Name Rascal/Expressions/Values/Relation/ReflexiveTransitiveClosure

Synopsis The reflexive transitive closure of a binary relation.

Syntax Exp *

Types

Exp	Exp *
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 = 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>}*;
rel[int,int]: {
  <4,4>,
  <1,4>,
  <2,2>,
  <2,4>,
  <1,3>,
  <2,3>,
  <1,2>,
  <3,4>,
  <1,1>,
  <3,3>
}

Questions

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