Partial polymorphic type inference and higher-order unification
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Finitely stratified polymorphism
Information and Computation
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
Handbook of logic in computer science (vol. 2)
On the type structure of standard ML
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of the ACM (JACM)
On the undecidability of partial polymorphic type reconstruction
Fundamenta Informaticae - Special issue: lambda calculus and type theory
Information and Computation
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
Putting type annotations to work
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Basic simple 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
Type inference with rank 1 polymorphism for type-directed compilation of ML
Proceedings of the fourth ACM SIGPLAN international conference on Functional programming
Semi-explicit first-class polymorphism for ML
Information and Computation
Principal type-schemes for functional programs
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Type Inference Problems: A Survey
MFCS '90 Proceedings of the Mathematical Foundations of Computer Science 1990
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Explicitly Typed lambda µ-Calculus for Polymorphism an Call-by-Value
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Partial polymorphic type inference is undecidable
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Existential Type Systems with No Types in Terms
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Type checking and inference for polymorphic and existential types
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
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
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We introduce several structures between Church-style and Curry-style based on partially typed terms formalism. In the uniform framework, we study the static properties of the λ-terms between the two styles. It is proved that type checking, typability, and type inference for domain-free λ2 are in general undecidable. A simple instance of the second-order unification problem is reduced to the problem of type inference for domain-free λ2. The typability problem is undecidable even for a predicative fragment of domain-free λ2, called the rank 2 fragment. It is also found that making polymorphic domains free and the use of type-holes [] are independently responsible for the undecidability of the partial polymorphic type reconstruction problem.