Related papers: Parallel Algebraic Effect Handlers
Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…
In process algebras such as ACP (Algebra of Communicating Processes), parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as found in contemporary programming languages, parallel processes…
Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
The multimodal Lambek calculus is an extension of the Lambek calculus that includes several product operations (some of them being commutative or/and associative), unary modalities, and corresponding residual implications. In this work, we…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
NumPyro is a lightweight library that provides an alternate NumPy backend to the Pyro probabilistic programming language with the same modeling interface, language primitives and effect handling abstractions. Effect handlers allow Pyro's…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We have previously defined synchronization (Gomez, E. and K. Schubert 2011) as a relation between the times at which a pair of events can happen, and introduced an algebra that covers all possible relations for such pairs. In this work we…
Speculative decoding has proven to be an efficient solution to large language model (LLM) inference, where the small drafter predicts future tokens at a low cost, and the target model is leveraged to verify them in parallel. However, most…
Network latency distributions, their algebra, and use examples. This paper considers modeling of capacity-insensitive processes and distributed systems. It provides algebraic properties of the latency distribution algebra and Haskell code…
I present a model of universal parallel computation called $\Delta$-Nets, and a method to translate $\lambda$-terms into $\Delta$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the…
Variable environment is the time-honored way of making sense of free variables, used in programming language theory as well when writing interpreters and some compilers. Algebraic effects give another way, as was pointed already at HOPE…
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…
Effectful programs interact in ways that go beyond simple input-output, making compositional reasoning challenging. Existing work has shown that when such programs are ``separate'', i.e., when programs do not interfere with each other, it…