Semirings, automata, languages
Semirings, automata, languages
Formal languages
Probabilistic analysis of algorithms
Probabilistic analysis of algorithms
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Latex: a document preparation system
Latex: a document preparation system
Introduction to algorithms
The C programming language
The SGML handbook
ML for the working programmer
The C++ programming language (2nd ed.)
The C++ programming language (2nd ed.)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Hilbert's tenth problem
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Object-oriented software construction (2nd ed.)
Object-oriented software construction (2nd ed.)
The Java programming language (2nd ed.)
The Java programming language (2nd ed.)
Coinductive axiomatization of recursive type equality and subtyping
Fundamenta Informaticae - Special issue: typed lambda-calculi and applications, selected papers
The XML handbook
Journal of the ACM (JACM)
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Proceedings of the International Conference on Theoretical Aspects of Computer Software
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Subtyping with Union Types, Intersection Types and Recursive Types
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A Complete Type Inference System for Subtyped Recursive Types
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Mockingbird: Flexible Stub Compilation from Pairs of Declarations
ICDCS '99 Proceedings of the 19th IEEE International Conference on Distributed Computing Systems
Efficient algorithms for isomorphisms of simple types
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Isomorphisms of generic recursive polynomial types
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A short survey of isomorphisms of types
Mathematical Structures in Computer Science
Efficient algorithms for isomorphisms of simple types
Mathematical Structures in Computer Science
Simple and safe SQL queries with c++ templates
GPCE '07 Proceedings of the 6th international conference on Generative programming and component engineering
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We consider the type system formed by a finite set of primitive types such as integer, character, real, etc., and three type construction operators: (i) Cartesian product, (ii) disjoint sum, and (iii) recursive type definitions. Type equivalence is defined to obey the arithmetical rules: commutativity and associativity of product and sum and distributivity of product over sum. We offer a compact representation of the types in this system as multivariate algebraic functions. This type system admits two natural notions of subtyping: "multiplicative", which roughly corresponds to the notion of object-oriented subtyping, and "additive", which seems to be more appropriate in our context. Both kinds of subtyping can be efficiently computed if no recursive definitions are allowed. Our main result is that additive subtyping is undecidable in the general case. Perhaps surprisingly, this undecidability result is by reduction from Hilbert's Tenth Problem (HIO): the solution of Diophantine equations.