Related papers: On counting untyped lambda terms
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming…
Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model…
As NLP tools become ubiquitous in today's technological landscape, they are increasingly applied to languages with a variety of typological structures. However, NLP research does not focus primarily on typological differences in its…
A fully-automated algorithm is developed able to show that evaluation of a given untyped lambda-expression will terminate under CBV (call-by-value). The ``size-change principle'' from first-order programs is extended to arbitrary untyped…
We further explore the notion of Ulam words considered by Bade, Cui, Labelle, and Li, giving some lower bounds on how many there are of a given length. Gaps between words and words of special type also reveal remarkable structure. By…
We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot…
We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The…
We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by…
Large language models have the potential to simplify formal theorem proving and make it more accessible. But how to get the most out of these models is still an open question. To answer this question, we take a step back and explore the…
We explore various methods for computing sentence representations from pre-trained word embeddings without any training, i.e., using nothing but random parameterizations. Our aim is to put sentence embeddings on more solid footing by 1)…
We introduce a group of related methods for binary classification tasks using probes of the hidden state activations in large language models (LLMs). Performance is on par with the largest and most advanced LLMs currently available, but…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We give an example of a finitely based locally finite variety which has uncountably many term clones. (Such varieties were known before.)
In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…
Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…