Related papers: Declarative Combinatorics: Isomorphisms, Hylomorph…

We describe Haskell implementations of interesting combinatorial generation algorithms with focus on boolean functions and logic circuit representations. First, a complete exact combinational logic circuit synthesizer is described as a…

Using specializations of unfold and fold on a generic tree data type we derive unranking and ranking functions providing natural number encodings for various Hereditarily Finite datatypes. In this context, we interpret unranking operations…

The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available…

e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…

We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type…

The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…

Haskell is a popular choice for hosting deeply embedded languages. A recurring challenge for these embeddings is how to seamlessly integrate user defined algebraic data types. In particular, one important, convenient, and expressive feature…

We present a statically typed embedding of relational programming (specifically a dialect of miniKanren with disequality constraints) in Haskell. Apart from handling types, our dialect extends standard relational combinator repertoire with…

Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…

Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…

In recent years, languages like Haskell have seen a dramatic surge of new features that significantly extends the expressive power of their type systems. With these features, the challenge of kind inference for datatype declarations has…

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while…

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term…

We present a new, uniform semantics for Haskell-style overloading. We realize our approach in a new core language, System F$_\mathrm{D}$, whose metatheory we mechanize in the Lean4 interactive theorem prover. System F$_\mathrm{D}$ is…

The recent notion of graded modal types provides a framework for extending type theories with fine-grained data-flow reasoning. The Granule language explores this idea in the context of linear types. In this practical setting, we observe…

Liquid Haskell's refinement-reflection feature augments the Haskell language with theorem proving capabilities, allowing programmers to retrofit their existing code with proofs. But many of these proofs require routine, boilerplate code…

Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but…

Deep learning is moving towards increasingly sophisticated optimization objectives that employ higher-order functions, such as integration, continuous optimization, and root-finding. Since differentiable programming frameworks such as…

This work uses visual knowledge discovery in parallel coordinates to advance methods of interpretable machine learning. The graphic data representation in parallel coordinates made the concepts of hypercubes and hyperblocks (HBs) simple to…

Scientific progress increasingly depends on data management, particularly to clean and curate data so that it can be systematically analyzed and reused. A wealth of techniques for managing and curating data (and its provenance) have been…