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
Finitely stratified polymorphism
Information and Computation
On the undecidability of partial polymorphic type reconstruction
Fundamenta Informaticae - Special issue: lambda calculus and type theory
A direct algorithm for type inference in the rank-2 fragment of the second-order &lgr;-calculus
LFP '94 Proceedings of the 1994 ACM conference on LISP and functional programming
A type inference algorithm for a stratified polymorphic type discipline
Information and Computation - Special conference issue: international conference on theoretical aspects of computer software
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
On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
CPS Translations and Applications: The Cube and Beyond
Higher-Order and Symbolic Computation
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
ML Typability is DEXTIME-Complete
CAAP '90 Proceedings of the 15th Colloquium on Trees in Algebra and Programming
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
Existential Type Systems with No Types in Terms
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
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We consider here a number of variations on System F that are predicative second-order systems whose terms are intermediate between the Curry style and the Church style. As in the Church style, the terms we deal with here contain the information on where universal quantifier elimination and introduction in the type inference process must take place. However, they omit the information on what types are involved in the rules, which is similar to Curry forms. This can be viewed as a version of the partial type reconstruction problem considered by Boehm and Pfenning in which type erasure is done in a systematic way. In this paper we prove the undecidability of the type checking, type inference, and typability problems for the system. This demonstrates that the reason for undecidability is not the absence of the information where the second-order rules should be applied but the actual shape of the polymorphic types to be used in the derivation. Moreover, the proof works for the predicative version of the system with finitely stratified polymorphic types. The result includes bounds on the Leivant levels of types used in the instances leading to undecidability.