Abstract types have existential type
ACM Transactions on Programming Languages and Systems (TOPLAS)
Deciding ML typability is complete for deterministic exponential time
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The undecidability of the semi-unification problem
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Handbook of logic in computer science (vol. 2)
Type reconstruction in the presence of polymorphic recursion
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the undecidability of partial polymorphic type reconstruction
Fundamenta Informaticae - Special issue: lambda calculus and type theory
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
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
Journal of Functional Programming
Lectures on the Curry-Howard Isomorphism, Volume 149 (Studies in Logic and the Foundations of Mathematics)
Partial polymorphic type inference is undecidable
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Undecidability of Type-Checking in Domain-Free Typed Lambda-Calculi with Existence
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Galois embedding from polymorphic types into existential types
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Type checking and typability in domain-free lambda calculi
Theoretical Computer Science
Type checking and inference are equivalent in lambda calculi with existential types
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
A note on subject reduction in (→,∃)-Curry with respect to complete developments
Information Processing Letters
| Hi-index | 0.00 |
We study type checking, typability, and type inference problems for type-free style and Curry style second-order existential systems where the type-free style differs from the Curry style in that the terms of the former contain information on where the existential quantifier elimination and introduction take place but omit the information on which types are involved. We show that all the problems are undecidable employing reduction of second-order unification in case of the type-free system and semiunification in case of the Curry style system. This provides a fine border between problems yielding to a reduction of second-order unification problem and the semiunification problem. In addition, we investigate the subject reduction property of the system in the Curry-style.