Related papers: A Rewriting View of Simple Typing
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed.…
By the sometimes so-called MAIN THEOREM of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS'2000), Brattka (MLQ'2005), and Ziegler (ToCS'2006) have considered different relaxed notions…
A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by…
The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter…
We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
Can we improve machine translation (MT) with LLMs by rewriting their inputs automatically? Users commonly rely on the intuition that well-written text is easier to translate when using off-the-shelf MT systems. LLMs can rewrite text in many…
Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…
Handwritten Text Recognition (HTR) remains a challenging problem to date, largely due to the varying writing styles that exist amongst us. Prior works however generally operate with the assumption that there is a limited number of styles,…
This paper is an expository contribution reporting on published work. It focusses on an approach followed in the rewriting community to formalize the concept of strategy. Based on rewriting concepts, several definitions of strategy are…
Finding the right reviewers to assess the quality of conference submissions is a time consuming process for conference organizers. Given the importance of this step, various automated reviewer-paper matching solutions have been proposed to…
The field of scientific publishing that is served by LaTeX is increasingly dependent on the availability of metadata about publications. We discuss how to use LaTeX classes and BibTeX styles to curate metadata throughout the life cycle of a…
We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed lambda-mu-calculus. We also extend Mendler's result on…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…
The Normalization transformation plays a key role in the compilation of Diderot programs. The transformations are complicated and it would be easy for a bug to go undetected. To increase our confidence in normalization part of the compiler…