Related papers: Rational functions via recursive schemes
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
The polarized SILL programming language uniformly integrates functional programming and session-typed message-passing concurrency. It supports general recursion, asynchronous and synchronous communication, and higher-order programs that…
We prove that every proper subclass of the 321-avoiding permutations that is defined either by only finitely many additional restrictions or is well quasi-ordered has a rational generating function. To do so we show that any such class is…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
Natural language processing for programming aims to use NLP techniques to assist programming. It is increasingly prevalent for its effectiveness in improving productivity. Distinct from natural language, a programming language is highly…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
The idea of functional programming has played a big role in shaping today's landscape of mainstream programming languages. Another concept that dominates the current programming style is Dijkstra's structured programming. Both concepts have…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A particular kind of rational relations is the sequential functions. Sequential functions are the functions that…