Related papers: Explicit Refinement Types
Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…
Refinement type checkers are a powerful way to reason about functional programs. For example, one can prove properties of a slow, specification implementation, porting the proofs to an optimized implementation that behaves the same. Without…
When scripts in untyped languages grow into large programs, maintaining them becomes difficult. A lack of explicit type annotations in typical scripting languages forces programmers to must (re)discover critical pieces of design information…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
In recent years, there has been an increased interest in tools that establish \emph{incorrectness} rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…
Refinement types decorate types with assertions that enable automatic verification. Like assertions, refinements are limited to binders that are in scope, and hence, cannot express higher-order specifications. Ghost variables circumvent…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
We introduce Flux, which shows how logical refinements can work hand in glove with Rust's ownership mechanisms to yield ergonomic type-based verification of low-level pointer manipulating programs. First, we design a novel refined type…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
Toman et al. have proposed a type system for automatic verification of low-level programs, which combines ownership types and refinement types to enable strong updates of refinement types in the presence of pointer aliases. We extend their…
Liquid Haskell is an extension to the Haskell programming language that adds support for refinement types: data types augmented with SMT-decidable logical predicates that refine the set of values that can inhabit a type. Furthermore, Liquid…
The pattern-match safety problem is to verify that a given functional program will never crash due to non-exhaustive patterns in its function definitions. We present a refinement type system that can be used to solve this problem. The…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a…
Quantifier elimination theorems show that each formula in a certain theory is equivalent to a formula of a specific form -- usually a quantifier-free one, sometimes in an extended language. Model theoretic embedding tests are a frequently…
We formalize a new type system for Elixir, a dynamically typed functional programming language of growing popularity that runs on the Erlang virtual machine. Our system combines gradual typing with semantic subtyping to enable precise,…