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ESOP '96 Proceedings of the 6th European Symposium on Programming Languages and Systems
Refinement-Type Checker for Standard ML
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
Inductive Definitions and Type Theory: an Introduction (Preliminary Version)
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Constructive Membership Predicates as Index Types
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POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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This paper explores a new point in the design space of formal reasoning systems - part programming language, part logical framework. The system is built on a programming language where the user expresses equality constraints between types and the type checker then enforces these constraints. This simple extension to the type system allows the programmer to describe properties of his program in the types of witness objects which can be thought of as concrete evidence that the program has the property desired. These techniques and two other rich typing mechanisms, rank-N polymorphism and extensible kinds, create a powerful new programming idiom for writing programs whose types enforce semantic properties.A language with these features is both a practical programming language and a logic. This marriage between two previously separate entities increases the probability that users will apply formal methods to their programming designs. This kind of synthesis creates the foundations for the languages of the future.