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83
Type Inclusion Constraints and Type Inference
 In Proceedings of the 1993 Conference on Functional Programming Languages and Computer Architecture
, 1993
"... We present a general algorithm for solving systems of inclusion constraints over type expressions. The constraint language includes function types, constructor types, and liberal intersection and union types. We illustrate the application of our constraint solving algorithm with a type inference sys ..."
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Cited by 230 (21 self)
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We present a general algorithm for solving systems of inclusion constraints over type expressions. The constraint language includes function types, constructor types, and liberal intersection and union types. We illustrate the application of our constraint solving algorithm with a type inference system for the lambda calculus with constants. In this system, every pure lambda term has a (computable) type and every term typable in the Hindley/Milner system has all of its Hindley/Milner types. Thus, the inference system is an extension of the Hindley/Milner system that can type a very large set of lambda terms. 1 Introduction Type inference systems for functional languages are based on solving systems of type constraints. The best known and most widely used type inference algorithm was first discovered by Hindley and later independently by Milner [Hin69, Mil78]. In its simplest form, the algorithm generates type equations from the program text and then solves the equations. If the equati...
Soft Typing
, 1991
"... This paper presents a soft type systems that retains the expressiveness of dynamic typing, but offers the early error detection and improved optimization capabilities of static typing. The key idea underlying soft typing is that a type checker need not reject programs containing "illtyped" ..."
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Cited by 215 (2 self)
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This paper presents a soft type systems that retains the expressiveness of dynamic typing, but offers the early error detection and improved optimization capabilities of static typing. The key idea underlying soft typing is that a type checker need not reject programs containing "illtyped" phrases. Instead, the type checker can insert explicit runtime checks, transforming "illtyped" programs into typecorrect ones.
Soft typing with conditional types
 In TwentyFirst Annual ACM Symposium on Principles of Programming Languages
, 1994
"... We present a simple and powerful type inference method for dynamically typed languages where no type information is supplied by the user. Type inference is reduced to the problem of solvability of a system of type inclusion constraints over a type language that includes function types, constructor t ..."
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Cited by 197 (15 self)
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We present a simple and powerful type inference method for dynamically typed languages where no type information is supplied by the user. Type inference is reduced to the problem of solvability of a system of type inclusion constraints over a type language that includes function types, constructor types, union, intersection, and recursive types, and conditional types. Conditional types enable us to analyze control flow using type inference, thus facilitating computation of accurate types. We demonstrate the power and practicrdity of the method with examples and performance results from an implementation. 1
Efficient Type Inference for HigherOrder BindingTime Analysis
 In Functional Programming and Computer Architecture
, 1991
"... Bindingtime analysis determines when variables and expressions in a program can be bound to their values, distinguishing between early (compiletime) and late (runtime) binding. Bindingtime information can be used by compilers to produce more efficient target programs by partially evaluating prog ..."
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Cited by 98 (4 self)
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Bindingtime analysis determines when variables and expressions in a program can be bound to their values, distinguishing between early (compiletime) and late (runtime) binding. Bindingtime information can be used by compilers to produce more efficient target programs by partially evaluating programs at compiletime. Bindingtime analysis has been formulated in abstract interpretation contexts and more recently in a typetheoretic setting. In a typetheoretic setting bindingtime analysis is a type inference problem: the problem of inferring a completion of a λterm e with bindingtime annotations such that e satisfies the typing rules. Nielson and Nielson and Schmidt have shown that every simply typed λterm has a unique completion ê that minimizes late binding in TML, a monomorphic type system with explicit bindingtime annotations, and they present exponential time algorithms for computing such minimal completions. 1 Gomard proves the same results for a variant of his twolevel λcalculus without a socalled “lifting ” rule. He presents another algorithm for inferring completions in this somewhat restricted type system and states that it can be implemented in time O(n 3). He conjectures that the completions computed are minimal.
Type inference with simple subtypes
 J. Funct. Program
, 1991
"... Subtyping appears in a variety of programming languages, in the form of the "automatic coercion " of integers to reals, Pascal subranges, and subtypes arising from class hierarchies in languages with inheritance. A general framework based on untyped lambda calculus provides a simple seman ..."
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Cited by 96 (2 self)
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Subtyping appears in a variety of programming languages, in the form of the "automatic coercion " of integers to reals, Pascal subranges, and subtypes arising from class hierarchies in languages with inheritance. A general framework based on untyped lambda calculus provides a simple semantic model of subtyping and is used to demonstrate that an extension of Curry’s type inference rules are semantically complete. An algorithm G for computing the most general typing associated with any giv en expression, and a restricted, optimized algorithm GA using only atomic subtyping hypotheses are developed. Both algorithms may be extended to insert type conversion functions at compile time or allow polymorphic function declarations as in ML. 1.
Type Inference for Records in a Natural Extension of ML
 Theoretical Aspects of ObjectOriented Programming: Types, Semantics, and Language Design
, 1994
"... We describe an extension of ML with records where inheritance is given by ML generic polymorphism. All common operations on records but concatenation are supported, in particular the free extension of records. Other operations such as renaming of fields are added. The solution relies on an extension ..."
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Cited by 90 (7 self)
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We describe an extension of ML with records where inheritance is given by ML generic polymorphism. All common operations on records but concatenation are supported, in particular the free extension of records. Other operations such as renaming of fields are added. The solution relies on an extension of ML, where the language of types is sorted and considered modulo equations, and on a record extension of types. The solution is simple and modular and the type inference algorithm is efficient in practice.
A Polymorphic Record Calculus and Its Compilation
 ACM Transactions on Programming Languages and Systems
, 1995
"... this article appeared in Proceedings of ACM Symposium on Principles of Programming Languages, 1992, under the title \A compilation method for MLstyle polymorphic record calculi." This work was partly supported by the Japanese Ministry of Education under scienti c research grant no. 06680319. A ..."
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Cited by 80 (10 self)
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this article appeared in Proceedings of ACM Symposium on Principles of Programming Languages, 1992, under the title \A compilation method for MLstyle polymorphic record calculi." This work was partly supported by the Japanese Ministry of Education under scienti c research grant no. 06680319. Author's address: Research Institute for Mathematical Sciences, Kyoto University, Sakyoku, Kyoto 60601, JAPAN; email: ohori@kurims.kyotou.ac.jp Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of ACM. To copy otherwise, or to republish, requires a fee and/or speci c permission. c 1999 ACM 01640925/99/01000111 $00.75
Subtyping Constrained Types
, 1996
"... A constrained type is a type that comes with a set of subtyping constraints on variables occurring in the type. Constrained type inference systems are a natural generalization of Hindley/Milner type inference to languages with subtyping. This paper develops several subtyping relations on polymorphic ..."
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Cited by 64 (2 self)
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A constrained type is a type that comes with a set of subtyping constraints on variables occurring in the type. Constrained type inference systems are a natural generalization of Hindley/Milner type inference to languages with subtyping. This paper develops several subtyping relations on polymorphic constrained types of a general form that allows recursive constraints and multiple bounds on type variables. We establish a full type abstraction property that equates a novel operational notion of subtyping with a semantic notion based on regular trees. The decidability of this notion of subtyping is open; we present a decidable approximation. Subtyping constrained types has applications to signature matching and to constrained type simplification. The relation will thus be a critical component of any programming language incorporating a constrained typing system. 1 Introduction A constrained type is a type that is additionally constrained by a set of subtyping constraints on the free ty...
Objective ML: An effective objectoriented extension to ML
 THEORY AND PRACTICE OF OBJECT SYSTEMS
, 1998
"... Objective ML is a small practical extension to ML with objects and top level classes. It is fully compatible with ML; its type system is based on ML polymorphism, record types with polymorphic access, and a better treatment of type abbreviations. Objective ML allows for most features of objectorien ..."
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Cited by 61 (5 self)
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Objective ML is a small practical extension to ML with objects and top level classes. It is fully compatible with ML; its type system is based on ML polymorphism, record types with polymorphic access, and a better treatment of type abbreviations. Objective ML allows for most features of objectoriented languages including multiple inheritance, methods returning self and binary methods as well as parametric classes. This demonstrates that objects can be added to strongly typed languages based on ML polymorphism.
Efficient Inference of Object Types
, 1995
"... Abadi and Cardelli have recently investigated a calculus of objects [2]. The calculus supports a key feature of objectoriented languages: an object can be emulated by another object that has more refined methods. Abadi and Cardelli presented four firstorder type systems for the calculus. The simpl ..."
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Cited by 58 (6 self)
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Abadi and Cardelli have recently investigated a calculus of objects [2]. The calculus supports a key feature of objectoriented languages: an object can be emulated by another object that has more refined methods. Abadi and Cardelli presented four firstorder type systems for the calculus. The simplest one is based on finite types and no subtyping, and the most powerful one has both recursive types and subtyping. Open until now is the question of type inference, and in the presence of subtyping "the absence of minimum typings poses practical problems for type inference" [2]. In this paper...