### Generating

[
  Type   atoms
  Entity used-atom-set
  Funcon initialise-generating
  Funcon fresh-atom
  Funcon use-atom-not-in
]


Meta-variables
  T <: values


Built-in Type
  atoms
/*
  `atoms` is the type of values used as distinguishable tags.
  Notation for individual atoms is not provided.
*/


Entity
  < _ , used-atom-set(_:sets(atoms)) > ---> < _ , used-atom-set(_:sets(atoms)) >


Built-in Funcon
  initialise-generating(_:=>T) : =>T
/*
  The initial value of the `used-atom-set(SA)` entity is unspecified. It could
  contains atoms that are reserved for internal use.
*/


Funcon
  fresh-atom : =>atoms
/*
  `fresh-atom` computes an atom distinct from all previously computed atoms.
*/
Rule
  element-not-in(atoms, SA) ~> A
  -----------------------------------------------
  < fresh-atom , used-atom-set(SA) > 
    ---> < A , used-atom-set(set-insert(A, SA)) >


Funcon
  use-atom-not-in(_:sets(atoms)) : =>atoms
/*
  `use-atom-not-in(SA)` computes an atom not in the set `SA`, and inserts it
  in the `used-atom-set(SA')` entity, in case it was not previously used.
*/
Rule
  element-not-in(atoms, SA) ~> A
  --------------------------------------------------------
  < use-atom-not-in(SA:sets(atoms)) , used-atom-set(SA') >
    ---> < A , used-atom-set(set-insert(A, SA')) >