PLAN-2443 - Include allReduce in the Pattern docs where QPPs are described (#1407)

Author: WilcoNeo

modules/ROOT/pages/functions/predicate.adoc

@@ -110,7 +110,9 @@ RETURN all(i in emptyList WHERE true) as allTrue, all(i in emptyList WHERE false
 |===
 | *Syntax* 3+| `allReduce(accumulator = initial, stepVariable IN list \| reductionFunction, predicate)`
 | *Description* 3+| Returns true if, during the stepwise evaluation of a value across the elements in a given `LIST<ANY>`, the accumulated result satisfies a specified predicate at every step.
-Where that list is a xref:patterns/variable-length-patterns.adoc#group-variables[group variable] defined in a xref:patterns/variable-length-patterns.adoc#quantified-path-patterns[quantified path pattern], it allows for the early pruning of paths that do not satisfy the predicate.
+If that list is a xref:patterns/variable-length-patterns.adoc#group-variables[group variable] defined in a xref:patterns/variable-length-patterns.adoc#quantified-path-patterns[quantified path pattern], its predicate is inlined where applicable.
+This inlining allows for early pruning of the search space by discarding paths as soon as the predicate is not satisfied.
+Note that `allReduce()` predicates are not inlined when used in a xref:patterns/shortest-paths.adoc[shortest path pattern], and therefore do not benefit from this pruning.
 .7+| *Arguments* | *Name* | *Type* | *Description*
 | `accumulator` | `ANY` | A variable that holds the result of the `reductionFunction` as the `list` is iterated.
 It is initialized with the value of `initial`.

modules/ROOT/pages/patterns/variable-length-patterns.adoc

@@ -380,6 +380,10 @@ For example, all relationships in the path must be of type `EMPLOYED_BY`.
 * Nodes or relationships must have properties satisfying some condition.
 For example, all relationships must have the property `distance > 10`.
 
+* For every iteration of the quantified path pattern, an aggregated value over the constructed path so far must satisfy a predicate.
+For example, the sum of the property `distance` of the relationships in the path must be less than 50 for every step in the construction of the path.
+See xref::functions/predicate.adoc#functions-allreduce[allReduce] for more information about this predicate.
+
 To demonstrate the utility of predicates in quantified path patterns, this section considers an example of finding the shortest path by physical distance and compares that to the results yielded by using the xref:patterns/shortest-paths.adoc[`SHORTEST`] keyword.
 The graph in this example continues with `Station` nodes, but adds both a geospatial `location` property to the `Stations`, as well as `LINK` relationships with a `distance` property representing the distance between pairs of `Stations`:
 
@@ -558,6 +562,26 @@ This query avoids having to find all possible paths and then imposing a `LIMIT 1
 It also shows that there is only one path to solving the query (a number that remains constant even if the data from the rest of the UK railway network was included).
 Using inline predicates or making quantified path patterns more specific where possible can thus greatly improve query performance.
 
+An alternative is to use an upper bound for the total distance, for example `6.05`.
+Once a path exceeds this upper bound, you can prune it and continue searching other paths.
+The xref::functions/predicate.adoc#functions-allreduce[allReduce] predicate function expresses this as follows:
+
+.Query
+[source,cypher]
+----
+MATCH (bfr:Station {name: "London Blackfriars"}),
+      (ndl:Station {name: "North Dulwich"})
+MATCH p = (bfr) ((a)-[l:LINK]-(b:Station))+ (ndl)
+WHERE allReduce(
+  pathLength = 0,
+  link IN l | pathLength + link.distance,
+  pathLength < 6.05
+)
+RETURN reduce(acc = 0, r in relationships(p) | round(acc + r.distance, 2))
+  AS distance
+ORDER BY distance LIMIT 1
+----
+
 [[further-reading]]
 == Further reading