Related papers: A Unified Formal Description of Arithmetic and Set…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
The field of directed type theory seeks to design type theories capable of reasoning synthetically about (higher) categories, by generalizing the symmetric identity types of Martin-L\"of Type Theory to asymmetric hom-types. We articulate…
Structured data summarization involves generation of natural language summaries from structured input data. In this work, we consider summarizing structured data occurring in the form of tables as they are prevalent across a wide variety of…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being…
In the classical herding model, asymptotic learning refers to situations where individuals eventually take the correct action regardless of their private information. Classical results identify classes of information structures for which…
We describe Haskell implementations of interesting combinatorial generation algorithms with focus on boolean functions and logic circuit representations. First, a complete exact combinational logic circuit synthesizer is described as a…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.
In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…
We introduce two approximate variants of inclusion dependencies and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in the database and differ in…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the…
This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…