Mathematical Expression Parser

The Mathematical Expression Parser is a simple parser to convert Mathematical Expressions written as a string, to Symbolic Expression trees, as shown in the following picture:

How to use:

Parser.parseExpression function

The entry point of the the Mathematical Expression Parser is the parseExpression function defined in the Parser module. This function takes a string, and will return either Success of ExpressionTree or Failure of String where the string contains the error message.

ExpressionTrees

The expression tree is defined as follows:

The base object is the ExpressionType. Which describes a complete (sub-)tree. An ExpressionType is either a ComposedExpression of type ComposedExpressionType or an AtomicExpression of the type AtomicExpressionType, which cannot be subdivided further. A ComposedExpressionType is a record consisting of an operator, and two other ExpressionTypes. An AtomicExpressionType is either a Parameter or a Constant.

Defined syntax

The supported syntax is defined as follows:

• Parameter: any term starting with a capitalised letter or an underscore, containing letters, numbers, and/or underscores.
• Constant: Any floating point value, e.g. 1, 1.0, 1E-3. This includes negative values.
• Infix functions: Infix functions are defined as <operand1> <infix-function> <operand2>. The following infix functions are currently defined:
  • Multiplication: *
  • Division: /
  • Addition: +
  • Subtraction: -
• Binary functions: Binary functions are defined as terms starting with a lowercase letter, containing letters, numbers, and/or underscores, followed by a set of parentheses (without white space). The set of accepted binary functions is currently limited to the following:
  • Minimum: min
  • Maximum: max

If no precedence is defined through parentheses, then standard precedence of mathematical operators assumed, i.e. division and multiplication take precedence over subtraction and addition.

Whitespace inbetween terms, as well as at the beginning and end will be ignored, this includes new lines.

How to add to an existing solution

There are two ways to incorporate the Mathematical Expression Parser into a project. The recommended approach is to generate a NuGet package of the MathematicalExpressionParser.Core as described in the How to build section. This package can then be added to your existing project.

Alternatively, the packages can be added directly to a .net solution. This does require the F# tooling within Visual Studio. The projects can then be referenced directly from within the solution.

How to build:

The repository can be obtained by running

git clone https://github.com/Deltares/mathematical_expression_parser.git

Once downloaded, the .sln file can be opened with Visual Studio. This should allow you to build the project, and run the tests. Keep in mind that this requires the F# build tools, which can be obtained through the Visual Studio installer.

In order to build the NuGet package, first build the solution in Release. Then navigate to the MathematicalExpressionParser.Core folder and run the following command:

nuget pack -properties Configuration=Release

This will create the MathematicalExpressionParser.core NuGet Package of the current version.

Technologies

The Mathematical Expression Parser has been build with the following technologies:

• Visual Studio 2019: Used to build the project. This requires the F# build tools.
• FParsec: Parser combinator library used to transform the mathematical expression into symbolic expression trees.
• FParsec-Pipes: Additional extensions for FParsec
• FsUnit: Used to write the test suite.