---
layout: default
title: "Sequences"
parent: Composite
ancestor: Funcons-beta
---
[Funcons-beta] : [Sequences.cbs]
-----------------------------
### Sequences of values
Sequences of two or more values are not themselves values, nor is the empty
sequence a value. However, sequences can be provided to funcons as arguments,
and returned as results. Many operations on composite values can be expressed
by extracting their components as sequences, operating on the sequences, then
forming the required composite values from the resulting sequences.
A sequence with elements X1, ..., Xn is written X1,...,Xn.
A sequence with a single element X is identified with (and written) X.
An empty sequence is indicated by the absence of a term.
Any sequence X* can be enclosed in parentheses (X*), e.g.:
( ), (1), (1,2,3). Superfluous commas are ignored.
The elements of a type sequence T1,...,Tn are the value sequences V1,...,Vn
where V1:T1, ..., Vn:Tn. The only element of the empty type sequence ( )
is the empty value sequence ( ).
(T)^N is equivalent to T,...,T with N occurrences of T.
(T)* is equivalent to the union of all (T)^N for N>=0,
(T)+ is equivalent to the union of all (T)^N for N>=1, and
(T)? is equivalent to T | ( ).
The parentheses around T above can be omitted when they are not needed for
disambiguation.
(Non-trivial) sequence types are not values, so not included in types.
Meta-variables
T, T′ <: values
length(V*) gives the number of elements in V*.
#### Sequence indexing
index(N, V*) gives the Nth element of V*, if it exists, otherwise ( ).
Total indexing funcons:
#### Homogeneous sequences
Funcon
intersperse(_:T′, _:(T)*) : =>(T, (T′, T)*)?
Rule
intersperse(_:T′, ( )) ~> ( )
Rule
intersperse(_:T′, V) ~> V
Rule
intersperse(V′:T′, V1:T, V2:T, V*:(T)*) ~> (V1, V′, intersperse(V′, V2, V*))