Generates & auto-grades functional dependency problems
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.


Generates & auto-grades functional dependency problems.

mostly, the pseudocode for lib.php

// Since array_rand($arr, 1) returns a single value,
// we wrap it in ensure_array to always get an array.
function ensure_array($x) {
// This class encapsulates a set of attributes (ex. ABCD)
// and adds some behavior.
// I have not tested with attributes that aren't single-character strings,
// but theoretically that should also work.
class AttributeSet {
    // Contents are public so iteration is easier
    // Construct by passing in the contents directly
    function __construct($contents) {
    // When coercing to a string, just give the contents as a string
    function __toString() {
    // Construct from a range of letters
    static function range($start, $end) {
    // Construct from a string (ex. 'ACE')
    static function from($str) {
    // Render a given attribute. I don't think I ever use this, plus it's not useful.
    function renderAttr($i) {
    // Render the attribute set as a tuple (A, B, C).
    function renderTuple() {
    // Render the attribute set as a set {A, B, C}.
    function renderSet() {
    // Render the attribute set as a list ABC.
    function renderList() {
    // Check if this set contains all the attributes in another set.
    function containsAll($other) {
    // Add all the attributes from another set into this set.
    function addAll($other) {
    // Check if this set equals another set.
    function equals($other) {
    // Get a subset by number: 0b1101 means include attributes 1, 2, and 4
    function getSubset($n) {
        $arr = array_filter($arr, function($v) {
    // Get a random subset that isn't the empty set (but can be the entire set)
    function randSubset() {
    // Get all of the subsets, including the empty set and the entire set
    function allSubsets() {
        $arr = array_map(function($n) {return $this->getSubset($n);}, $arr);
// Checks if two sets of closures are equal.
// Assumes they are in the same order.
function closuresEqual($one, $two) {
    return array_reduce($pairs, function ($wasGood, $pair) {
// Encapsulates a relation, including attributes and dependencies.
class Relation {
    // $attrs is an AttributeSet
    // $deps is an array of arrays of AttrSets (AB->C, C->A is [[AB, C], [C, A]])
    // Build the relation by passing in attributes and dependencies
    // Deps are good iff they only contain the attributes included in the relation
    function __construct($attrs, $deps, $depsGood = true) {
        // If the deps aren't known to be good, clean them up
            // For each dependency...
                // Grab the left-hand and right-hand sides
                // If we're missing things from the left...
                    // Erase the dependency entirely and move on
                // Filter the RHS down to things we care about
                // If that was nothing...
                    // Skip the dependency
                    // Otherwise, use that RHS instead
        // Since we may have used unset() on $deps, rekey it
    // Make a random Relation
    static function random() {
            // This winds up generating a lot of trivial dependencies
    // Render an individual dependency, optionally in TeX
    function renderDep($dep, $tex = false) {
    // Render all the dependencies, optionally in TeX
    function renderDeps($tex = false) {
    // Render the entire relation
    function render() {
    // Find the closure of a given set of attributes
    function closure($attrs) {
        // Start with the given attributes
        // While you just added new things to the closure...
            // For every dependency in the relation...
                // If you satisfy the LHS...
                    // If you don't already have the entire RHS...
                        // Add the RHS to the closure
    // Get the closure of every possible set of attributes
    // (which is equivalent to the closure of the dependencies)
    function allClosures() {
    // Get the list of superkeys of the relation
    function superkeys() {
        // Get all the closures
        // Find the ones that contain all the attributes in the relation
        $superkeys = array_filter($allClosures, function ($c) {
        return array_map(function ($x) {return AttributeSet::from($x);}, $superkeys);
    // Get the list of candidate keys of the relation
    function candidateKeys() {
        // Get the superkeys
        // To check if some superkey is a candidate key...
        $isCandidate = function($key) use ($superkeys) {
            // Look at all the other superkeys
                // If this superkey is a proper superset of the other superkey...
                    // ...this can't be a candidate key
            // If it isn't a superset of a superkey, no superkey is a subset of it, so it's a candidate key
    // Get the canonical cover of the dependencies in the relation (F)
    function canonicalCover($verbose = true) {
        // Make a copy of F to work on
        // Grab the original F+ (by grabbing the closure of every possible set of attributes)
        // Don't loop infinitely (this doesn't still happen but it's good to be safe)
        // While we just changed something and haven't been running for too long...
            // Map LHS => index of first dependency with given LHS
            // For all dependencies...
                // If another dependency exists with the same LHS...
                    // Merge this RHS into the other's RHS
                    // Remove this dependency
                // If LHS or RHS is entirely empty...
                    // Remove this dependency
                    // Since indices shifted, quit removing things
                    // If not removing, save index in map
            // For every dependency in the relation...
                // For every side of that dependency...
                    // For every attribute on that side of that dependency...
                        // Try removing that attribute from F
                        // Find F+ without the attribute
                        // If we didn't create or remove any information...
                            // Remove that attribute
                            // PHP magic: break out of all three loops at once
                            // some languages have labeled breaks, some wouldn't let you do this at all
                            // this is probably less intuitive than a labeled break
        // Erase any leftover dependencies with empty sides
        $deps = array_filter($deps, function ($dep) {
    // Check if this relation is in BCNF
    function isBCNF($verbose = false) {
        // Grab the superkeys
        // For each dependency...
            // If it's trivial...
                // we're good
                // If the LHS is a superkey, we're good
                // If neither of those holds, this is not BCNF
    // Check if this relation is in 3NF
    function is3NF($verbose = false) {
        // Grab the superkeys
        // Grab the candidate keys
        // Union all the candidate keys together
        // For each dependency...
            // If it's trivial...
                // we're good
                // If LHS is a superkey, we're good
                // Attrs in RHS can be in a candidate key or in LHS as well
                // If some attr in RHS is neither...
                    // this is not 3NF
    // Check if this relation is in 4NF
    function is4NF($verbose = false) {
        // Check if it's in BCNF first
        // Look for a simple key
    // Check if this relation is in 5NF
    function is5NF($verbose = false) {
        // Check if it's in 3NF first
        // Check that all candidate keys are simple
    // Make [R-$beta, $alpha$beta] from this relation R and an $alpha and $beta, given all the closures
    function fracture($alpha, $beta, $closures) {
        // make a new Relation with only those attributes
        // find out the dependencies that matter
        // make a new Relation without beta
        // find its dependencies too
        // give both back
    // Decompose this relation into BCNF
    // Algorithm from Silberschatz, Korth, Sudarshan "Database System Concepts" 6th ed. fig. 8.11
    function decomposeBCNF($verbose = false) {
        // Start with only R
        // Find F+
        // Until we're done...
            // For each relation in the result...
                // If it's not in BCNF...
                    // Find some a->b where a is not a superkey of ri and a and b share nothing
                    // We want only alphas that determine a nontrivial beta
                    $riAlphas = array_filter($riAlphas, function ($alpha) use ($ri) {
                    // Break up $ri into [$ri-$beta, $alpha$beta]
                    // Replace $ri with those fragments in the result
                    // Don't keep looking through the result
    // Decompose this relation into 3NF
    // Algorithm from Silberschatz, Korth, Sudarshan "Database System Concepts" 6th ed. fig. 8.12
    function decompose3NF($verbose = false) {
        // Grab the canonical cover
        // For each dependency in the canonical cover...
            // Find all the attributes involved
            // Add a new relation with only those attributes
        // Grab the candidate keys
        // For each relation we already have...
            // For each candidate key...
                // If this relation contains this candidate key...
                    // We found a candidate key!
                    // Don't look for any others
        // If we never found a candidate key...
            // Throw one in
        // For every relation in the result...
            // For every other relation in the result...
                // If they aren't the same but this one is a subset of that one...
                    // Remove this one
    // Check if a decomposition of this relation is dependency preserving
    function isDepPres($decomp, $verbose = false) {
        // For each dependency...
            // Build up the closure within the decomposition
                // For each relation in the composition...
                    // Merge in the closure of what we already have
            // If the closure in the decomposition doesn't contain the RHS of the dependency...
                // The decomposition can't be dependency preserving
    // Check if a decomposition of this relation is lossless
    function isLossless($decomp) {
        // If there's only one relation in the decomposition...
            // It's lossless iff it has all the same attributes
            // If it's a binary decomposition...
            // Find the attributes both relations have in common
            // Find attribute sets that are superkeys of either relation
            // It's lossless iff the common attributes are a superkey of either relation
            // If it's more than a binary decomposition...
            // For every pair of decompositions...
                    // Make a copy of the decomposition
                    // Extract the pair
                    // Merge the pair
                    // If the pair can be combined losslessly...
                        // Replace the split pair with the merged pair
                        // Promise we got rid of a relation and aren't recursing infinitely
                        // If merging that pair resulted in a lossless decomposition...
                            // The original decomposition was also lossless
    // Print out a whole bunch of stuff
    function debug() {
        usort($subsets, function ($a, $b) { return strlen($a) - strlen($b); });