being both sound and complete. 1.
True HigherOrder Modules, Separate Compilation, and Signature Calculi
, 2009
"... In the past three decades, the ML module system has been the focal point of tremendous interest in the research community. The combination of parameterized modules and finegrain data abstraction control have proven to be quite powerful in practice. Mainstream languages have slowly adopted features ..."
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In the past three decades, the ML module system has been the focal point of tremendous interest in the research community. The combination of parameterized modules and finegrain data abstraction control have proven to be quite powerful in practice. Mainstream languages have slowly adopted features inspired by the ML module system. However, programmers have run into various limitations and complexities in implementations of the ML module system. In the presence of common extensions such as true higherorder modules, true separate compilation becomes a problem. This conflict reflects a fundamental tension in module system design. Module systems should both propagate as much type information across module boundaries as is unconstrained by the programmer and be able to separately typecheck modules.
Applicative (functional) languages
"... MLF is a type system that seamlessly merges MLstyle type inference with SystemF polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or MLF. We show that this constraint system is a small extension of the formalism of graphic types, ..."
Abstract
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MLF is a type system that seamlessly merges MLstyle type inference with SystemF polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or MLF. We show that this constraint system is a small extension of the formalism of graphic types, originally introduced to represent MLF types. We give a few semantic preserving transformations on constraints and propose a strategy for applying them to solve constraints. We show that the resulting algorithm has optimal complexity for MLF type inference, and argue that, as for ML, this complexity is linear under reasonable assumptions.