Related papers: The Functional Machine Calculus II: Semantics
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
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…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
Algebraic effects & handlers are a modular approach for modeling side-effects in functional programming. Their syntax is defined in terms of a signature of effectful operations, encoded as a functor, that are plugged into the free monad;…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
We present a calculus that models a simple sort of process interaction. Our calculus consists of a collection of terms together with a rewrite relation, parameterised by an arbitrary multicategory whose morphisms we understand as…
It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…