Set-theoretic types for polymorphic variants

Gradual Set-Theoretic Types

Problem and motivation. A static type system can be an extremely powerful tool for a programmer, providing early error detection, and offering strong compile-time guarantees on the behavior of a program. However, compared to dynamic typing, static typing often comes at the expense of development speed and flexibility, as statically-typed code might be more difficult to adapt to changing require...

A Classical Set-Theoretic Model of Polymorphic Extensional Type Theory

We give a new semantic foundation for type theories in the lineage of Martin-LL of's \polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational semantics of an untyped programming language. We show how to integrate classical set-theoretic objects, such as funct...

Algebraic Specifications, Higher-Order Types, and Set-Theoretic Models

In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higher-order types, interpreted set-theoretically as Cartesian products, function spaces, and power-sets. This paper presents a simple framework for algebraic specifications with higher-...

Algebraic Speciications, Higher-order Types, and Set-theoretic Models

In most algebraic speciication frameworks, the type system is restricted to sorts, subsorts, and rst-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higher-order types, interpreted set-theoretically as Cartesian products , function spaces, and power-sets. This paper presents a simple framework for algebraic speciications with higher-ord...

A Set-Theoretic Model for a Typed Polymorphic Lambda Calculus - A Contribution to MetaSoft