# RecursiveAggregate SΒΆ

A recursive aggregate over a type S is a model for a a directed graph containing values of type S. Recursively, a recursive aggregate is either empty or a node consisting of a value from S and 0 or more children which are also nodes. A node with no children is called a leaf node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.

#: % -> NonNegativeInteger if % has finiteAggregate

from Aggregate

=: (%, %) -> Boolean if % has finiteAggregate and S has BasicType or S has SetCategory

from BasicType

~=: (%, %) -> Boolean if % has finiteAggregate and S has BasicType or S has SetCategory

from BasicType

any?: (S -> Boolean, %) -> Boolean if % has finiteAggregate

from HomogeneousAggregate S

child?: (%, %) -> Boolean if S has BasicType

child?(u, v) tests if node u is a child of node v.

children: % -> List %

children(u) returns a list of the children of aggregate u. Error: if u is empty.

coerce: % -> OutputForm if S has CoercibleTo OutputForm
copy: % -> %

from Aggregate

count: (S -> Boolean, %) -> NonNegativeInteger if % has finiteAggregate

from HomogeneousAggregate S

count: (S, %) -> NonNegativeInteger if % has finiteAggregate and S has BasicType

from HomogeneousAggregate S

cyclic?: % -> Boolean

cyclic?(u) tests if u has a cycle.

distance: (%, %) -> Integer

distance(u, v) returns the path length (an integer) from node u to v.

elt: (%, value) -> S

elt(u, "value") (also written: u.value) is equivalent to value(u).

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, Equation S) -> % if S has SetCategory and S has Evalable S

from Evalable S

eval: (%, List Equation S) -> % if S has SetCategory and S has Evalable S

from Evalable S

eval: (%, List S, List S) -> % if S has SetCategory and S has Evalable S

from InnerEvalable(S, S)

eval: (%, S, S) -> % if S has SetCategory and S has Evalable S

from InnerEvalable(S, S)

every?: (S -> Boolean, %) -> Boolean if % has finiteAggregate

from HomogeneousAggregate S

hash: % -> SingleInteger if S has SetCategory

from SetCategory

hashUpdate!: (HashState, %) -> HashState if S has SetCategory

from SetCategory

latex: % -> String if S has SetCategory

from SetCategory

leaf?: % -> Boolean

leaf?(u) tests if u is a terminal node.

leaves: % -> List S

leaves(u) returns the list of leaves in aggregate u.

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

map!: (S -> S, %) -> % if % has shallowlyMutable

from HomogeneousAggregate S

map: (S -> S, %) -> %

from HomogeneousAggregate S

max: % -> S if S has OrderedSet and % has finiteAggregate

from HomogeneousAggregate S

max: ((S, S) -> Boolean, %) -> S if % has finiteAggregate

from HomogeneousAggregate S

member?: (S, %) -> Boolean if % has finiteAggregate and S has BasicType

from HomogeneousAggregate S

members: % -> List S if % has finiteAggregate

from HomogeneousAggregate S

min: % -> S if S has OrderedSet and % has finiteAggregate

from HomogeneousAggregate S

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

node?: (%, %) -> Boolean if S has BasicType

node?(u, v) tests if node u is contained in node v (either as a child, a child of a child, etc.).

nodes: % -> List %

nodes(u) returns a list of all of the nodes of aggregate u.

parts: % -> List S if % has finiteAggregate

from HomogeneousAggregate S

sample: %

from Aggregate

setchildren!: (%, List %) -> % if % has shallowlyMutable

setchildren!(u, v) replaces the current children of node u with the members of v in left-to-right order.

setelt!: (%, value, S) -> S if % has shallowlyMutable

setelt!(u, "value", x) (also written u.value := x) is equivalent to setvalue!(u, x)

setvalue!: (%, S) -> S if % has shallowlyMutable

setvalue!(u, x) sets the value of node u to x.

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

value: % -> S

value(u) returns the value of the node u.

Aggregate

BasicType if % has finiteAggregate and S has BasicType or S has SetCategory

Evalable S if S has SetCategory and S has Evalable S

InnerEvalable(S, S) if S has SetCategory and S has Evalable S

SetCategory if S has SetCategory