Related papers: Refinement Types as Higher Order Dependency Pairs

We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…

Relative correctness is the property of a program to be more-correct than another program with respect to a given specification. Among the many properties of relative correctness, that which we found most intriguing is the property that…

Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the…

This article presents liquid resource types, a technique for automatically verifying the resource consumption of functional programs. Existing resource analysis techniques trade automation for flexibility -- automated techniques are…

Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…

We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capturesome programming patterns used in untyped languages. Although occurrence typing was tied from its inceptionto set-theoretic…

Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the…

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following…

We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to \emph{tuples} of natural numbers and higher-order…

We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…

Session types are abstractions of communication protocols enabling the static analysis of message-passing processes. Refinement notions for session types are key to support safe forms of process substitution while preserving their…

We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…

We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non…

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…

This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…

Specifications of significant systems can be made short and perspicuous by using abstract data types; data reification can provide a clear, stepwise, development history of programs that use more efficient concrete representations. Data…

We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2)…

Recent years have seen growing interest in the retrofitting of type systems onto dynamically-typed programming languages, in order to improve type safety, programmer productivity, or performance. In such cases, type system developers must…

This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…

The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…