Provable isomorphisms and domain equations in models of typed languages
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Polymorphic type inference and containment
Information and Computation - Semantics of Data Types
Introduction to algorithms
Algorithmic aspects of type inference with subtypes
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Type fixpoints: iteration vs. recursion
Proceedings of the fourth ACM SIGPLAN international conference on Functional programming
Efficient and flexible matching of recursive types
Information and Computation
Efficient algorithms for isomorphisms of simple types
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Products and polymorphic subtypes
Fundamenta Informaticae
Remarks on Isomorphisms in Typed Lambda Calculi with Empty and Sum Types
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A Decidable Variant of Higher Order Matching
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
The "Hardest'' Natural Decidable Theory
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Deciding Isomorphisms of Simple Types in Polynomial Time
Deciding Isomorphisms of Simple Types in Polynomial Time
Decidability of bounded second order unification
Information and Computation
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A game-theoretic approach to deciding higher-order matching
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Bounded second-order unification is NP-complete
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Proof systems for retracts in simply typed lambda calculus
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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A simple type σ is retractable to a simple type τ if there are two terms Cσ→τ and Dτ→σ such that D ○ C λx.x. The retractability of types is affine if the terms C and D are affine, that is, when every bound variable occurs in them at most once in the scope of its declaration. This paper presents a system that derives affine retractability for simple types. It also studies the complexity of constructing these affine retractions. The problem of affine retractability is NP-complete even for the class of types over a single type atom and having limited functional order. In addition, a polynomial algorithm for types of orders less than three is presented.