Related papers: Congruence Closure in Intensional Type Theory
This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can…
Algebraic data types (ADTs) are a construct classically found in functional programming languages that capture data structures like enumerated types, lists, and trees. In recent years, interest in ADTs has increased. For example, popular…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Transformer-based large language models (LLMs) have displayed remarkable creative prowess and emergence capabilities. Existing empirical studies have revealed a strong connection between these LLMs' impressive emergence abilities and their…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…
We consider type inference for guarded recursive data types (GRDTs) -- a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference.…
We propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demonstrate that a safe multi-threaded program runs in…
This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint…
The closure principle is fundamental in multiple testing and has been used to derive many efficient procedures with familywise error rate control. However, it is often unsuitable for modern research, which involves flexible multiple testing…
In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…
Assessment of proficiency of the learner is an essential part of Intelligent Tutoring Systems (ITS). We use Item Response Theory (IRT) in computer-aided language learning for assessment of student ability in two contexts: in test sessions,…
We present a type-theoretic framework for reasoning about incorrectness in functional programs that interact with effectful, opaque library APIs. Our approach centers on traces -- temporally-ordered sequences of library API invocations --…
We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…
This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against…
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…