ram6ler / function-tree

A simple dart library for parsing strings into callable function-trees.

Welcome to function_tree, a simple library for parsing strings into callable function-trees.

Parsing strings as mathematical expressions

At the simplest (and least efficient) level, we can interpret strings as mathematical expressions.

Example:

  final expressions = [
    '2 + 2',
    '(3 + 2)^3',
    '3 * pi / 4',
    '3 * sin(5 * pi / 6)',
    'e^(-1)'
  ];
  for (final expression in expressions) {
    print("'$expression' -> ${expression.interpret()}");
  }

Output:

'2 + 2' -> 4.0
'(3 + 2)^3' -> 125.0
'3 * pi / 4' -> 2.356194490192345
'3 * sin(5 * pi / 6)' -> 1.5000000000000009
'e^(-1)' -> 0.36787944117144233

Function Trees

The library supports two types of callable, function-trees, namely SingleVariableFunction and MultiVariableFunction.

Single variable functions

We can create a single variable function from a string either by constructing a SingleVariableFunction instance or by calling the toSingleVariableFunction string extension directly on a string, as in the following example:

Example:

  final f = '20 * (sin(x) + 1)'.toSingleVariableFunction(),
      pi = 'pi'.interpret();
  for (var x = 0.0; x < 2 * pi; x += pi / 20) {
    print('|' + ' ' * f(x).round() + '*');
  }

Output:

|                    *
|                       *
|                          *
|                             *
|                                *
|                                  *
|                                    *
|                                      *
|                                       *
|                                        *
|                                        *
|                                        *
|                                       *
|                                      *
|                                    *
|                                  *
|                                *
|                             *
|                          *
|                       *
|                    *
|                 *
|              *
|           *
|        *
|      *
|    *
|  *
| *
|*
|*
|*
| *
|  *
|    *
|      *
|        *
|           *
|              *
|                 *

Multi-variable functions

Similarly, we can construct a MultiVariableFunction instance or call the toMultiVariableFunction string extension to create a multi-variable functional tree, as in the following example.

Example:

  final times = 'a * b'.toMultiVariableFunction(['a', 'b']),
      values = [1, 2, 3, 4, 5];
  for (final a in values) {
    final sb = StringBuffer();
    for (final b in values) {
      sb..write(times({'a': a, 'b': b}).floor())..write('\t');
    }
    print(sb);
  }

Output:

1	2	3	4	5	
2	4	6	8	10	
3	6	9	12	15	
4	8	12	16	20	
5	10	15	20	25	

TeX expressions

Function tree instances have a tex property for TeX expressions.

Example:

  final f = 'x * cos(y) + y * sin(x)'.toMultiVariableFunction(['x', 'y']);
  print(f.tex);

Output:

x \cdot \cos\left( y \right) + y \cdot \sin\left( x \right)

Interpreter

The interpreter has support for the following:

Functions

One-parameter functions

abs     acos    asin    atan    ceil
cos     cosh    cot     coth    csc
csch    exp     floor   ln      log
round   sec     sech    sin     sinh
sqrt    tan     tanh

Two-parameter functions

log     nrt     pow

Constants

e       pi      ln2     ln10    log2e
log10e  sqrt1_2 sqrt2

Operations

+   -   *   /   %   ^

Thanks!

Thanks for your interest in this library. Please file any bugs or requests here.