Mathematica Parser

A library for parsing Mathematica's programming language written in Scala. It uses parser combinators and packrat parsers from Scala's standard library. Currently only a subset of Mathematica's language is supported.

Supported features

• function applications: f[x], PrimeQ[a]
• arithmetics: a + b, a b, a*b, a/b, a^b
• patterns: _, x_, x_Integer
• assignment operators: f[n_] := 1, x += 127
• conditions: f[n_ /; n > 0] := 1, n ? PrimeQ
• rules: Factor[x^2 + 1, Modulus->2]
• compound expressions: x = 0; x += 1
• factorials: x!, x!!
• indexing and slices: a[[0;;3]] = 1
• logical and comparison operators: x == 0 || a < b <= c

Operator grouping is preserved so a + b + c parses as Plus[a, b, c], not Plus[Plus[a, b], c], and a^b^c parses as Power[a, Power[b, c]]. No flattening is performed, nor other transformations applied by default that could change structure of abstract syntax trees.

See src/test/scala/MathematicaParser.scala for examples.

Usage

Run ./sbt. This can take awhile on the first run, because it has to download runner's and project's dependencies (e.g. Scala compiler). Then you can use the following commands:

• compile : compile the project
• test : run tests
• console : run Scala REPL (imports are done automatically)
• run -e "2 + 2" : parse and output full form of the input expression (see run --help)

Note that compile is automatically invoked by test and others if needed.

Example

~/mathematica-parser$ ./sbt
[info] Loading project definition from ~/mathematica-parser/project
[info] Set current project to mathematica_parser (in build file:~/mathematica-parser/)
refptr (mathematica_parser)> console
[info] Compiling 1 Scala source to ~/mathematica-parser/target/scala-2.10/classes...
[info] Starting scala interpreter...
[info]
import org.refptr.parsing.mathematica._
Welcome to Scala version 2.10.0-M4 (OpenJDK 64-Bit Server VM, Java 1.6.0_23).
Type in expressions to have them evaluated.
Type :help for more information.

scala> MathematicaParser.parse("1 + 2*3")
res0: org.refptr.parsing.mathematica.ParseOutput = ParseResult(Plus(Num(1), Times(Num(2), Num(3))))

scala> res0.toPrettyForm
res1: String = Plus[1, Times[2, 3]]

License

Copyright © 2012-2014 by Mateusz Paprocki and contributors.

Published under The MIT License, see LICENSE.