scholarly journals Type Inference of SELF: Analysis of Objects with Dynamic and Multiple Inheritance

1993 ◽  
Vol 22 (436) ◽  
Author(s):  
Ole Agesen ◽  
Jens Palsberg ◽  
Michael I. Schwartzbach
Keyword(s):  
Type Inference ◽  
Inference Algorithm ◽  
Optimizing Compilers ◽  
Multiple Inheritance

We have designed and implemented a type inference algorithm for the full <strong>SELF</strong> language. The algorithm can guarantee the safety and disambiguity of message sends, and provide useful information for browsers and optimizing compilers.

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

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 Constraint handling rules with binders, patterns and generic quantification

2017 ◽  
Vol 17 (5-6) ◽  
pp. 992-1009
Author(s):  
ALEJANDRO SERRANO ◽  
JURRIAAN HAGE
Keyword(s):  
Type Inference ◽  
Constraint Handling ◽  
Inference Algorithm ◽  
Higher Rank ◽  
Binding Structure

AbstractConstraint handling rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by λ-tree syntax, in which binding is explicit, and a new ∇ generic quantifier is introduced, which is used to create new fresh constants.

scholarly journals An existential crisis resolved: type inference for first-class existential types

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-29
Author(s):  
Richard A. Eisenberg ◽  
Guillaume Duboc ◽  
Stephanie Weirich ◽  
Daniel Lee
Keyword(s):  
Pattern Matching ◽  
Type Inference ◽  
Great Success ◽  
Inference Algorithm ◽  
Existential Crisis ◽  
Refinement Types ◽  
Core Language ◽  
Abstract Types

Despite the great success of inferring and programming with universal types, their dual—existential types—are much harder to work with. Existential types are useful in building abstract types, working with indexed types, and providing first-class support for refinement types. This paper, set in the context of Haskell, presents a bidirectional type-inference algorithm that infers where to introduce and eliminate existentials without any annotations in terms, along with an explicitly typed, type-safe core language usable as a compilation target. This approach is backward compatible. The key ingredient is to use strong existentials, which support (lazily) projecting out the encapsulated data, not weak existentials accessible only by pattern-matching.

scholarly journals Type Inference with Nonstructural Subtyping

1995 ◽  
Vol 2 (33) ◽  
Author(s):  
Jens Palsberg ◽  
Mitchell Wand ◽  
Patrick O'Keefe
Keyword(s):  
Type A ◽  
Type Inference ◽  
Inference Algorithm ◽  
Minimal Size ◽  
The One ◽  
Time Type

We present an O(n^3) time type inference algorithm for a type<br />system with a largest type !, a smallest type ?, and the usual ordering<br />between function types. The algorithm infers type annotations of<br />minimal size, and it works equally well for recursive types. For the<br />problem of typability, our algorithm is simpler than the one of Kozen,<br />Palsberg, and Schwartzbach for type inference without ?. This may<br />be surprising, especially because the system with ? is strictly more<br />powerful.

scholarly journals Type Inference with Inequalities

1990 ◽  
Vol 19 (336) ◽  
Author(s):  
Michael I. Schwartzbach
Keyword(s):  
General Result ◽  
Existence Of Solutions ◽  
Finite Automata ◽  
Minimal Solution ◽  
Type Inference ◽  
Constraint Solving ◽  
Multiple Inheritance ◽  
Exponential Time ◽  
Systems Of Inequalities ◽  
Infinite Collection

Type inference can be phrased as constraint-solving over types. We consider an implicitly typed language equipped with recursive types, multiple inheritance, 1st order parametric polymorphism, and assignments. Type correctness is expressed as satisfiability of a possibly infinite collection of (monotonic) inequalities on the types of variables and expressions. A general result about systems of inequalities over semilattices yields a solvable form. We distinguish between deciding <em>typability</em> (the existence of solutions) and <em>type inference</em> (the computation of a minimal solution). In our case, both can be solved by means of nondeterministic finite automata; unusually, the two problems have different complexities: polynomial vs. exponential time.

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