local M = {}

local GREEK = {
  alpha=true, beta=true, gamma=true, delta=true, epsilon=true, zeta=true,
  eta=true, theta=true, iota=true, kappa=true, lambda=true, mu=true, nu=true,
  xi=true, pi=true, rho=true, sigma=true, tau=true, phi=true, chi=true,
  psi=true, omega=true, Gamma=true, Delta=true, Theta=true, Lambda=true,
  Xi=true, Pi=true, Sigma=true, Phi=true, Psi=true, Omega=true,
}
local BIGOP = { sum="\\sum", prod="\\prod", int="\\int" }
local UNDEROP = { lim="\\lim" }

function M.mathlite(s)
  local n = #s
  local pos = 1

  local function skipws() while pos <= n and s:sub(pos,pos):match("%s") do pos = pos + 1 end end

  local read_atom
  read_atom = function()
    skipws()
    if pos > n then return "" end
    local c = s:sub(pos, pos)

    if c == "(" then
      local depth, j = 0, pos
      while j <= n do
        local d = s:sub(j,j)
        if d == "(" then depth = depth + 1
        elseif d == ")" then depth = depth - 1; if depth == 0 then break end end
        j = j + 1
      end
      local inner = s:sub(pos + 1, j - 1)
      pos = j + 1
      return "(" .. M.mathlite(inner) .. ")"
    end

    if c == "\\" then
      local j = pos + 1
      if s:sub(j,j):match("%a") then
        while j <= n and s:sub(j,j):match("%a") do j = j + 1 end
      else
        j = pos + 2
      end
      local cmd = s:sub(pos, j - 1)
      pos = j
      return cmd
    end

    if c:match("%a") then
      local word = s:sub(pos):match("^(%a+)")
      local after = pos + #word
      if word == "sqrt" and s:sub(after, after) == "(" then
        pos = after
        local arg = read_atom()
        arg = arg:gsub("^%((.*)%)$", "%1")
        return "\\sqrt{" .. arg .. "}"
      elseif word == "abs" and s:sub(after, after) == "(" then
        pos = after
        local arg = read_atom():gsub("^%((.*)%)$", "%1")
        return "\\left|" .. arg .. "\\right|"
      elseif word == "norm" and s:sub(after, after) == "(" then
        pos = after
        local arg = read_atom():gsub("^%((.*)%)$", "%1")
        return "\\left\\|" .. arg .. "\\right\\|"
      elseif word == "vec" and s:sub(after, after) == "(" then
        pos = after
        local arg = read_atom():gsub("^%((.*)%)$", "%1")
        return "\\overrightarrow{" .. arg .. "}"
      elseif UNDEROP[word] and s:sub(after, after) == "(" then
        pos = after
        local grp = read_atom():gsub("^%((.*)%)$", "%1")
        grp = grp:gsub("%->", "\\to ")
        return UNDEROP[word] .. "_{" .. grp:gsub("^%s+",""):gsub("%s+$","") .. "}"
      elseif BIGOP[word] and s:sub(after, after) == "(" then
        pos = after
        local grp = read_atom()
        grp = grp:gsub("^%((.*)%)$", "%1")
        local lo, hi = grp:match("^(.-),(.*)$")
        if lo then
          return BIGOP[word] .. "_{" .. lo:gsub("^%s+",""):gsub("%s+$","")
              .. "}^{" .. hi:gsub("^%s+",""):gsub("%s+$","") .. "}"
        else
          return BIGOP[word] .. "_{" .. grp .. "}"
        end
      elseif word == "inf" then
        pos = after; return "\\infty "
      elseif GREEK[word] then
        pos = after; return "\\" .. word .. " "
      else
        pos = after; return word
      end
    end

    if c:match("%d") then
      local num = s:sub(pos):match("^([%d.]+)")
      pos = pos + #num
      if M.decsep and M.decsep ~= "." then
        num = num:gsub("%.", M.decsep)
      end
      return num
    end

    pos = pos + 1
    return c
  end

  local out = {}
  while pos <= n do
    skipws()
    if pos > n then break end
    local c = s:sub(pos, pos)

    if c == "*" then out[#out+1] = " \\times "; pos = pos + 1
    elseif c == "+" and s:sub(pos+1,pos+1) == "-" then out[#out+1] = " \\pm "; pos = pos + 2
    elseif c == "<" and s:sub(pos+1,pos+1) == "=" then out[#out+1] = " \\leq "; pos = pos + 2
    elseif c == ">" and s:sub(pos+1,pos+1) == "=" then out[#out+1] = " \\geq "; pos = pos + 2
    elseif c == "!" and s:sub(pos+1,pos+1) == "=" then out[#out+1] = " \\neq "; pos = pos + 2
    elseif c == "/" then
      -- Left-associative chained division: a/b/c reads as (a/b)/c.
      local num = table.remove(out) or ""
      num = num:gsub("^%((.*)%)$", "%1")
      pos = pos + 1
      local den = read_atom()
      den = den:gsub("^%((.*)%)$", "%1")
      local frac = "\\frac{" .. num .. "}{" .. den .. "}"
      skipws()
      while s:sub(pos, pos) == "/" do
        pos = pos + 1
        local nxt = read_atom():gsub("^%((.*)%)$", "%1")
        frac = "\\frac{" .. frac .. "}{" .. nxt .. "}"
        skipws()
      end
      out[#out+1] = frac
    elseif c == "^" or c == "_" then
      pos = pos + 1
      skipws()
      if s:sub(pos, pos) == "{" then
        local depth, j = 0, pos
        while j <= n do
          local d = s:sub(j,j)
          if d == "{" then depth = depth + 1
          elseif d == "}" then depth = depth - 1; if depth == 0 then break end end
          j = j + 1
        end
        out[#out+1] = c .. s:sub(pos, j)
        pos = j + 1
      else
        local sign = ""
        local sc = s:sub(pos, pos)
        if sc == "-" or sc == "+" then sign = sc; pos = pos + 1 end
        local term = read_atom()
        term = term:gsub("^%((.*)%)$", "%1")
        out[#out+1] = c .. "{" .. sign .. term .. "}"
      end
    elseif c == "+" or c == "-" or c == "=" or c == "<" or c == ">"
        or c == "," or c == ")" then
      out[#out+1] = c; pos = pos + 1
    else
      out[#out+1] = read_atom()
    end
  end
  return table.concat(out)
end

return M