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Selectors match Style variables against Substance variables to produce multiple matches. Each match is independent from another. This characteristic makes it difficult to implement features that require aggregations over multiple matches. For example, we can't compute the sum of center fields of all Substance variables that a selector matches on.

Collectors enable these types of aggregations by introducing collections of Substance variables. The syntax is as follows:

collect <COLLECT> into <INTO>
where <WHERE>
with <WITH>
foreach <FOREACH> { }

The where, with, and foreach clauses are optional, and if they are empty, they must be omitted.

  • <COLLECT> is an object declaration. The <COLLECT> object is accessible, via the name given in the <INTO> clause, in the Style block body.
  • <INTO> is the name assigned to the collection. The collection includes all the Substance objects that <COLLECT> matches to. Within the Style block, <INTO> conceptually represents a list of Substance objects.
  • The <WHERE> clause has the same meaning as in standard forall Style selectors.
  • <WITH> is a semicolon-separated list of object declarations. Objects in the <WITH> clause aren't collected, but may be used in <WHERE>.
  • <FOREACH> is a semicolon-separated list of object declarations. Objects in the <FOREACH> clause are also not collected, but they arrange the <COLLECT> objects into groups. The entire collect block runs once for each distinct match of the <FOREACH> clause. The <FOREACH> list can contain multiple declarations.

For example, suppose we have the Substance program that defines one set s1 that contains elements e1, e2, and another set s2 that contains elements e3, e4, e5, as follows:

Set s1
Element e1, e2
In(e1, s1)
In(e2, s1)

Set s2
Element e3, e4, e5
In(e3, s2)
In(e4, s2)
In(e5, s2)

We can write a Collector:

collect Element e into es
where In(e, s)
foreach Set s {

Under the above Substance program, this Collector would run twice:

  • once with mapping es -> [e1, e2] and s -> s1
  • once with mapping es -> [e3, e4, e5] and s -> s2.

Notice that we have splitted the set of all elements [e1, e2, e3, e4, e5] into two groups based on the Set object that they are contained within.

Within the body of the Collectors, we can do everything that can be done in Selector Blocks, with the one exception that we can only access Style variables in <INTO> and <FOREACH>.

Repeatable vs Non-Repeatable Matching

Collectors run the same underlying matching algorithm as described here. As such, by default, it disallows two style variables that map to the same substance variable. To override this behavior, just as in here, one can add the repeatable keyword:

collect repeatable Set s into ss
where IsSubset(s, a)
with Set a

Collection Access Expression

Within the Collector, the name in the <INTO> clause conceptually means a list of Substance objects. We can access the fields of each element in the collection using the "Collection Access" expression with syntax:


This expression takes the <FIELD NAME> field of each Substance variable in the collection <COLLECTION NAME>, and compiles these fields into an appropriate list.

For example, suppose elements is the name in the <INTO> block, conceptually representing some list of Substance objects [e1, e2, ..., en]. Then, we would expect the expression listof field from elements to produce a list [e1.field, e2.field, ..., en.field].

Due to technical constraints, we cannot access any field of each element of the collection. In the above example, if e1.field gives a color, then we cannot really put the color into a list, since Penrose does not support lists of colors. We restrict allowable types to as follows:

Type of fieldCollects into
FloatV (number)VectorV (vector)
VectorV (vector)MatrixV (matrix)
ListV (list)LListV (list of lists)
TupV (2-tuple)PtListV (list of 2d points)
some shapeShapeListV (list of shapes)

If, in the above example, e1.field, e2.field, etc. are numbers, then the expresion listof field from elements gives us a vector that contains all the values. We can directly plug the vector into accumulation functions such as average and sum.

Collection Count Expression

We may want to count the number of elements in a collection of Substance variables. This is particularly useful when computing the spacing required between two objects. Using the aforementioned listof expressions, we can write

collect Object o into os {
    total = count(listof someprop from os)

The count function takes a vector of numbers and returns the number of elements in the vector. Though this method works, it relies on the assumption that the someprop field exists in each Object o and that such a field is a number. To simplify this, we support the numberof expression:


This expression simply returns the number of elements in <COLLECTION NAME>.

Released under the MIT License.