Partial polymorphic type inference and higher-order unification

Authors:
Frank Pfenning
Affiliations:
Department of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania
Venue:
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Year:
1988

Citing 9
Cited 23

Type inference and type containment.

Proc. of the international symposium on Semantics of data types
The typechecking of programs with implicit type structure.

Proc. of the international symposium on Semantics of data types
Natural deduction as higher-order resolution

Journal of Logic Programming
Higher-order logic programming

Proceedings on Third international conference on logic programming
Higher-order abstract syntax

PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Abstract types have existential types

POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Polymorphic type inference

POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Towards a theory of type structure

Programming Symposium, Proceedings Colloque sur la Programmation
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)

The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)

Conception, evolution, and application of functional programming languages

ACM Computing Surveys (CSUR)
Type inference in the presence of type abstraction

PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Type reconstruction with first-class polymorphic values

PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Higher-order Horn clauses

Journal of the ACM (JACM)
Deciding ML typability is complete for deterministic exponential time

POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algebraic reconstruction of types and effects

POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Putting type annotations to work

POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Local type inference

POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Second-order unification and type inference for Church-style polymorphism

POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Local type inference

ACM Transactions on Programming Languages and Systems (TOPLAS)
Colored local type inference

POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Type classes with more higher-order polymorphism

Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Higher Order Unification 30 Years Later

TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Partially Typed Terms between Church-Style and Curry-Style

TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Higher-order unification and matching

Handbook of automated reasoning
MLF: raising ML to the power of system F

ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
A treatment of higher-order features in logic programming

Theory and Practice of Logic Programming
Simple, partial type-inference for System F based on type-containment

Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
FPH: first-class polymorphism for Haskell

Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Scrap Your Type Applications

MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Recasting MLF

Information and Computation
Ur: statically-typed metaprogramming with type-level record computation

PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Implementing polymorphic typing in a logic programming language

Computer Languages

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that the problem of partial type inference in the nth-order polymorphic &lgr;-calculus is equivalent to nth-order unification. On the one hand, this means that partial type inference in polymorphic &lgr;-calculi of order 2 or higher is undecidable. On the other hand, higher-order unification is often tractable in practice, and our translation entails a very useful algorithm for partial type inference in the &ohgr;-order polymorphic &lgr;-calculus. We present an implementation in &lgr;Prolog in full.