Related papers: Toward Hole-Driven Development with Liquid Haskell

Modern Haskell supports zero-cost coercions, a mechanism where types that share the same run-time representation may be freely converted between. To make sure such conversions are safe and desirable, this feature relies on a mechanism of…

Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…

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…

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…

DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…

Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have…

Existing query languages for data discovery exhibit system-driven designs that emphasize database features and functionality over user needs. We propose a re-prioritization of the client through an introduction of a language-driven approach…

That the Haskell Compiler GHC is capable of proving non-trivial equalities between Haskell code, by virtue of its aggressive optimizer, in particular the term rewriting engine in the simplifier. We demonstrate this with a surprising little…

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover…

Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…

For many years, GHC has implemented an extension to Haskell that allows type variables to be bound in type signatures and patterns, and to scope over terms. This extension was never properly specified. We rectify that oversight here. With…

Dependent types help programmers write highly reliable code. However, this reliability comes at a cost: it can be challenging to write new prototypes in (or migrate old code to) dependently-typed programming languages. Gradual typing makes…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…

UCLID5 is a tool for the multi-modal formal modeling, verification, and synthesis of systems. It enables one to tackle verification problems for heterogeneous systems such as combinations of hardware and software, or those that have…

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…

We present a new type system combining occurrence typing, previously used to type check programs in dynamically-typed languages such as Racket, JavaScript, and Ruby, with dependent refinement types. We demonstrate that the addition of…