#!/usr/bin/env lua

function splitTokens(s)
    local tokens = {}
    for i in string.gmatch(s, '%w+') do 
        table.insert(tokens, i) 
    end
    return tokens
end

PLUS = 'a'
MINUS = 's'
TIMES = 'm'
DIVIDE = 'd'

function isDash(token)
    return token == PLUS or token == MINUS
end

function isDot(token)
    return token == TIMES or token == DIVIDE
end

function parseNum(tokens)
    local val = table.remove(tokens, 1)
    val = tonumber(val)
    return {
        ['type'] = 'num',
        ['num'] = val
    }
end

function parseFactor(tokens)
    local lhs = parseNum(tokens)
    while isDot(tokens[1]) do
        local op = table.remove(tokens, 1)
        local rhs = parseNum(tokens)
        lhs = {
            ['type'] = 'op',
            ['op'] = op,
            ['lhs'] = lhs,
            ['rhs'] = rhs
        }
    end
    return lhs
end

function parseTerm(tokens)
    local lhs = parseFactor(tokens)
    while isDash(tokens[1]) do
        local op = table.remove(tokens, 1)
        local rhs = parseFactor(tokens)
        lhs = {
            ['type'] = 'op',
            ['op'] = op,
            ['lhs'] = lhs,
            ['rhs'] = rhs,
        }
    end
    return lhs
end

function parseExpr(tokens)
    return parseTerm(tokens)
end

function eval(expr)
    if expr['type'] == 'num' then
        return expr['num']
    elseif expr['type'] == 'op' then
        local lval = eval(expr['lhs'])
        local rval = eval(expr['rhs'])
        if expr['op'] == PLUS then
            return lval + rval
        elseif expr['op'] == MINUS then
            return lval - rval
        elseif expr['op'] == TIMES then
            return lval * rval
        elseif expr['op'] == DIVIDE then
            return lval / rval
        else
            print('invalid operator!')
        end
    else
        print('invalid expr type!')
    end
end

function printTree(expr, depth)
    local indent = string.rep('  ', depth)
    print(indent .. 'type: ' .. expr['type'])
    if expr['type'] == 'num' then
        print(indent .. 'num: ' .. expr['num'])
    elseif expr['type'] == 'op' then
        print(indent .. 'op: ' .. expr['op'])
        print(indent .. 'lhs:')
        printTree(expr['lhs'], depth + 1)
        print(indent .. 'rhs:')
        printTree(expr['rhs'], depth + 1)
    else
        print('invalid expr type!')
    end
end

tree = parseExpr(splitTokens(arg[1]))
print('tree:')
printTree(tree, 0)
print('result: ' .. eval(tree))