Related papers: The Sketch of a Polymorphic Symphony
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
Pretrained encoders for mathematical texts have achieved significant improvements on various tasks such as formula classification and information retrieval. Yet they remain limited in representing and capturing student strategies for entire…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the…
This paper presents a SysML-based approach to enhance functional and software development process within an industrial context. The recent changes in technology such as electromobility and increased automation in heavy construction…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
Traversal strategies \'a la Stratego (also \'a la Strafunski and 'Scrap Your Boilerplate') provide an exceptionally versatile and uniform means of querying and transforming deeply nested and heterogeneously structured data including terms…
Graph mining applications analyze the structural properties of large graphs, and they do so by finding subgraph isomorphisms, which makes them computationally intensive. Existing graph mining techniques including both custom graph mining…
We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…
This paper presents a so-called maramafication of an essential part of functional programming languages such as Haskell or Clean: the construction of fully polymorphic well-typed algebraic data structures based on type definitions with at…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
We explore an approach to type-directed program synthesis rooted in constraint-based type inference techniques. By doing this, we aim to more efficiently synthesize polymorphic code while also tackling advanced typing features such as GADTs…
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may…
Programming systems incorporating aspects of functional programming, e.g., higher-order functions, are becoming increasingly popular for large-scale distributed programming. New frameworks such as Apache Spark leverage functional techniques…
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…
Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…