scholarly journals Coercions in a polymorphic type system

2008 ◽  
Vol 18 (4) ◽  
pp. 729-751 ◽  
Author(s):  
ZHAOHUI LUO
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Type System ◽  
Type Inference ◽  
Inference Algorithm ◽  
Functional Programming Languages ◽  
Polymorphic Type ◽  
And Function ◽  
Dependent Type

We incorporate the idea of coercive subtyping, a theory of abbreviation for dependent type theories, into the polymorphic type system in functional programming languages. The traditional type system with let-polymorphism is extended with argument coercions and function coercions, and a corresponding type inference algorithm is presented and proved to be sound and complete.

scholarly journals A Mechanized Proof of a Textbook Type Unification Algorithm

2020 ◽  
Vol 27 (3) ◽  
pp. 13-24
Author(s):  
André Rauber Du Bois ◽  
Rodrigo Ribeiro ◽  
Maycon Amaro
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Functional Programming ◽  
Type Inference ◽  
Inference Algorithm ◽  
Functional Programming Languages ◽  
Unification Algorithm ◽  
The Core ◽  
Inference Algorithms ◽  
Language Textbooks

Unification is the core of type inference algorithms for modern functional programming languages, like Haskell and SML. As a first step towards a formalization of a type inference algorithm for such programming languages, we present a formalization in Coq of a type unification algorithm that follows classic algorithms presented in programming language textbooks. We also report on the use of such formalization to build a correct type inference algorithm for the simply typed λ-calculus.

FIRST-CLASS CONTEXTS IN ML

2000 ◽  
Vol 11 (01) ◽  
pp. 65-87
Author(s):  
MASATOMO HASHIMOTO
Keyword(s):  
Programming Language ◽  
Operational Semantics ◽  
Type System ◽  
Type Inference ◽  
Inference Algorithm ◽  
Hole Filling ◽  
Dynamic Binding ◽  
Polymorphic Type ◽  
Open Program ◽  
Program Modules

This paper develops an ML-style programming language with first-class contexts i.e. expressions with holes. The crucial operation for contexts is hole-filling. Filling a hole with an expression has the effect of dynamic binding or macro expansion which provides the advanced feature of manipulating open program fragments. Such mechanisms are useful in many systems including distributed/mobile programming and program modules. If we can treat a context as a first-class citizen in a programming language, then we can manipulate open program fragments in a flexible and seamless manner. A possibility of such a programming language was shown by the theory of simply typed context calculus developed by Hashimoto and Ohori. This paper extends the simply typed system of the context calculus to an ML-style polymorphic type system, and gives an operational semantics and a sound and complete type inference algorithm.

Weak polymorphism can be sound

1996 ◽  
Vol 6 (1) ◽  
pp. 111-141 ◽  
Author(s):  
John Greiner
Keyword(s):  
New Jersey ◽  
Type System ◽  
Type Systems ◽  
Type Inference ◽  
Inference Algorithm ◽  
Standard Ml ◽  
Polymorphic Type

AbstractThe weak polymorphic type system of Standard ML of New Jersey (SML/NJ) (MacQueen, 1992) has only been presented as part of the implementation of the SML/NJ compiler, not as a formal type system. As a result, it is not well understood. And while numerous versions of the implementation have been shown unsound, the concept has not been proved sound or unsound. We present an explanation of weak polymorphism and show that a formalization of this is sound. We also relate this to the SML/NJ implementation of weak polymorphism through a series of type systems that incorporate elements of the SML/NJ type inference algorithm.

Linearization of the lambda-calculus and its relation with intersection type systems

2004 ◽  
Vol 14 (5) ◽  
pp. 519-546 ◽  
Author(s):  
MÁRIO FLORIDO ◽  
LUÍS DAMAS
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Type System ◽  
Lambda Calculus ◽  
Type Systems ◽  
Functional Programming Languages

In this paper we present a notion of expansion of a term in the lambda-calculus which transforms terms into linear terms. This transformation replaces each occurrence of a variable in the original term by a fresh variable taking into account non-trivial implications in the structure of the term caused by these simple replacements. We prove that the class of terms which can be expanded is the same of terms typable in an Intersection Type System, i.e. the strongly normalizable terms. We then show that expansion is preserved by weak-head reduction, the reduction considered by functional programming languages.

scholarly journals V: a language with extensible record accessors and a trait-based type system

2018 ◽  
Vol 25 (3) ◽  
pp. 89
Author(s):  
Arthur Giesel Vedana ◽  
Rodrigo Machado ◽  
Álvaro Freitas Moreira
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Functional Programming ◽  
Type System ◽  
Functional Programming Languages ◽  
Functional Programming Language ◽  
Novel Approach ◽  
Type Traits

This article introduces the V language, a purely functional programming language with a novel approach to records.Based on a system of type traits, V attempts to solve issues commonly found when manipulating records in purely functional programming languages.

scholarly journals Dynamic game semantics

2020 ◽  
pp. 1-60
Author(s):  
Norihiro Yamada ◽  
Samson Abramsky
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Dynamic Game ◽  
Standard Interpretation ◽  
Functional Programming Languages ◽  
Game Semantics ◽  
Wide Range ◽  
Cartesian Closed Categories ◽  
Cartesian Closed

Abstract The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

scholarly journals A Type Inference Algorithm for a Stratified Polymorphic Type Discipline

1994 ◽  
Vol 109 (1-2) ◽  
pp. 115-173 ◽  
Author(s):  
P. Giannini ◽  
S.R. Dellarocca
Keyword(s):  
Type Inference ◽  
Inference Algorithm ◽  
Polymorphic Type
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