A Path is a list of Path elements which represents a path to a file, directory of symbolic link
Path elements are non-empty strings. The exact set of valid strings MAY be specific to a particular FileSystem implementation.
Path elements MUST NOT be in {"", ".", "..", "/"}.
Path elements MUST NOT contain the characters {'/', ':'}.
Filesystems MAY have other strings that are not permitted in a path element.
When validating path elements, the exception InvalidPathException SHOULD be raised when a path is invalid [HDFS]
Predicate: valid-path-element:List[String];
A path element pe is invalid if any character in it is in the set of forbidden characters, or the element as a whole is invalid
forall e in pe: not (e in {'/', ':'})
not pe in {"", ".", "..", "/"}
Predicate: valid-path:List<PathElement>
A Path p is valid if all path elements in it are valid
def valid-path(pe): forall pe in Path: valid-path-element(pe)
The set of all possible paths is Paths; this is the infinite set of all lists of valid path elements.
The path represented by empty list, [] is the root path, and is denoted by the string "/".
The partial function parent(path:Path):Path provides the parent path can be defined using list slicing.
def parent(pe) : pe[0:-1]
Preconditions:
path != []
The last Path Element in a Path is called the filename.
def filename(p) : p[-1]
Preconditions:
p != []
The partial function childElements:(Path p, Path q):Path is the list of path elements in p that follow the path q.
def childElements(p, q): p[len(q):]
Preconditions:
# The path 'q' must be at the head of the path 'p' q == p[:len(q)]
The list of all paths that are either the direct parent of a path p, or a parent of ancestor of p.
This definition handles absolute paths but not relative ones; it needs to be reworked so the root element is explicit, presumably by declaring that the root (and only the root) path element may be [‘/’].
Relative paths can then be distinguished from absolute paths as the input to any function and resolved when the second entry in a two-argument function such as rename.
A filesystem FS contains a set of directories, a dictionary of paths and a dictionary of symbolic links
(Directories:set[Path], Files:[Path:List[byte]], Symlinks:set[Path])
Accessor functions return the specific element of a filesystem
def FS.Directories = FS.Directories def file(FS) = FS.Files def symlinks(FS) = FS.Symlinks def filenames(FS) = keys(FS.Files)
The entire set of a paths finite subset of all possible Paths, and functions to resolve a path to data, a directory predicate or a symbolic link:
def paths(FS) = FS.Directories + filenames(FS) + FS.Symlinks)
A path is deemed to exist if it is in this aggregate set:
def exists(FS, p) = p in paths(FS)
The root path, “/”, is a directory represented by the path [“/”], which must always exist in a filesystem.
def isRoot(p) = p == ["/"]. forall FS in FileSystems : ["/"] in FS.Directories
A path MAY refer to a directory in a FileSystem:
isDir(FS, p): p in FS.Directories
Directories may have children, that is, there may exist other paths in the FileSystem whose path begins with a directory. Only directories may have children. This can be expressed by saying that every path’s parent must be a directory.
It can then be declared that a path has no parent in which case it is the root directory, or it MUST have a parent that is a directory:
forall p in paths(FS) : isRoot(p) or isDir(FS, parent(p))
Because the parent directories of all directories must themselves satisfy this criterion, it is implicit that only leaf nodes may be files or symbolic links:
Furthermore, because every filesystem contains the root path, every filesystem must contain at least one directory.
A directory may have children:
def children(FS, p) = {q for q in paths(FS) where parent(q) == p}
There are no duplicate names in the child paths, because all paths are taken from the set of lists of path elements. There can be no duplicate entries in a set, hence no children with duplicate names.
A path D is a descendant of a path P if it is the direct child of the path P or an ancestor is a direct child of path P:
def isDescendant(P, D) = parent(D) == P where isDescendant(P, parent(D))
The descendants of a directory P are all paths in the filesystem whose path begins with the path P -that is their parent is P or an ancestor is P
def descendants(FS, D) = {p for p in paths(FS) where isDescendant(D, p)}
The home directory of a user is an implicit part of a filesystem, and is derived from the userid of the process working with the filesystem:
def getHomeDirectory(FS) : Path
The function getHomeDirectory returns the home directory for the Filesystem and the current user account. For some FileSystems, the path is ["/","users", System.getProperty("user-name")]. However, for HDFS,
A path cannot refer to more than one of a file, a directory or a symbolic link
FS.Directories ^ keys(data(FS)) == {}
FS.Directories ^ symlinks(FS) == {}
keys(data(FS))(FS) ^ symlinks(FS) == {}
This implies that only files may have data.
This condition is invariant and is an implicit postcondition of all operations that manipulate the state of a FileSystem FS.
Not covered: hard links in a FileSystem. If a FileSystem supports multiple references in paths(FS) to point to the same data, the outcome of operations are undefined.
This model of a FileSystem is sufficient to describe all the FileSystem queries and manipulations excluding metadata and permission operations. The Hadoop FileSystem and FileContext interfaces can be specified in terms of operations that query or change the state of a FileSystem.