Rhema¶

Rhema is a language for writing mathematics questions. A file describes a kind of question as a grammar: what shapes it may take, how hard it is, what its answer is and how it reads. The rhema compiler checks the file and writes the questions out for WeBWorK.

# The smallest useful question: the sum of two numbers.

synth value on E
synth latex on E

start E

E -> integer_between(10, 99) "+" integer_between(10, 99) {
  value = $1.value + $3.value
  latex = str($1.value) ++ " + " ++ str($3.value)
}

prompt "What is [`{E.latex}`]?"
answer E.value

$ rhema run first.rhm --count 2
 1. What is [`82 + 40`]?
    answer: 122
 2. What is [`83 + 52`]?
    answer: 135

The question and its answer come from the same tree, so they cannot disagree. Difficulty is a budget the grammar spends exactly, chosen when the questions are generated. Grammars import one another, and a file can describe a whole assignment, which compiles to the same paper every time.

Install¶

opam install rhema

This installs the rhema command and a library of grammars for arithmetic, algebra, calculus, limits, series, propositional logic, sets and inequalities, vectors, complex numbers, sequences, linear algebra and eigenvalues, counting and probability, and number theory. Until the package reaches the opam repository:

opam pin add rhema https://github.com/Project-RHM/Project-RHM.git#v0.1.1 --subpath generator

For VS Code, the repository's editors/vscode directory holds an extension for .rhm files: highlighting, problems from rhema check as you type, and commands to run and compile; its README says how to install it.

Where to go next¶

The tutorial

Eight short chapters, from the file above to a complete assignment in WeBWorK. Every example on the site is checked by the compiler on each change to the repository.

The rhema command

Compiling, checking, running and listing files, and how imported files are found.

The name¶

RHM, the project Rhema belongs to, stands for Reversible Hierarchical Mathesis, with the motto Regula · Hierarchia · Mathesis.

Reversible

A parser reads text into a tree. RHM runs that direction backwards: it builds the tree first and writes the question from it, so the question and its answer are two readings of one object. The first version did this literally, running the Menhir parser's grammar in reverse; the letters R-H-M are Menhir read backwards without its vowels.

Hierarchical

Questions are trees of productions. Difficulty is a budget passed down the tree, results are computed back up it, and grammars compose into assignments by import.

Mathesis

After Leibniz's mathesis universalis, a universal method of reasoning by calculation: here, a method of producing mathematics questions by rule.

Rhema (Greek ῥῆμα, that which is said, an utterance) is the name of the language. Its letters sit inside RHM, and it names what a grammar does: it says a question.

Authors¶

Jingming Zhang, Jiaming Lei, Xiaobo Huang, Jiesen Long and Zhiyuan Li, at Beijing Normal-Hong Kong Baptist University; see Authors. Rhema is free software under the MIT licence; the source is on GitHub.