Search Results for "algebraic"
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Showing 26 open source projects for "algebraic"
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Flix
The Flix Programming Language
Flix is a statically typed programming language combining functional, imperative, and logic paradigms, with first‑class Datalog constraints and a polymorphic effect system. Designed to run on the JVM, Flix enforces purity tracking at compile time, supports algebraic data types, tail‑call elimination, and allows entire Datalog programs as values. -
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Catlab.jl
A framework for applied category theory in the Julia language
...Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory. First and foremost, Catlab provides data structures, algorithms, and serialization for applied category theory. Macros offer a convenient syntax for specifying categorical doctrines and type-safe symbolic manipulation systems. Wiring diagrams (aka string diagrams) are supported through specialized data structures and can be serialized to and from GraphML (an XML-based format) and JSON. -
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Peroxide
Rust numeric library with high performance and friendly syntax
...Peroxide uses a 1D data structure to represent matrices, making it straightforward to integrate with BLAS (Basic Linear Algebra Subprograms). This means that Peroxide can guarantee excellent performance for linear algebraic computations by leveraging the optimized routines provided by BLAS. For users familiar with numerical computing libraries like NumPy, MATLAB, or R, Rust's syntax might seem unfamiliar at first. This can make it more challenging to learn and use Rust libraries that heavily rely on Rust's unique features and syntax. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique. ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. -
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C++ Library of Abstract Algebra concepts and arithmetic algorithms defined in terms of these concepts, using Instigate Generic Programming Methodology. Based on this library we plan to develop Linear Algebra and Optimization concepts and algorithms.
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CasADi
CasADi is a symbolic framework for numeric optimization
...These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or exported to stand-alone C code. Initial value problems in ordinary or differential-algebraic equations (ODE/DAE) can be calculated using explicit or implicit Runge-Kutta methods or interfaces to IDAS/CVODES from the SUNDIALS suite. Derivatives are calculated using sensitivity equations, up to arbitrary order. -
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koka
Koka language compiler and interpreter
Koka is a strongly typed functional-style language with effect types and handlers. The core of Koka consists of a small set of well-studied language features, like first-class functions, a polymorphic type- and effect system, algebraic data types, and effect handlers. Each of these is composable and avoid the addition of “special” extensions by being as general as possible. Koka tracks the (side) effects of every function in its type, where pure and effectful computations are distinguished. The precise effect typing gives Koka rock-solid semantics backed by well-studied category theory, which makes Koka particularly easy to reason about for both humans and compilers. ... -
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PureScript
A strongly-typed language that compiles to JavaScript
...Excellent tooling and editor support with instant rebuilds. An active community with many learning resources. Build real-world applications using functional techniques and expressive types, such as: Algebraic data types and pattern matching. Row polymorphism and extensible records. Higher kinded types and type classes with functional dependencies, as well as higher-rank polymorphism. Precompiled binaries are available for OSX, Linux, and Windows. The Pursuit package database hosts searchable documentation for PureScript packages. The recommended build tool for PureScript is Spago, which can be installed using npm. -
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Scalaz
Principled Functional Programming in Scala
...Its type class–oriented design lets you write generic algorithms over capabilities rather than concrete types, improving reuse and testability. Scalaz also contributes optics, equality/ordering abstractions, and lawful instances with property-based tests to ensure algebraic laws hold. While the Scala ecosystem now includes sibling projects, Scalaz remains a deep toolbox for principled FP in Scala and a reference point for category-theory-inspired design on the JVM. -
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Hasktorch
Tensors and neural networks in Haskell
Hasktorch is a powerful Haskell library for tensor computation and neural network modeling, built on top of libtorch (the backend of PyTorch). It brings differentiable programming, automatic differentiation, and efficient tensor operations into Haskell’s strongly typed functional paradigm. This project is in active development, so expect changes to the library API as it evolves. We would like to invite new users to join our Hasktorch discord space for questions and discussions.... -
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Metatheory.jl
General purpose algebraic metaprogramming
Metatheory.jl is a general purpose term rewriting, metaprogramming and algebraic computation library for the Julia programming language, designed to take advantage of the powerful reflection capabilities to bridge the gap between symbolic mathematics, abstract interpretation, equational reasoning, optimization, composable compiler transforms, and advanced homoiconic pattern matching features. The core features of Metatheory.jl are a powerful rewrite rule definition language, a vast library of functional combinators for classical term rewriting and an e-graph rewriting, a fresh approach to term rewriting achieved through an equality saturation algorithm. ... -
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Algebird
Abstract Algebra for Scala
Algebird is Twitter’s Apache‑licensed Scala library providing abstract algebra data structures and algorithms, especially for online/streaming aggregation. It includes Monoid, Approximate, HyperLogLog, CMS, BloomFilter, Min/Max, Averaged Value types, supporting efficient distributed aggregation and approximate analytics. -
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Fantasy Land Specification
Specification for interoperability of JavaScript algebraic structures
This project specifies interoperability of common algebraic structures like Setoid, Ord, Semigroupoid, Category, Semigroup, Monoid, Group, Filterable, Functor, Contravariant, Apply, Applicative, etc. An algebra is a set of values, a set of operators that it is closed under and some laws it must obey. Each Fantasy Land algebra is a separate specification. An algebra may have dependencies on other algebras which must be implemented. -
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Spire
Powerful new number types and numeric abstractions for Scala
Spire is a numeric and algebraic library for Scala, offering type-safe, generic, and high-precision arithmetic. It introduces abstractions like Rings, Fields, and Rationals and supports specialized number types (e.g. Rational, Complex, Interval), macros, and seamless integration with Cats for abstract numeric programming. -
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Cyclops
An advanced platform for writing functional applications in Java 8
Fast purely functional datastructures (Vector, Seq / List, LazySeq / LazyList, NonEmptyList, HashSet, TreeSet, TrieSet, HashMap, LinkedMap, MultiMap, TreeMap, BankersQueue, LazyString, Discrete Interval Encoded Tree, Zipper, Range, Tree, DifferenceList, HList, Dependent Map). Structural Pattern Matching API (deconstruct algebraic product and sum types). Improved type safety via the removal of unsafe APIs -- E.g. Unlike Optional, Option has no get method (which could throw a null pointer) -- New data structures do not support operations that would throw exceptions (you can't call head on an empty list for example). Eager and Lazy alternatives for most datastructures (Option is eager, Maybe is lazy + reactive). ... -
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Advanced Numerical Instruments 3D
Advanced numerical instruments: adaptive meshing, FE methods, solvers
Ani3D provides portable libraries for each step in the numerical solution of systems of PDEs with variable tensorial coefficients: (1) unstructured adaptive mesh generation, (2) metric-based mesh adaptation, (3) finite element discretization and interpolation, (4) algebraic solvers. -
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Advanced Numerical Instruments 2D
Advanced numerical instruments: adaptive meshing, FE methods, solvers
Ani2D provides portable libraries for each step in the numerical solution of systems of PDEs with variable tensorial coefficients: (1) unstructured adaptive mesh generation, (2) metric-based mesh adaptation, (3) finite element discretization and interpolation, (4) algebraic solvers. -
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algebrain
Math Parser for Java
Moved to GitHub https://github.com/fedups Algebraic equation processing at run time for Java programs. Supports variables, functions with parameters, rate table lookups, an embedded "if" function... Infinitely extensible, very small footprint. -
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Interdependent Java frameworks: AMath (abstract numbers support); AFuzzy (fuzzy numbers and methods); AMathSys (flexible solvers of linear and nonlinear algebraic and differential equations); ADSM (multi-criteria ranking and grading of alternatives).
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aal
The Advanced Algebraic Language.
The Advanced Algebraic Language (AAL) is a very dynamic programming language designed to fill the void that has appeared between mainstream languages and algebra. As a result its main focus is ease of use for math problems. To download AAL check out the source code repository. There are versions available for windows and linux with both 32 and 64 bit native binaries: http://svn.code.sf.net/p/aal-lang/code/trunk/bin/ -
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Dapar
Parsing for everybody.
...It will interpret any grammar you give it in a BNF-like format, and constructs a matching expression tree for any given input. This makes developing a new parser for any language simple and reliable. Includes an ABNF parser, EBNF parser, XML parser and algebraic math parser. -
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Manufactured Analytical Solution Abstraction (MASA): a library for applying the Method of Manufactured Solutions to verification of numerical software used for solving systems of nonlinear algebraic and differential equations.
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Prop is a pattern matching language based on C++. It implements algebraic datatypes, pattern matching and rewriting, and generates C++ code as output.
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An adaptive mini database learns algorithmic operations for data intensive algebraic computational methods within a pervasive computing graph. It also provides generic structures and algorithms as a data fabric.
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MIC* comes with a new vision of multi-agent system engineering: The multi-agent system is devided explicitly into two dimensions: the deployment environment and the autonomous agents. MIC* is an algebraic model of a deployment environment (container of a
