## macfja/lexer-expression

Library to transform a Doctrine lexer into a RPN expression and solve it

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Requires

- doctrine/lexer: ~1.0

This package is auto-updated.

Last update: 2020-10-16 17:02:16 UTC

# README

- Description
- What is Shunting Yard algorithm
- The Shunting Yard implementation
- The RPN expression Solver
- The AST Tree builder
- Install
- Usage
- Similar projects
- Documentations

## Description

The main goal of this library is to transform an expression into a computer understandable expression, by using

- Doctrine Lexer
- The Shunting Yard algorithm

As the input of the Shunting Yard is a Doctrine Lexer, the library is not limited to mathematics expression.

The library provide an "evaluator" of the Shunting Yard algorithm output, or transform it into a AST Tree

## What is Shunting Yard algorithm

The best explanation can by found on Wikipedia, or on this article of @igorw.

But to make simple, the main idea is to transform a list of chars into multiple of small group.

Simple example: `(1 + 2) * 3`

is really simple for us (human) to process, but a computer can do it, it need to split it into small chunk. And evaluate it piece by piece.
For a computer, the expression need to be evaluate like this:

```
*
/ \
+ 3
/ \
1 2
```

This a binary tree, and yes it's also a kind of AST.
So to solve the expression a computer first evaluate the group (we will name the result as **(a)**):

```
+
/ \
1 2
```

And then it evaluate the group:

```
*
/ \
(a) 3
```

The Shunting Yard algorithm transform your expression into an intermediate expression: a RPN expression.
The RPN expression of `(1 + 2) * 3`

is `1 2 + 3 *`

.

This expression can be read as:

- Parameter
`1`

- Parameter
`2`

- Operator
`+`

(that take 2 parameters: the two previous parameters) - Parameter
`3`

- Operator
`*`

(that take 2 parameters: the result of the operation and the previous parameter)

## The Shunting Yard implementation

Like most of Shunting Yard implementation, it can parse "simple" expression (with simple operator) and make parenthesis reduction.
It can parse unary, and binary functions (like `sin(x)`

, `max(x,y)`

) but also any functions (ex: `fct(a,b,c,x,y,z)`

).

But the main "feature" it's the use of Doctrine Lexer.

## The RPN expression Solver

The RPN solver allow you to solve a RPN expression (a list of Doctrine Lexer token). It support Operator/Function with any arity.

## The AST Tree builder

The AST Tree builder can transform the RPN expression (a list of Doctrine Lexer token) into an AST Tree.

The tree root is a node, the last(final) node (in the **What is Shunting Yard algorithm**, it's the `*`

operator).
This root node is composed of values (leafs of a tree) and nodes (branches).

### Limitation

The Solver can not solver function with variable arity (or optional parameters)

## Install

To install with composer:

```
composer require macfja/lexer-expression
```

## Usage

### Very simple Doctrine DQL

use \Doctrine\ORM\Query\Lexer; $dql = 'SELECT u FROM User u WHERE u.id = MAX(5, 7)'; $lexer = new Lexer($dql); $sy = new ShuntingYard(); $sy->setLexer($lexer); $sy->setOpenParenthesis(Lexer::T_OPEN_PARENTHESIS); $sy->setCloseParenthesis(Lexer::T_CLOSE_PARENTHESIS); $sy->setOperators(array( new ShuntingYardOperator(Lexer::T_MAX, 10, ShuntingYardOperator::ASSOCIATIVITY_LEFT), new ShuntingYardOperator(Lexer::T_SELECT, 10, ShuntingYardOperator::ASSOCIATIVITY_LEFT), new ShuntingYardOperator(Lexer::T_FROM, 10, ShuntingYardOperator::ASSOCIATIVITY_LEFT), new ShuntingYardOperator(Lexer::T_WHERE, 2, ShuntingYardOperator::ASSOCIATIVITY_LEFT), new ShuntingYardOperator(Lexer::T_DOT, 10, ShuntingYardOperator::ASSOCIATIVITY_LEFT), new ShuntingYardOperator(Lexer::T_EQUALS, 10, ShuntingYardOperator::ASSOCIATIVITY_LEFT) )); $sy->setArgumentSeparator(Lexer::T_COMMA); var_dump($sy->parse());

### Very simple Mathematics expression

3 examples are available in the `test`

directory. The expression is `(1 + 2) / ((3 + 4 * 5) - 6)`

.

`test/MathRPN.php`

: Just an expression to RPN example`test/MathSolve.php`

: An example with the solver`test/MathAST.php`

: An example with the tree builder

The tree of the expression is:

```
"/"
/ \
/ \
/ "-"
/ / \
/ "+" 6
/ / \
"+" 3 "*"
/ \ / \
1 2 4 5
```

## Similar projects

- droptable/php-shunting-yard
- ircmaxell/php-math-parser
- ngorchilov/psy
- rbnvrw/PHPShuntingMathParser
- Isinlor/php-shunting-yard
- igorw/rpn
- mephir/rpn
- rn0/php-calc
- pear/Math_RPN