Completeness results for a polymorphic type system

1983 ◽  
pp. 179-190 ◽  
Author(s):  
M. Coppo ◽  
E. Giovannetti
Keyword(s):  
Type System ◽  
Polymorphic Type

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.

scholarly journals Featherweight generic confinement

2006 ◽  
Vol 16 (6) ◽  
pp. 793-811 ◽  
Author(s):  
ALEX POTANIN ◽  
JAMES NOBLE ◽  
DAVE CLARKE ◽  
ROBERT BIDDLE
Keyword(s):  
Programming Languages ◽  
Ad Hoc ◽  
Type System ◽  
Type Systems ◽  
General Purpose ◽  
Ownership Type ◽  
Essential Change ◽  
Polymorphic Type ◽  
Syntactic Restrictions

Existing approaches to object encapsulation either rely on ad hoc syntactic restrictions or require the use of specialised type systems. Syntactic restrictions are difficult to scale and to prove correct, while specialised type systems require extensive changes to programming languages. We demonstrate that confinement can be enforced cheaply in Featherweight Generic Java, with no essential change to the underlying language or type system. This result demonstrates that polymorphic type parameters can simultaneously act as ownership parameters and should facilitate the adoption of confinement and ownership type systems in general-purpose programming languages.

A polymorphic type system for prolog

1984 ◽  
Vol 23 (3) ◽  
pp. 295-307 ◽  
Author(s):  
Alan Mycroft ◽  
Richard A. O'Keefe
Keyword(s):  
Type System ◽  
Polymorphic Type

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 Typing first-class continuations in ML

1993 ◽  
Vol 3 (4) ◽  
pp. 465-484 ◽  
Author(s):  
Robert Harper ◽  
Bruce F. Duba ◽  
David Macqueen
Keyword(s):  
Operational Semantics ◽  
Type System ◽  
Type Systems ◽  
Functional Language ◽  
Type Assignment ◽  
Polymorphic Type ◽  
Alternative Type

AbstractAn extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional language, and the soundness of the Damas–Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas–Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness.

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