array2

collect the contents of this Sequence into an array

create an array backed version of this sequence in case this is not array
backed. This will ensure that operations like index[] or drop perform
in constant time.

returns Sequence.this if is_array_backed.

create a list from this array

create a list from this array starting at the given index

returns a copy of this array as a mutable array

convenience feature to work around type inference issues
NYI remove when type inference gets better

create a string representation of this Sequence including all the string
representations of its contents, separated by 'sep'.

NOTE: In case this Sequence is not finite, this will attempt to create an
infinitely long string resulting in failure due to resource exchaustion.

create a string representation of this array including all the string
representations of its contents, separated by ',' and enclosed in '['
and ']'. Arrays in inner dimensions are grouped using '[' and ']'.

create a string representation of this Sequence including all the string
representations of its contents, separated by ", " and enclosed in '['
and ']'.

NOTE: In case this Sequence is not finite, this will attempt to create an
infinitely long string resulting in failure due to resource exchaustion.

call 'as_string' on the elements

the arithmetic mean of the sequence
https://en.wikipedia.org/wiki/Arithmetic_mean

create a new list that contains the first elements of
this Sequence for which 'f e' is false

chop this Sequence into chunks of `chunk_size`.
the last chunk may be smaller than `chunk_size`.

create a new Sequence from the result of applying 'f' to the
elements all combinations of elements of this Sequence and
all elements of 'b' iterating of 'b' repeatedly as follows

Sequence.this[0] , b[0]
Sequence.this[0] , b[1]
Sequence.this[0] , b[2]
Sequence.this[0] , ...
Sequence.this[0] , b.last
Sequence.this[1] , b[0]
Sequence.this[1] , b[1]
Sequence.this[1] , ...
... , ...
Sequence.this.last, b.last

create a Sequence that consists of all the elements of this Sequence followed
by all the elements of s

does the Sequence contain element x?

redefines Sequence.count for array,
reducing complexity from O(n) to O(1).

get the number of non-overlapping matches of l within this

get the number of matches of l

create a list that repeats the current Sequence indefinitely. In case 'Sequence.this'
is empty, returns 'nil'

create a list that consists of the elements of this Sequence except the first
n elements

For arrays, this has performance in O(1).

Lazily drop the first elements of this Sequence for which predicate 'p' holds.

Get the dynamic type of this instance. For value instances `x`, this is
equal to `type_of x`, but for `x` with a `ref` type `x.dynamic_type` gives
the actual runtime type, while `type_of x` results in the static
compile-time type.

There is no dynamic type of a type instance since this would result in an
endless hierarchy of types. So for Type values, dynamic_type is redefined
to just return Type.type.

get a list of tuples indices and elements in this array

get a list of tuples indices and elements in this array

the euclidean norm of this sequence
i.e. the square of the sum of squares of this sequence

filter elements using predicate f
values for which f is false are dropped

get the index of pattern within this Sequence or nil if it does not exist

uses the Knuth-Morris-Pratt algorithm
port of racket code from this paper:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8EFA77D663D585B68630E372BCE1EBA4/S0956796824000017a.pdf/knuth-morris-pratt-illustrated.pdf

worst-case performance: O( seq_length ) + O( pattern_length )
worst-case space complexity: O( pattern_length )

is this sequence known to be finite? For infinite sequences, features like
count diverge.

get the first element of this Sequence

get the first element of this Sequence or default if sequence is empty

map each element of this Sequence to Sequence
Then flatten the result by one level,
essentially combining all the sequences.

fold the elements of this array using the given monoid.

e.g., to sum the elements of an array of i32, use a.fold i32.sum

fold the elements of this array using the given monoid and initial value

Used to fold an array tail-recursively

fold the elements of this non-empty Sequence using the given function

e.g., to find the minimum of a Sequence of i32, use `s.fold1 (<=)`

fold the elements of this Sequence using the given function and initial
value.

In case this Sequence is empty, the result is `e`.

e.g., to find the product of a Sequence of i32, use `s.foldf (*) 1`

apply f to all elements in this array

apply 'f' to each element 'e' as long as 'f e'

get a function that, given an index, returns the element at that index

get the contents of this array at the given index

determine the index of element x within this list. 0 if x is at the
head of the list, 1 if it comes directly after head, etc. nil if x is
not in the list.

all pairs of indices: (0,0), (0,1), (0,2), .. (length0-1, length1-1)

adds the corresponding index to
every element in the sequence

adds an index to every element
in the sequence starting at start_idx

a sequence of all valid indices to access this array. Useful e.g., for
`for`-loops:

for i in arr.indices do

indices range in first dimension

indices range in second dimension

consume all elements of this Sequence by f. This is an infix operator alias
for for_each.

Ex.: To print all the elements of a list, you can use

1..10 ! say

filter elements using predicate f, infix operator
synonym of filter.

NYI: What is better, 'infix |&' or 'infix &', or something else?

infix operand synonym for concat_sequences

map the Sequence to a new Sequence applying function f to all elements

This is an infix operator alias of map enabling piping code like

l := 1..10 | *10 | 300-

to obtain 290,280,270,...200

Note that map and therefore also this operator is lazy, so

_ := (1..10 | say)

will not print anything while

(1..10 | say).for_each _->unit

will print the elements since `for_each` is not lazy.

filter elements using predicate f, infix operator
synonym of filter.

check if predicate f holds for all elements

check if predicate f holds for at least one element

insert element v at position at

apply transducer to sequence, returning a sequence of results

example usage:
human(age i32) is
ages := map (Sequence i32) human i32 (x -> x.age)
gt_ten := filter (Sequence i32) i32 (x -> x > 10)
xf := ages ∘ gt_ten
say ([human(4), human(12), human(30)].into xf) # [12,30]

is this Sequence known to be array backed? If so, this means that operations
like index[] are fast.

is this Sequence empty?

check if argument is a valid index in this array.

Unlike for general Sequences, this performs in O(1).

get the last element of this Sequence

This may take time in O(count), in particular, it may not terminate
for an infinite Sequence.

get the last element of this Sequence or default if sequence is empty

map the Sequence to a new Sequence applying function f to all elements

This performs a lazy mapping, f is called only when the elements
in the resulting list are accessed.

variant of map which additionally passes the index to
the mapping function f

Map this Sequence to f applied to neighboring pairs of values
in this Sequence.

In case this Sequence has less than two elements, the result will
be the empty list.

ex. to obtain a list of differences you, you may use `map_pairs (-)`:

[2,3,5,7,11,13,17,19,23,29].map_pairs a,b->b-a

results in `[1,2,2,4,2,4,2,4,6]`

map the array to a new array applying function f to all elements

maximum value in the sequence

the median of the sequence
https://en.wikipedia.org/wiki/Median

minimum value in the sequence

the nth element in the sequence if it exists, wrapped in an option,
nil otherwise.

Complexity: if Sequence is array backed O(1) otherwise O(n)

create a new Sequence from tuples of all combinations of elements
of this Sequence and all elements of 'b' iterating of 'b' repeatedly
as follows

(Sequence.this[0] , b[0] )
(Sequence.this[0] , b[1] )
(Sequence.this[0] , b[2] )
(Sequence.this[0] , ... )
(Sequence.this[0] , b.last)
(Sequence.this[1] , b[0] )
(Sequence.this[1] , b[1] )
(Sequence.this[1] , ... )
(... , ... )
(Sequence.this.last, b.last)

calls `f` for element in the Sequence.

Unlike `for_each` this returns itself
allowing easier composition with
other Sequence features.

example:
[1,2,3,4,5]
.filter is_prime
.peek say
.drop_while <10

convenience prefix operator to create a string from a value.

This permits usage of `$` as a prefix operator in a similar way both
inside and outside of constant strings: $x and "$x" will produce the
same string.

create a new array with element i set to v. Grow the array in case i == length.

Complexity: O(array.this.length)

create a new array with element i set to v. Grow the array in case i >= length.
New array elements at indices array.this.length..i-1 will be set to z.

Complexity: O(max(i, array.this.length))

reduce this Sequence to R with an initial value init
and a reducing function f.
the reduction is finished once f yields abort or
if the end of the sequence is reached.

reduce this Sequence to `outcome R`
with an initial value `init` and a reducing function `f`.
the reduction is finished once `f` yields `abort` or
if the end of the sequence is reached.

replace all occurrences of old by new

replace the first n occurrences of old by new

reverse the order of the elements in this array

reverse the order of the elements in this array

map this Sequence to a list that contains the result of folding
all prefixes using the given monoid.

e.g., for a Sequence of i32 s, s.scan i32.sum creates a list of
partial sums (0..).map x->(s.take x).fold i32.sum

create a slice from this array's elements at index 'from' (included)
up to 'to' (excluded).

Complexity:
index access : O(1)
count : O(1)

sort this Sequence

sort this Sequence using the order defined by less_or_equal

create a tuple of two Sequences by splitting this at the given index, i.e.,
a Sequence of length 'at' and one of length 'count-at'.

at may be <= 0 or >= count, in which case the resulting tuple will be the
(empty list, Sequence.this.as_list) or (Sequence.this.as_list, empty list), resp.

does this sequence start with l?

the standard deviation of the sequence
https://en.wikipedia.org/wiki/Standard_deviation

create a lazy list of all the tails of this Sequence, including the complete Sequence
as a list and the empty list 'nil'.

create a list that consists only of the first n elements of this
Sequence, fewer if this Sequence has fewer elements

Lazily take the first elements of this Sequence for which predicate 'p' holds.

takes a transducer xf, a reducer f and an initial value
returns the result of applying the reducer xf f to the Sequence

the transpose of the array

flips the array along its diagonal

the variance of the sequence
https://en.wikipedia.org/wiki/Variance

create a new list from the result of applying 'f' to the
elements of this Sequence and 'b' in order.

string representation of this type to be used for debugging.

result has the form "Type of '<name>'", but this might change in the future

Maximum number of elements shown for on a call to `as_string` for a non-finite
Sequence.

monoid of Sequences with infix concatentation operation.

create an array2 from a Sequence of a Sequence of elements

There is no dynamic type of a type instance since this would result in an
endless hierarchy of types, so dynamic_type is redefined to just return
Type.type here.

equality implements the default equality relation for values of this type.

This relation must be

- reflexive (equality a b),
- symmetric (equality a b = equality b a), and
- transitive ((equality a b && equality b c) : equality a c).

result is true iff 'a' is considered to represent the same abstract value
as 'b'.

Is this type assignable to a type parameter with constraint `T`?

The result of this is a compile-time constant that can be used to specialize
code for a particular type.

is_of_integer_type(n T : numeric) => T : integer
say (is_of_integer_type 1234) # true
say (is_of_integer_type 3.14) # false

it is most useful in conjunction preconditions or `if` statements as in

pair(a,b T) is

=>

or

val(n T) is

Sequence is equatable only if T is

name of this type, including type parameters, e.g. 'option (list i32)'.

array -- create initialized one-dimensional immutable array

convenience prefix operator to create a string from a value.

This permits usage of `$` as a prefix operator in a similar way both
inside and outside of constant strings: $x and "$x" will produce the
same string.

NYI: Redefinition allows the type feature to be distinguished from its normal counterpart, see #3913

Get a type as a value.

This is a feature with the effect equivalent to Fuzion's `expr.type` call tail.
It is recommended to use `expr.type` and not `expr.type_value`.

`type_value` is here to show how this can be implemented and to illustrate the
difference to `dynamic_type`.