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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 21 (1 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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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
Concoqtion: Mixing dependent types and HindleyMilner type inference (extended version
, 2006
"... This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approa ..."
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Cited by 2 (0 self)
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This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approached used by Shao et al. for certified binaries. This approach maintains a phase distinction between the computational and logical languages, thereby limiting effects and nontermination to the computational language, and maintaining the decidability of the type system. The extension subsumes language features such as impredicative firstclass (higherrank) polymorphism and type operators, that are notoriously difficult to integrate with the HindleyMilner style of type inference that is used in OCaml. We make the observation that these features can be more easily integrated with type inference if the inference algorithm is free to adapt the order in which it solves typing constraints to each program. To this end we define a novel “orderfree ” type inference algorithm. The key enabling technology is a graph representation of constraints and a constraint solver that performs HindleyMilner inference with just three graph rewrite rules. 1
Concoqtion: Mixing dependent types and HindleyMilner type inference
, 2006
"... This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approa ..."
Abstract
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This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approached used by Shao et al. for certified binaries. This approach maintains a phase distinction between the computational and logical languages, thereby limiting effects and nontermination to the computational language, and maintaining the decidability of the type system. The extension subsumes language features such as impredicative firstclass (higherrank) polymorphism and type operators, that are notoriously difficult to integrate with the HindleyMilner style of type inference that is used in OCaml. We make the observation that these features can be more easily integrated with type inference if the inference algorithm is free to adapt the order in which it solves typing constraints to each program. To this end we define a novel “orderfree ” type inference algorithm. The key enabling technology is a graph representation of constraints and a constraint solver that performs HindleyMilner inference with just three graph rewrite rules.
Concoqtion: Mixing Indexed Types and HindleyMilner Type Inference
, 2006
"... This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approa ..."
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This paper addresses the question of how to extend OCaml’s HindleyMilner type system with types indexed by logical propositions and proofs of the Coq theorem prover, thereby providing an expressive and extensible mechanism for ensuring finegrained program invariants. We propose adopting the approached used by Shao et al. for certified binaries. This approach maintains a phase distinction between the computational and logical languages, thereby limiting effects and nontermination to the computational language, and maintaining the decidability of the type system. The extension subsumes language features such as impredicative firstclass (higherrank) polymorphism and type operators, that are notoriously difficult to integrate with the HindleyMilner style of type inference that is used in OCaml. We make the observation that these features can be more easily integrated with type inference if the inference algorithm is free to adapt the order in which it solves typing constraints to each program. To this end we define a novel “orderfree” type inference algorithm. The key enabling technology is a graph representation of constraints and a constraint solver that performs HindleyMilner inference with just three graph rewrite rules.
Contents
, 2005
"... Hindley and Milner’s type system is at the heart of programming languages such as Standard ML, Objective Caml, and Haskell. Its expressive power, as well the existence of a type inference algorithm, have made it quite successful. Traditional presentations of this algorithm, such as Milner’s Algorith ..."
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Hindley and Milner’s type system is at the heart of programming languages such as Standard ML, Objective Caml, and Haskell. Its expressive power, as well the existence of a type inference algorithm, have made it quite successful. Traditional presentations of this algorithm, such as Milner’s Algorithm W, are somewhat obscure. These short lecture notes, written for the APPSEM’05 summer school, begin with a presentation of a more modern, constraintbased specification of the algorithm, and explain how it can be extended to accommodate features such as algebraic data types, recursion, and (lexically scoped) type annotations. Then, two chapters, yet to be written, review two recent proposals for incorporating more advanced features, known as arbitraryrank predicative polymorphism and generalized algebraic data types. These proposals combine a traditional constraintbased type inference algorithm with a measure of local type inference. 1