Type reconstruction in F ω

Authors:
Paweł Urzyczyn
Affiliations:
Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland urzy@mimuw.edu.pl
Venue:
Mathematical Structures in Computer Science
Year:
1997

Citing 18
Cited 10

The system F of variable types, fifteen years later

Theoretical Computer Science
Polymorphic type inference and containment

Information and Computation - Semantics of Data Types
Polymorphic unification and ML typing

POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Discrete polymorphism

LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Deciding ML typability is complete for deterministic exponential time

POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Type reconstruction in finite rank fragments of the second-order &lgr;-calculus

Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Lambda calculi with types

Handbook of logic in computer science (vol. 2)
The undecidability of the semi-unification problem

Information and Computation
Type reconstruction in the presence of polymorphic recursion

ACM Transactions on Programming Languages and Systems (TOPLAS)
An analysis of ML typability

Journal of the ACM (JACM)
Type inference: some results, some problems

Fundamenta Informaticae - Special issue: lambda calculus and type theory
On the undecidability of partial polymorphic type reconstruction

Fundamenta Informaticae - Special issue: lambda calculus and type theory
Polymorphic type inference

POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Types in Lambda Calculi and Programming Languages

ESOP '90 Proceedings of the 3rd European Symposium on Programming
Positive Recursive Type Assignment

MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Type Inference in Polymorphic Type Discipline

TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Type reconstruction in F-omega is undecidable

TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Generic Terms Having No Polymorphic Types

ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming

Principality and decidable type inference for finite-rank intersection types

Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Branching Types

ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
The Essence of Principal Typings

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Rank 2 intersection types for local definitions and conditional expressions

ACM Transactions on Programming Languages and Systems (TOPLAS)
A calculus with polymorphic and polyvariant flow types

Journal of Functional Programming
Principality and type inference for intersection types using expansion variables

Theoretical Computer Science
Type inference with expansion variables and intersection types in system E and an exact correspondence with β-reduction

PPDP '04 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming
THEORETICAL PEARLS: A bargain for intersection types: a simple strong normalization proof

Journal of Functional Programming
A typed lambda calculus with intersection types

Theoretical Computer Science
Expansion: the Crucial Mechanism for Type Inference with Intersection Types: A Survey and Explanation

Electronic Notes in Theoretical Computer Science (ENTCS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate Girard's calculus F ω as a ‘Curry style’ type assignment system for pure lambda terms. First we show an example of a strongly normalizable term that is untypable in F ω. Then we prove that every partial recursive function is nonuniformly represented in Fω (even if quantification is restricted to constructor variables of level 1). It follows that the type reconstruction problem is undecidable and cannot be recursively separated from normalization.