'a seq is the type of sequences whose elements have type 'a.

empty is a sequence of length zero.

zero is a synonym for empty.

singleton x is a sequence of length one whose single element is x.

one is a synonym for singleton.

rev xs is the reverse of the sequence xs.

sum s1 s2 is the concatenation of the sequences s1 and s2.

(++) is a synonym for sum.

product s1 s2 is the Cartesian product of the sequences s1 and s2. Its length is the product of the lengths of s1 and s2. The first pair component is considered most significant.

( ** ) is a synonym for product.

map phi s is the image of the sequence s through the function phi. If the user wishes to work with sequences of pairwise distinct elements, then phi should be injective. If furthermore the user wishes to work with sequences that enumerate all elements of a type, then phi should be surjective.

up i j is the sequence of the integers from i included up to j excluded.

The type index is the type of integers used to represent indices and lengths.

length s is the length of the sequence s.

get s i is the i-th element of the sequence s. The index i must be comprised between zero included and length s excluded.

foreach s k iterates over all elements of the sequence s. Each element in turn is passed to the loop body k.

to_seq s k produces an explicit representation of the sequence s as a sequence in the sense of OCaml's standard library module Seq. This sequence is prepended in front of the existing sequence k.