### Lists

[
  Datatype lists
  Funcon   list
  Funcon   list-elements
  Funcon   list-nil       Alias nil
  Funcon   list-cons      Alias cons
  Funcon   list-head      Alias head
  Funcon   list-tail      Alias tail
  Funcon   list-length
  Funcon   list-append
]


Meta-variables
  T <: values


Datatype
  lists(T) ::= list(_:(T)*)
/*
  `lists(T)` is the type of possibly-empty finite lists `[V1,...,Vn]` 
  where `V1:T`, ..., `Vn:T`.
  
  N.B. `[T]` is always a single list value, and *not* interpreted as the
  type `lists(T)`.
  
  The notation `[V1, ..., Vn]` for `list(V1, ..., Vn)` is built-in.
*/
Assert
  [V*:values*] == list(V*)


Funcon
  list-elements(_:lists(T)) : =>(T)*
Rule
  list-elements(list(V*:values*)) ~> V*


Funcon
  list-nil : =>lists(_)
    ~> [ ]
Alias
  nil = list-nil


Funcon 
  list-cons(_:T, _:lists(T)) : =>lists(T) 
Alias
  cons = list-cons
Rule
  list-cons(V:values, [V*:values*]) ~> [V, V*]


Funcon
  list-head(_:lists(T)) : =>(T)? 
Alias
  head = list-head
Rule
  list-head[V:values, _*:values*] ~> V 
Rule
  list-head[ ] ~> ( )


Funcon
  list-tail(_:lists(T)) : =>(lists(T))?
Alias
  tail = list-tail
Rule
  list-tail[_:values, V*:values*] ~> [V*] 
Rule
  list-tail[ ] ~> ( )


Funcon
  list-length(_:lists(T)) : =>natural-numbers
Rule
  list-length[V*:values*] ~> length(V*)


Funcon
  list-append(_:(lists(T))*) : =>lists(T)
Rule
  list-append([V1*:values*], [V2*:values*]) ~> [V1*, V2*]
Rule
  list-append(L1:lists(_), L2:lists(_), L3:lists(_), L*:(lists(_))*)
   ~> list-append(L1, list-append(L2, L3, L*))
Rule
  list-append( ) ~> [ ]
Rule
  list-append(L:lists(_)) ~> L


/*
  Datatypes of infinite and possibly-infinite lists can be specified as
  algebraic datatypes using abstractions.
*/