Name Rascal/Expressions/Values/ListRelation/ReflexiveTransitiveClosure

Synopsis The reflexive transitive closure of a binary list relation.

Syntax Exp *

Types

Exp	Exp *
lrel[T1, T2]	lrel[T1, T2]

Description Reflexive transitive closure is defined by repeated composition of a list relation. If we define for a given list relation R:

• R⁰ = identity relation = [<a, a>, <b, b> | <a, b> <- R]
• R¹ = R
• R² = R o R
• R³ = R o R²
• ...

then the reflexive transitive closure R* can be defined in two ways: (also see TransitiveClosure):

• R* = R⁰ + R¹ + R² + R³ + ...
• R* = R⁰ + R+

Examples

rascal>[<1,2>, <2,3>, <3,4>]*;
lrel[int,int]: [
  <1,2>,
  <2,3>,
  <3,4>,
  <1,3>,
  <2,4>,
  <1,4>,
  <4,4>,
  <3,3>,
  <2,2>,
  <1,1>
]

Questions

[Edit] | [New Subconcept] | [Recompile Course] | [Warnings]