This page is a survey of software related to the Physics Derivation Graph. For a literature review, see this page.
The scope of the Physics Derivation Graph does not include proof assistants (HOL, COQ, Lean) or formal proofs. No Category theory is used. The Physics Derivation Graph does not use Natural Language Processing. The Physics Derivation Graph is not intended as a tutorial.
The purpose of these efforts is to contrast with the scope and intention of the Physics Derivation Graph.
Name and Website  Summary  Domain  Relation to PDG  Semantic Enrichment  Open source?  Free?  Active as of 20210725?  Author or group 

Physics Derivation Graph  Goal: Create software that supports writing down all known mathematical physics in a way that can be both read by humans and checked by a computer algebra system.  Mathematical Physics  Yes  Yes  Yes  Yes  ben.is.located AT gmail.com  
NIST Digital Library of Mathematical Functions 
In 1964 the National Institute of Standards and Technology published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. Stegun.DLMF is the culmination of a project that was conceived in 1996 at NIST. 
Math  Yes  No  Yes  Yes  NIST  
Google's Knowledge Graph  Everything  PDG is also a knowledge graph  Yes  No  Yes  Yes  
Sympy  Computer Algebra System (CAS) in Python  Math, Physics  PDG relies on SymPy for validation of steps  No  Yes  Yes  Yes  
Evidence Algorithm  System for Automated Deduction (SAD) = automated processing of formal mathematical texts written in a special language called ForTheL (FORmal THEory Language) or in a traditional firstorder language.  Math  Yes  Yes  Yes  Lyaletski, Verchinine, Paskevich  
OntoMathPro  a Linked Data Hub for mathematics  Math  Yes  Yes; https://github.com/CLLKazan/OntoMathPro  Yes  Yes  Intelligent Search Systems and Semantic Technologies laboratory at Kazan Federal University  
QUDT  Quantities, Units, Dimensions and dataTypes  Ontology for units  Physics  PDG should use QUDT instead of a custom approach.  N/A  Yes  Yes  Yes  
Semantic Web for Earth and Environmental Terminology (SWEET) Ontologies  SWEET is a highly modular ontology suite with ~6000 concepts in ~200 separate ontologies covering Earth system science. SWEET is a midlevel ontology and consists of nine toplevel concepts that can be used as a foundation for domainspecific ontologies that extend these toplevel SWEET components.  Science  No  Yes  Yes  Yes  
zbMath Open  "zbMATH Open (formerly known as Zentralblatt MATH) is the world's most comprehensive and longestrunning abstracting and reviewing service in pure and applied mathematics."  math search  No  Yes  Yes  
SearchOnMath.com  math search  No  Yes  Yes  
Sophize  Knowledge graph for Math. There is no original content  it's all aggregated (and copied to the Sophize database) from sources like planetmath, metamath Wikipedia  Math  No  ?  Yes  Yes  Abhishek Chugh  
Nanopublications  Scientific claims in RDF  Science  No  Yes  Yes  Yes  multiple  
reasoning features for ACE texts and  Attempto Controlled English. RACE documentation AIDA: a scheme for English sentences 
humanoriented controlled natural language  PDG is a machineoriented CNL.  No  Yes  Yes  Yes  Tobias Kuhn 
sTeX: Semantic Markup for LaTeX  sTeX system allows to embed /structural semantics into documents. Concretely sTeX is a “semantic version of LaTeX” that allows to use special macros to encode mathematical meaning explicitly.  Math  Yes  Yes  Yes  Yes  Knowledge Adaptation and Reasoning for Content  
Naproche project (Natural language Proof Checking)  A central goal of Naproche is to develop a controlled natural language (CNL) for mathematical texts and adapted proof checking software which checks texts written in the CNL for syntactical and mathematical correctness.  Math  Yes  Yes  Yes  
SnuggleTeX  Java library for converting fragments of LaTeX to XML (usually XHTML + MathML)  PDG could use MathML but does not currently.  Yes  Yes  
PlanetPhysics  Physics  PDG is a collection of Physics knowledge  Yes  Yes  No  
CmapTools  CMapTools knowledge modeling kit  Yes  Yes  Florida Institute for Human & Machine Cognition (IHMC)  
MathDox formula editor 
a webbased editor for mathematical formulas. Features:

Math  
Mizar 
Goal: "reconstruct mathematical vernacular in a computeroriented environment." Status: "a database which includes more than 9400 definitions of mathematical concepts and more than 49000 theorems." 
Math  Yes  Yes  Yes  
Wolfram Mathematical Functions  "World's largest collection of formulas and graphics about mathematical functions"  Math  Unknown  No  Yes  Yes  Stephen Wolfram  
European Digital Mathematics Library  "EuDML makes the mathematics literature available online in the form of an enduring digital collection, developed and maintained by a network of institutions."  Math  Unknown  Yes  
MioGatto annotation  A webbased annotation tool for Latex documents  Science  Yes  Yes  Yes  Yes  
Incredible Proof Machine 
Similar in intent to the Physics Derivation Graph, though IPM is focused on logic.
I am impressed by the interface for drawing proofs.
The source code is available. 
Logic  No  Yes  Yes  Yes  
Explorable Physics 
The source code The comment thread on Hacker News 
Physics  No  Yes  Yes  Yes  
Math / Physics Problem Solver 
The Math / Physics Problem Solver
"solves simple math and physics problems stated in English."
The source code (Lisp) and equations are available. See "Learning to Automatically Solve Algebra Word Problems" (2014) 
Physics  No  Yes  Yes  Yes  Gordon Novak  
Sciencewise 
a tagging mechanism for words that is integrated with arXiv.
WISE stands for Webbased Interactive Semantic Environment. 
Science  Yes  Yes  
General Problem Solver  a computer program intended to work as a universal problem solver machine.  logic  similar in that starts with sources (axioms) and sinks (desired conclusions). The Physics Derivation Graph does not claim to enable automation of steps.  No  unknown  unknown  as SOAR  
International Mathematical Knowledge Trust 
Goal is to create "a comprehensive mathematical knowledge base."
https://imkt.org/mathportal/mathematicsclassifications 
Math  Unknown  Yes  
MathFoldr 
Authors are category theorists.
Goal is to "use natural language processing on a corpus of texts to assemble an imperfect but large and useful hierarchy of concepts" according to this thread. The "Plan is to start with things that can be done with existing natural language processing software." 
Math  Yes?  
MurrayRust Group at University of Cambridge  Software "for the representation, extraction and processing of scientific data across chemistry, materials science and solidstate physics. We're particularly interested in the following areas: chemical data representation and semantics, scientific publication and scientific literature, polymer informatics and materials informatics and simulation."  Chemistry, Material Science, Physics  Unknown  Yes  Yes  Yes  MurrayRust Group  
Crystallography Open Database  For an example, see https://www.crystallography.net/cod/1000118.html  Unknown  Yes  Yes  Yes  
Numerical Atlas 
A webbased seach interface for variables in arxiv papers.
From the paper Towards Machine LearningBased MetaStudies: Applications to Cosmological Parameters 
Physics  Yes  Yes  
FormulaDatabase 
Input: web GUI for equations. Output: returns a list of equations similar to query. Each returned equation as the symbols defined.
Formula Database is a website described by the authors as a ``math search engine'' which has a builtin equation editor. The search feature is not just matching the \(\rm\LaTeX\) input  it understands dot product and cross product. They have created a browserbased equation editor, similar to the equation editor in Microsoft Word. The search is of a backend database of content. The backend database of equations and symbols was manually entered by the project authors. A team of people have been working since about 2010 on this project. The data is stored as a highdimensional graph. This project is not open source but access is currently free. A commercial launch is planned, though no date has been publicized. The objective is to allow students to search through literature. If you are a researcher, you might want to find whether the model already exists in literature. The grand view is that formuladatabase will serve as a universal reference for equations. Formula Database was founded in 2012 by a group of students and researchers at UWMadison. The idea originated three years prior, when one of our founders, then an undergraduate, was frustrated at the difficulty in finding the correct formula he needed to solve his engineering homework. This challenge has been leveraged into creating an innovative search engine to allow individuals to search for formulas based upon either their contents or mathematical structure. Formula Database lets users input measurable parameters—such as mass, distance, or time—and get equations that provide a relation between these items. Alternatively, using the Equation Editor, users can write a mathematical equation exactly as they would on a whiteboard or paper and discover information about the formula’s use and purpose. Currently we are developing the completed product to allow users to enjoy this functionality. We anticipate launching for a beta test at the end of August 2012. Below are a few screenshots from the Internet Archive. Frontpage of the FormulaDatabase. 
Science  Unknown  No  No  
Wikipedia 
Gather all knowledge in a textbased structure with hyperlinks. In contrast, the Physics Derivation Graph is effectively languageindependent. 
Everything  No  Yes  Yes  Yes  Wikimeda Foundation  
Equation Map 
An interface for putting expressions into a graph format. Inference rules and feeds were
not included, nor is checking of the graph via a computer algebra system.
The website EquationMap (http://equationmap.com; site not currently available) is an interface for derivations, focused primarily on mathematics. There is no backend database of content; instead content is dynamically generated by the user. Equations are manually entered using \LaTeX syntax and the graph of the derivation can be visualized using the same interface. The content is not open source and access is currently free. This is close to what the GUI for the Physics Derivation Graph is intended to behave like, with the exception that EquationMap doesn't include the concept of atomic inference rules. Screenshot of the EquationMap website. The input mechanism is not shown because this screenshot is from the Internet Archive. Screenshot of the option to provide .tex files to EquationMap website, and download .tex files. 
Mathematical Physics  No  No; proprietary  Yes  No  
SymboLab  A web interface for solving symbolic expressions. There is no graph. There is a backend database of content.  Math, Physics  Probably?  No  Yes  No  
HyperPhysics 
A static set of linked concept maps for topics in Physics.
Concept maps are linked to text, graphs, and equations.
Although hyperlinked concept maps are a departure from the standard textbook presentation of physics,
the leaves of this tree are the same content found in textbooks.
HyperPhysics is
similar to Wikipediain that
it is text based for edges. The number of levels can vary. For example, the main page links to mechanics links to Collisions links to Momentum. 
Physics  No  The licensing of the content is described as "not freeware or shareware" by the author, though the site is free to access.  Yes  Yes  Carl R. (Rod) Nave  
Wolfram Mathematica  A computer algebra system, whereas the Physics Derivation Graph is documentation of known mathematical physics relations.  Math, Physics  No  No  No  Yes  Stephen Wolfram  
Wolfram Physics  Uses graphs as a method of developing fundemental Physics concepts.
Completely unrelated to the Physics Derivation Graph. For a useful overview and assessment, listen to Episode 155 of Sean Carrl's Mindscape 
Physics  No  Yes  Stephen Wolfram  
Wolfram Alpha 
All science knowledge with a searchable web interface.
Computational Knowledge and the Future of Pure Mathematics Wolfram Alpha has a backend database of content which is not open source; access is a mix of free and paid. The closest to the Physics Derivation Graph is stepbystep solver 
Science  Probably?  No  mixture; stepbystep is $4.75/month as of 20210808  Yes  Stephen Wolfram  
OpenMath 
OpenMath is an extensible standard for representing the semantics of mathematical objects.https://en.wikipedia.org/wiki/OpenMath https://github.com/OpenMath 
Math  Yes  Yes  Yes  Yes  Knowledge Adaptation and Reasoning for Content  
PhysML 
PhysML is part of the OMdoc effort.
PhysML is for identifying categories of content. PhysML is distinct from http://sciencewise.info/ in that ScienceWise is about linking specific terms to a common database, whereas PhysML is for identifying categories of content. 
Physics  Yes  Knowledge Adaptation and Reasoning for Content  
OMdoc 
https://en.wikipedia.org/wiki/OMDoc "Both MathML and OpenMath address mathematical formulas in isolation, whereas OMDoc allows to express the structure of mathematical documents, for example the relation between definitions, theorems and proofs."(source: "Extracting Mathematical Semantics from LATEX Documents") 
Math  Yes  Knowledge Adaptation and Reasoning for Content  
Gellish.net 
https://en.wikipedia.org/wiki/Gellish See also Ajit Narayanan: A word game to communicate in any language which is about the app FreeSpeech. 
knowledge management  no  unknown  unknown  yes  Andries van Renssen  
MathML 
Presentation MathML (layout only) and Content MathML (semantics) 
Math, Mathematical Physics  Yes  Yes  Yes  Yes  
LaTeXML 
LatexML converts to Presentation MathML, not Content MathML https://dlmf.nist.gov/LaTeXML/
LaTeXML 2012  A Year of LaTeXML
Strategies for Parallel Markup 
Math, Mathematical Physics  Yes  Yes  Bruce Miller  
Formal Mathematical Language  a modeling and documentation language for mathematics.
the FMathL system might turn into a userfriendly automatic mathematical assistant for retrieving, editing, and checking mathematics (but also computer science and theoretical physics) in both informal, partially formalized, and completely formalized mathematical form. 
Math  Unknown  Yes  
Leibniz 
"Digital Scientific Notations as a HumanComputer Interface in ComputerAided Research" https://arxiv.org/abs/1802.09307 "Leibniz is a subset of Maude with different syntax" https://khinsen.net/leibnizexamples/examples/leibnizbyexample.html
"Scientific notations for the digital era" 
Science  Yes?  Yes: CRAPL  Yes  Yes  Konrad Hinsen  
PolyMath 
A "group blog" with the intent of
hosting "polymath" projects – massively collaborative mathematical research projects. Polymath projects are massively collaborative mathematical research programs, in which a single problem, group of problems, or other mathematical task is worked on by a large group of mathematicians. The Physics Derivation Graph is an effort to create the software infrastructure for a "PolyPhysics" 
Math  No  Yes  Yes  Yes  
MetaMath 
Metamath is a tiny language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. The site has a collection of web pages generated from those proofs and lets you see mathematics developed in complete detail from first principles, with absolute rigor. 
Math  Yes?  Yes  Yes  Yes  
directed graphs in linguistics  Examples include visuwords.com and synonym  Linguistics  varies  varies  varies  varies  
MathLingua 
MathLingua is a language for easily creating a collection of mathematical knowledge, including definitions, theorems, axioms, and conjectures. ... The goal is to allow one to express mathematical concepts in a higher level language that focuses on what a statement means instead of how it is represented in a logical framework. 
Math  Yes?  Yes: Apache 2.0  Yes  Yes  
Atlas IDE  IDE for math. Includes visualization. Automatic linking of variables. Variables have definitions.  Mathematical Physics  Yes  No  No  Yes  
calcula.tech IDE  Create Latex equations in a web browser and solve numerical equations.
source code 
Yes  Yes  Yes  
blockpad.net  mashup of MathCAD and Excel in a web browser  Math  No  No  Yes  
engineerjs.com  https://news.ycombinator.com/item?id=12825798  Yes  Yes 