Related papers: A Word Sampler for Well-Typed Functions
We explore the use of large pretrained language models as few-shot semantic parsers. The goal in semantic parsing is to generate a structured meaning representation given a natural language input. However, language models are trained to…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
Many multilingual NLP applications need to translate words between different languages, but cannot afford the computational expense of inducing or applying a full translation model. For these applications, we have designed a fast algorithm…
We propose a general framework for first-order functional logic programming, supporting lazy functions, non-determinism and polymorphic datatypes whose data constructors obey a set C of equational axioms. On top of a given C, we specify a…
The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a…
Sentence Simplification aims to rephrase complex sentences into simpler sentences while retaining original meaning. Large Language models (LLMs) have demonstrated the ability to perform a variety of natural language processing tasks.…
We sketch a simple language of concurrent objects which explores the design space between type systems and continuous testing. In our language, programs are collections of communicating automata checked automatically for multiparty…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This…
Ad hoc parsers are everywhere: they appear any time a string is split, looped over, interpreted, transformed, or otherwise processed. Every ad hoc parser gives rise to a language: the possibly infinite set of input strings that the program…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
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…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and…
The functional programming paradigm has a long and storied history, with its beginnings in the Lambda Calculus. In recent decades, pure functional languages such as Haskell have been shown to be highly effective in producing robust software…
We show that recent approaches of static analysis based on quantitative typing systems can be extended to programming languages with global state. More precisely, we define a call-by-value language equipped with operations to access a…
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments…
Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
Formal languages let us define the textual representation of data with precision. Formal grammars, typically in the form of BNF-like productions, describe the language syntax, which is then annotated for syntax-directed translation and…