FindIcon(icon, size) {
  theme = user selected theme
  do {
    filename = LookupIcon (icon, size, theme)
    if filename != none
      return filename
    theme = theme.parentTheme()
  } while (theme)
  return LookupFallbackIcon (iconname)
}
     

With the following helper functions:

LookupIcon (iconname, size, theme) {
  for each subdir in $(theme subdir list) {
    for each directory in $(basename list) {
      for extension in ("png", "svg", "xpm") {
        if DirectoryMatchesSize(subdir, size) {
          filename = directory/$(themename)/subdir/iconname.extension
          if exist filename
	    return filename
        }
      }
    }
  }
  minimal_size = MAXINT
  for each subdir in $(theme subdir list) {
    for each directory in $(basename list) {
      for extension in ("png", "svg", "xpm") {
        filename = directory/$(themename)/subdir/iconname.extension
        if exist filename and DirectorySizeDistance(subdir, size) < minimal_size {
	   closest_filename = filename
	   minimal_size = DirectorySizeDistance(subdir, size)
        }
      }
    }
  }
  if closest_filename set
     return closest_filename
  return none
}

LookupFallbackIcon (iconname) {
  for each directory in $(basename list) {
    for extension in ("png", "svg", "xpm") {
      if exists directory/iconname.extension
        return directory/iconname.extension
    }
  }
  return none
}

DirectoryMatchesSize(subdir, iconsize) {
  read Type and size data from subdir
  if Type is Fixed
    return Size == iconsize
  if Type is Scaled
    return MinSize <= iconsize <= MaxSize
  if Type is Threshold
    return Size - Threshold <= iconsize <= Size + Threshold
}

DirectorySizeDistance(subdir, size) {
  read Type and size data from subdir
  if Type is Fixed
    return abs(Size - iconsize)
  if Type is Scaled
    if iconsize < MinSize
        return MinSize - iconsize
    if iconsize > MaxSize
        return iconsize - MaxSize
    return 0
  if Type is Threshold
    if iconsize < Size - Threshold
        return MinSize - iconsize
    if iconsize > Size + Threshold
        return iconsize - MaxSize
    return 0
}