MathML generation algorithm for Javascript. Any recommended references

I am trying to build code that can generate MathML for Traditional Math Input. I am using JavaScript for coding. Are there any references or recommended readings I can go through to get a grasp of required algorithm? I am reading W3C standards for MathML which is a reference for standards but not for algorithm.

For Instance, for a sample input of

sqrt 9 * 5 + 20

I want to generate the MathML expression like below

<math xmlns='w3.org/1998/Math/MathML'>; <mrow> <mrow> <mn>5</mn> <mo>&#8290;</mo> <mn>9</mn> <mo>&#8290;</mo> <mi>SQRT</mi> </mrow> <mo>+</mo> <mn>20</mn> </mrow> </math>

Solution

I found a nice tutorial on MathML here: http://rypress.com/tutorials/mathml/basic-algebra.html and started to work out a very basic algebraic parser (for example, 4*sqrt(x+6)=(5-z)*y/7) with a crude stack for handling parentheses and an example sqrt function. Is this the direction you are after?

jsfiddle here: http://jsfiddle.net/alhambra1/bSJyE/

JavaScript code:

<script>
document.write('<p><input id="input" size=50>')
document.write('<button onclick="convertToMathML()">Convert</button></p>')
document.write('<div id="output"></div>')

function lex(str,ptr){
    var ascii = str.charCodeAt(ptr),
        lexeme = {string: "", type: ""},
        operators = {"+": "+"
                    , "-": "-"
                    , "*": "&times;"
                    , "/": "&divide;"
                    , "=": "="},
        functions = {sqrt: "msqrt"}

    //identify type
    if (ascii == 41)
        lexeme.type = "closeBracket"
    else if (ascii == 40){
        lexeme.type = "func"
        lexeme.func = "mfenced"
    }
    else if (ascii > 45 && ascii < 58 && ascii != 47)
        lexeme.type = "mn"
    else if ((ascii > 64 && ascii < 91) || (ascii > 96 && ascii < 123)){
        for (i in functions){
            if (str.substr(ptr,i.length).toLowerCase() == i){
                lexeme.type = "func"
                lexeme.func = functions[i]
                ptr += i.length - 1
            } else
                lexeme.type = "mi"
        }
    } else if (!operators[str.charAt(ptr)])
        return {string: str.charAt(ptr), type: "error", pointer: ptr}
    else
        lexeme.type = "mo"

    switch (lexeme.type){
        case "mo":
            lexeme.string = operators[str.charAt(ptr++)]
            break
        default:
            lexeme.string = str.charAt(ptr++)
            break
    }

    ascii = str.charCodeAt(ptr)

    //identify numbers and functions 
    if (lexeme.type == "mn"){
        while (ptr < str.length && ascii > 45 && ascii < 58 && ascii != 47){
            lexeme.string += str.charAt(ptr)
            ascii = str.charCodeAt(++ptr)
        }
    } else if (lexeme.type == "func" && lexeme.func != "mfenced"){
        while (ptr < str.length && str.substr(ptr).match(/^\s/)){
            ascii = str.charCodeAt(++ptr)
        }
        if (str.charAt(ptr) != "(")
            return {string: str.charAt(ptr), type: "error", pointer: ptr}
        else
            ptr++
    }

    lexeme["pointer"] = ptr

    return lexeme
}

function markup(lexeme){
    return "<" + lexeme.type + ">\n"
           + lexeme.string + "\n"
           + "</" + lexeme.type + ">\n"
}

function convertToMathML(){
    var str = document.getElementById('input').value,
        expression = "",
        ptr = 0,
        stack = []

    while (ptr < str.length){
        var currLexeme = lex(str,ptr)

        if (currLexeme.type == "closeBracket"){
            if (stack.length == 0)
                expression = "Extra bracket at: " + (currLexeme.pointer - 1)
            else
                expression += "</" + stack.pop().func + ">\n"
                            + "</mrow>"          
            ptr = currLexeme.pointer
        } else if (currLexeme.type == "error"){
            expression = "Cannot parse \"" + currLexeme.string
                       + "\" at " + currLexeme.pointer
            break
        } else if (currLexeme.type == "func"){
            expression += "<" + currLexeme.func + ">\n"
                        + "<mrow>\n"
            stack.push(currLexeme)
            ptr = currLexeme.pointer
        } else {
            expression += markup (currLexeme)
            ptr = currLexeme.pointer
        }
    }

    if (ptr >= str.length && stack.length > 0)
        expression = "Missing " +  stack.length + " closing bracket/s."

    expression = "<math xmlns='http://www.w3.org/1998/Math/MathML'>"
               + expression + "</math>"

    document.getElementById('output').innerHTML = expression
}
</script>