## 76 Citations

### Optimal Representations of Polymorphic Types with Subtyping (Extended Abstract)

- Computer ScienceTACS
- 1997

An algorithm for simplifying quantified types in the presence of subtyping is presented and it is proved it is sound and complete for non-recursive and recursive types.

### Optimal Representations of Polymorphic Types with Subtyping

- Computer ScienceHigh. Order Symb. Comput.
- 1999

An algorithm for simplifying quantified types in the presence of subtyping is presented and it is proved it is sound and complete for non-recursive and recursive types and an extension is shown that an extension of the algorithm is sound but not complete for a type language with intersection and union types.

### Pragmatic subtyping in polymorphic languages

- Computer ScienceICFP '98
- 1998

A partial type inference algorithm for the extended Hindley/Milner type system which favours succinctness over generality, in the sense that it never infers types with subtype constraints.

### Polymorphism, subtyping, and type inference in MLsub

- Computer SciencePOPL
- 2017

A type system combining subtyping and ML-style parametric polymorphism that supports type inference and has compact principal types is presented, which types a strict superset of core ML programs.

### Type inference in systems of recursive types with subtyping

- Computer Science, Mathematics
- 1997

The type inference algorithm generalizes a common idea of previous work: type inference is reduced to a constraint satisfaction problem, whose satisfiability can be decided by a process of closure and consistency checking, and a general correctness theorem is proved.

### Constraint Abstractions

- Computer SciencePADO
- 2001

The constraint language with constraint abstractions is extended so that instantiation can be expressed directly in the constraint language and a cubic-time algorithm for constraint solving is given.

### Polymorphic Subtyping for Effect Analysis: The Static Semantics

- BiologyLOMAPS
- 1996

This paper integrates all of polymorphism, effects, and subtyping into an annotated type and effect system for Concurrent ML and shows that the resulting system is a conservative extension of the ML type system.

### Type Inference for GADTs and Anti-unification

- Computer ScienceSBLP
- 2015

A type inference algorithm for GADTs is presented that is based on a closed-world approach to overloading and uses anti-unification and constraint-set satisfiability to infer the relationship between the types of function arguments and result.

### Subtyping Constrained Types

- Computer ScienceSAS
- 1996

This paper develops several subtyping relations on polymorphic constrained types of a general form that allows recursive constraints and multiple bounds on type variables.

### Type inference in systems of recursive types withsubtypingTrevor

- Computer Science, Mathematics
- 1997

The type inference algorithm generalizes a common idea of previous work and proves a general correctness theorem for this style of type inference, which provides deenitions of closure and consistency for recursive types with a greatest type, but not a least type.

## References

SHOWING 1-10 OF 24 REFERENCES

### Type Reconstruction with Recursive Types and Atomic Subtyping

- Mathematics, Computer ScienceTAPSOFT
- 1993

This work considers the problem of type reconstruction for A-terms over a type system with recursive types and atomic subsumptions and shows how to solve such inequalities by reduction to an infinite but well-structured set of inequalities over the base types.

### Parametric Overloading in Polymorphic Programming Languages

- Computer ScienceESOP
- 1988

This paper defines the concept of parametric overloading as a restricted form of overloading which is easily combined with parametric polymorphism, thereby allowing the design of efficient type inference algorithms.

### Polymorphic Type Inference for Languages with Overloading and Subtyping

- Computer Science
- 1991

This dissertation extends the Hindley/Milner/Damas type system to incorporate overloading and subtyping, and proves that it is undecidable whether a given constraint set is satisfiable; this difficulty leads us to impose restrictions on overloading.

### Coercion and type inference

- Computer SciencePOPL '84
- 1984

A simple semantic model of automatic coercion is proposed and an efficient type checking algorithm based on the first four rules is presented that is guaranteed to find a type whenever a type can be deduced using the four inference rules.

### Three Approaches to Type Structure

- Computer ScienceTAPSOFT, Vol.1
- 1985

We examine three disparate views of the type structure of programming languages: Milner's type deduction system and polymorphic let construct, the theory of subtypes and generic operators, and the…

### Type inference with subtypes

- Computer SciencePOPL '88
- 1988

A type system for deriving types of expressions in the language and an algorithm for type inference in a language with functions, records, and variant records is given, which is a synthesis of subtype polymorphism and universal polymorphism.

### Polymorphic Subtype Inference: Closing the Theory-Practice Gap

- Computer ScienceTAPSOFT, Vol.2
- 1989

Following the framework described above, a transformation is described, based on the lazy instance definition, that eliminates certain redundancies from typings that leads to a coercion set of size at most one.

### Constrained Quantification in Polymorphic Type Analysis

- Computer Science
- 1990

It is claimed that constrained quantification is a flexible, powerful, practical and formally comprehensible approach to polymorphic type analysis, especially when applied to languages with non-trivial subtyping.

### On the Complexity of ML Typability with Overloading

- MathematicsFPCA
- 1991

It is shown that under a correct notion of well-typed terms, the problem of determining whether a term is well typed with respect to an assumption set in an ML-style type system is undecidable, and a limited form of recursion called parametric recursion is considered.