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Relation ReflexiveTransitiveClosure

rascal-0.40.17

Synopsis​

The reflexive transitive closure of a binary relation.

Syntax​

Exp *

Types​

ExpExp *
rel[T₁, T₂]rel[T₁, T₂]

Description​

Reflexive transitive closure is defined by repeated composition of a relation. If we define for a given 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>}*;
rel[int,int]: {
  <4,4>,
  <1,1>,
  <1,3>,
  <1,2>,
  <1,4>,
  <3,3>,
  <3,4>,
  <2,3>,
  <2,2>,
  <2,4>
}