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/**

* Provides modules for computing dense `rank`s. See the `DenseRank` module

* below for a more detailed explanation.

*/

overlay[local?]

module;

/** Provides the input to `DenseRank`. */

signature module DenseRankInputSig {

/** An element that is ranked. */

bindingset[this]

class Ranked;

/** Gets the rank of `r`. */

int getRank(Ranked r);

}

/**

* Provides the `denseRank` predicate for computing dense `rank`s. For example,

* if we have

*

* ```ql

* query predicate names(string name) {

* name = ["Alice", "Bob", "Charles", "Charlie", "David"]

* }

*

* int rankByFirstLetter(string name) {

* name = rank[result](string n | names(n) | n order by n.charAt(0))

* }

* ```

*

* then `rankByFirstLetter` computes the following relation

*

* ```

* Alice 1

* Bob 2

* Charles 3

* Charlie 3

* David 5

* ```

*

* Note that `"David"` has rank 5 instead of 4. If we want a dense ranking instead,

* we can do

*

* ```ql

* module M implements DenseRankInputSig {

* class Ranked = string;

*

* predicate getRank = rankByFirstLetter/1;

* }

*

* predicate denseRank = DenseRank<M>::denseRank/1;

* ```

*/

module DenseRank<DenseRankInputSig Input> {

private import Input

private int getARank() { result = getRank(_) }

pragma[noinline]

private int getARankGap() { result = getARank() and not result - 1 = getARank() }

pragma[noinline]

private predicate isDenseFrom(int i) { i = unique( | | getARankGap()) }

pragma[noinline]

private int getRankNeedsDenseRank(Ranked r) { result = getRank(r) and not isDenseFrom(_) }

private int rankRank(Ranked r, int rnk) {

rnk = getRankNeedsDenseRank(r) and

rnk = rank[result](int rnk0 | rnk0 = getRankNeedsDenseRank(_) | rnk0)

}

/** Gets the `Ranked` value for which the dense rank is `rnk`. */

pragma[nomagic]

Ranked denseRank(int rnk) {

rnk = rankRank(result, getRankNeedsDenseRank(result))

or

exists(int i, int offset |

isDenseFrom(i) and

offset = i - 1 and

rnk = getRank(result) - offset

)

}

}

/** Provides the input to `DenseRank1`. */

signature module DenseRankInputSig1 {

/** A ranking context. */

bindingset[this]

class C;

/** An element that is ranked. */

bindingset[this]

class Ranked;

/** Gets the rank of `r` in the context provided by `c`. */

int getRank(C c, Ranked r);

}

/** Same as `DenseRank`, but allows for a context consisting of one element. */

module DenseRank1<DenseRankInputSig1 Input> {

private import Input

private int getARank(C c) { result = getRank(c, _) }

pragma[noinline]

private int getARankGap(C c) { result = getARank(c) and not result - 1 = getARank(c) }

pragma[noinline]

private predicate isDenseFrom(C c, int i) { i = unique( | | getARankGap(c)) }

pragma[noinline]

private int getRankNeedsDenseRank(C c, Ranked r) {

result = getRank(c, r) and not isDenseFrom(c, _)

}

private int rankRank(C c, Ranked r, int rnk) {

rnk = getRankNeedsDenseRank(c, r) and

rnk = rank[result](int rnk0 | rnk0 = getRankNeedsDenseRank(c, _) | rnk0)

}

/**

* Gets the `Ranked` value for which the dense rank in the context provided by

* `c` is `rnk`.

*/

pragma[nomagic]

Ranked denseRank(C c, int rnk) {

rnk = rankRank(c, result, getRankNeedsDenseRank(c, result))

or

exists(int i, int offset |

isDenseFrom(c, i) and

offset = i - 1 and

rnk = getRank(c, result) - offset

)

}

}

/** Provides the input to `DenseRank2`. */

signature module DenseRankInputSig2 {

/** A ranking context. */

bindingset[this]

class C1;

/** A ranking context. */

bindingset[this]

class C2;

/** An element that is ranked. */

bindingset[this]

class Ranked;

/** Gets the rank of `r` in the context provided by `c1` and `c2`. */

int getRank(C1 c1, C2 c2, Ranked r);

}

/** Same as `DenseRank`, but allows for a context consisting of two elements. */

module DenseRank2<DenseRankInputSig2 Input> {

private import Input

private int getARank(C1 c1, C2 c2) { result = getRank(c1, c2, _) }

pragma[noinline]

private int getARankGap(C1 c1, C2 c2) {

result = getARank(c1, c2) and not result - 1 = getARank(c1, c2)

}

pragma[noinline]

private predicate isDenseFrom(C1 c1, C2 c2, int i) { i = unique( | | getARankGap(c1, c2)) }

pragma[noinline]

private int getRankNeedsDenseRank(C1 c1, C2 c2, Ranked r) {

result = getRank(c1, c2, r) and not isDenseFrom(c1, c2, _)

}

private int rankRank(C1 c1, C2 c2, Ranked r, int rnk) {

rnk = getRankNeedsDenseRank(c1, c2, r) and

rnk = rank[result](int rnk0 | rnk0 = getRankNeedsDenseRank(c1, c2, _) | rnk0)

}

/**

* Gets the `Ranked` value for which the dense rank in the context provided by

* `c1` and `c2` is `rnk`.

*/

pragma[nomagic]

Ranked denseRank(C1 c1, C2 c2, int rnk) {

rnk = rankRank(c1, c2, result, getRankNeedsDenseRank(c1, c2, result))

or

exists(int i, int offset |

isDenseFrom(c1, c2, i) and

offset = i - 1 and

rnk = getRank(c1, c2, result) - offset

)

}

}