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195 lines (165 loc) · 4.95 KB
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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
)
}
}