llang

It's a pleasure to introduce you llang - an interpreter of well-formed formulas in propositional calculus written in JavaScript (both browser and node.js). Use is simple, just pass a formula and input evaluation for variables in formula and see the result. And there will be more! I am going to make some extension functions such as truth table generator, function to decide whether formula is either tautology, contradiction or satisfiable or one formula is semantic consequence/equivalence of another or not.

Example

llang.evaluate('A | B', [1, 0]); //returns true
llang.evaluate('A & B', [0, 1]); //returns false
llang.evaluate('(A -> (B -> C)) -> ((A -> B) -> (A -> C))', [0, 0, 0]); //returns true

Installation

Node

$ npm install llang

Browser

<script type="text/javascript" src="path/to/llang.js"></script>

Operators

Negation

Unary operator which returns true if the following variables is false and vice versa.

Symbol: !

| A | R | |-------|-------| | 0 | 1 | | 1 | 0 |

Disjunction

Binary operator which returns false if both operands are false, otherwise returns true.

Symbol: |

Truth table:

| A | B | R | |-------|-------|-------| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 |

Conjunction

Binary operator which returns true if both operands are true, otherwise returns false.

Symbol: &

Truth table:

| A | B | R | |-------|-------|-------| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |

Implication

Binary operator which returns false if the first operand are true and the second is false, otherwise returns true.

Symbol: ->

Truth table:

| A | B | R | |-------|-------|-------| | 0 | 0 | 1 | | 0 | 1 | 1 | | 1 | 0 | 0 | | 1 | 1 | 1 |

Equivalence

Binary operator which returns true if both operands have the same value, otherwise returns false.

Symbol: <->

Truth table:

| A | B | R | |-------|-------|-------| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |

Variables

Variables are representations of values which will be replaced by actual values passed in evaluation argument. Valid values are letters from A to Z. Evaluation will be used on variables in alphabetical order. It doesn't matter if you use upper case or lower case letters.

Parentheses

Parentheses set priority of evaluation. They delimit the subexpression which will be evaluated with higher priority.

See it in action!

You want to try it but you are lazy to write a small script which uses this library? No problem! There are two files in evaluations folder. The first is a small node script which runs in console. Just run node <path/to/script>/node.js and type your formulas. The second file is an HTML page which asks you using JavaScript prompts. Just open it in your browser.

Weaknesses

There is poor syntax error detection yet. It will be improved but for this moment, write your formulas correctly.

License

llang is MIT licensed. Feel free to use it, contribute or spread the word. Created with love by Petr Nevyhoštěný (Twitter).