Skip to main content

ListRelation Reflexive Transitive Closure

rascal-0.41.2

Synopsis​

The reflexive transitive closure of a binary list relation.

Syntax​

Exp *

Types​

ExpExp *
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 = [<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>
]