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num_option

num_option

num_option -- optional numeric values

This is a pseudo-numeric type that handles one additional
value: nil. Any operation on nil will result in nil for a
numeric result or false for a boolean result.

Functions

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.
§
:
Any
 => 
list switch.A 
[Inherited from  switch]
converts switch into a list of either a single element in case
switch.this.exists or `nil`otherwise

redefines:

convenience feature to work around type inference issues
NYI remove when type inference gets better
§(sep String)
:
Any
 => 
String 
[Inherited from  Sequence]
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.
§
:
Any
 => 
String 
[Inherited from  Sequence]
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
monadic operator

Same as non-generic >>=, but also maps to a different type B.
§(chunk_size i32)
:
Any
 => 
list (list Sequence.T) 
[Inherited from  Sequence]
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
§
:
Any
 => 
i32 
[Inherited from  Sequence]
count the number of elements in this Sequence. Note that this typically
runs forever if executed on an endless list

For lists that are not array backed, this might require time in O(count).
get the number of non-overlapping matches of l within this
get the number of matches of l
§
:
Any
 => 
list Sequence.T 
[Inherited from  Sequence]
create a list that repeats the current Sequence indefinitely. In case 'Sequence.this'
is empty, returns 'nil'
§(n i32)
:
Any
 => 
list Sequence.T 
[Inherited from  Sequence]
create a list that consists of the elements of this Sequence except the first
n elements

NOTE: this may have performance in O(n) unless it is backed by an immutable array.
Lazily drop the first elements of this Sequence for which predicate 'p' holds.
§
:
Any
 => 
Type 
[Inherited from  Any]
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.
§
:
Any
 => 
Sequence.T 
[Inherited from  Sequence]
the euclidean norm of this sequence
i.e. the square of the sum of squares of this sequence
§
:
Any
 => 
bool 
[Inherited from  switch]
Does this switch contain a value of type A?
filter elements using predicate f
values for which f is false are dropped
§(pattern Sequence Sequence.T)
:
Any
 => 
option i32 
[Inherited from  Sequence]
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 )
§
:
Any
 => 
bool 
[Inherited from  Sequence]
is this sequence known to be finite? For infinite sequences, features like
count diverge.
§
:
Any
 => 
Sequence.T 
[Inherited from  Sequence]
get the first element of this Sequence

Sequence must not be empty, causes precondition failure if debug is enabled.
§(default Sequence.T)
:
Any
 => 
Sequence.T 
[Inherited from  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.
§(m Monoid Sequence.T)
:
Any
 => 
Sequence.T 
[Inherited from  Sequence]
fold the elements of this Sequence using the given monoid.

e.g., to sum the elements of a Sequence of i32, use s.fold i32.sum
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 (<=)`
§(B 
type
, f Function Sequence.foldf.B Sequence.foldf.B Sequence.T, e Sequence.foldf.B)
:
Any
 => 
Sequence.foldf.B 
[Inherited from  Sequence]
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`
create a list and call 'for_each f' on it
apply 'f' to each element 'e' as long as 'f e'
§
:
Any
 => 
switch.A 
[Inherited from  switch]
unwraps a switch that is known to contain a value

this can only be called in cases where it is known for sure that this switch
is not nil. A runtime error will be created otherwise.
§(default Lazy switch.A)
:
Any
 => 
switch.A 
[Inherited from  switch]
unwrap value or get default
group the elements of this sequence by a key of type K

f determines the key of an element
get a function that, given an index, returns the element at that index
§(i i32)
:
Any
 => 
Sequence.T 
[Inherited from  Sequence]
the nth element in the sequence, must exist
§(x Sequence.T)
:
Any
 => 
option i32 
[Inherited from  Sequence]
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.
adds the corresponding index to
every element in the sequence
§(I 
type
, start_idx Sequence.indexed.I)
:
Any
 => 
list (tuple Sequence.indexed.I Sequence.T) 
[Inherited from  Sequence]
adds an index to every element
in the sequence starting at start_idx
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
basic infix operations
comparison
monadic operator

redefines:

§(B 
type
, MB 
type
, f Unary (monad.infix >>=~.MB) monad.A)
:
Any
 => 
monad.infix >>=~.MB 
[Inherited from  monad]
 
[Abstract feature]
monadic operator to another monad

Apply f to elements of type A and wrap them in MB.

NYI: This is currently useless since a redefinition is not
allowed for features with generic arguments. Is there a way
we could allow this anyway?
monadic operator for bool result, false for nil
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
§(at i32, v Sequence.T)
:
Any
 => 
list Sequence.T 
[Inherited from  Sequence]
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]
§
:
Any
 => 
bool 
[Inherited from  Sequence]
is this Sequence known to be array backed? If so, this means that operations
like index[] are fast.
§
:
Any
 => 
bool 
[Inherited from  Sequence]
is this Sequence empty?
§(i i32)
:
Any
 => 
bool 
[Inherited from  Sequence]
check if argument is a valid index in this sequence.

Note that this may have a performance in O(i) unless this
Sequence is_array_backed.
§(MMA 
type
:monad monad.MA (monad monad.A monad.MA), a monad.join.MMA)
:
Any
 => 
monad.MA 
[Inherited from  monad]
 
[Abstract feature]
join operator

NYI: useless since redefinition currently not supported for
feature with generics.
§
:
Any
 => 
Sequence.T 
[Inherited from  Sequence]
get the last element of this Sequence

Sequence must not be empty, causes precondition failure if debug is enabled.

This may take time in O(count), in particular, it may not terminate
for an infinite Sequence.
§(default Sequence.T)
:
Any
 => 
Sequence.T 
[Inherited from  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.
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]`
§
:
Any
 => 
option Sequence.T 
[Inherited from  Sequence]
maximum value in the sequence
§
:
Any
 => 
option Sequence.T 
[Inherited from  Sequence]
the median of the sequence
https://en.wikipedia.org/wiki/Median
§
:
Any
 => 
option Sequence.T 
[Inherited from  Sequence]
minimum value in the sequence
§(n i32)
:
Any
 => 
option Sequence.T 
[Inherited from  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)
§
:
Any
 => 
bool 
[Inherited from  switch]
Does this switch contain a value of type A?
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
§
:
Any
 => 
bool 
[Inherited from  switch]
short-hand postfix operator for '!exists'
§
:
Any
 => 
bool 
[Inherited from  switch]
short-hand postfix operator for 'exists'
§
:
Any
 => 
bool 
[Inherited from  switch]
short-hand prefix operator for '!exists'
§
:
Any
 => 
String 
[Inherited from  Any]
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.
basic prefix operations
§(R 
type
, init Sequence.reduce.R, f Function (choice Sequence.reduce.R (abort Sequence.reduce.R)) Sequence.reduce.R Sequence.T)
:
Any
 => 
Sequence.reduce.R 
[Inherited from  Sequence]
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 Sequence
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
§(from i32, to i32)
:
Any
 => 
Sequence Sequence.T 
[Inherited from  Sequence]
create a slice from this Sequence that consists of the elements starting at index
from (including) up to index to (excluding).
sort this Sequence using the total order defined by less_or_equal
sort this Sequence using total order defined for 'f a[i]'
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'.
§(n i32)
:
Any
 => 
list Sequence.T 
[Inherited from  Sequence]
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
§
:
Any
 => 
switch.A 
[Inherited from  switch]
unwrap this switch

redefines:

§
:
Any
 => 
switch.A 
[Inherited from  switch]
value of a switch that is known to contain a value

This can only be called in cases where it is known for sure that this
switch is not a B. A runtime error will be created otherwise.
§(default switch.A)
:
Any
 => 
switch.A 
[Inherited from  switch]
value of a switch or default if switch contains B
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.

Type Features

§
:
Any
 is
 
[Inherited from  Type]
string representation of this type to be used for debugging.

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

redefines:

Maximum number of elements shown for on a call to `as_string` for a non-finite
Sequence.
monoid of Sequences with infix concatentation operation.
§
:
Any
 is
 
[Inherited from  Type]
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.

redefines:

§(T 
type
)
:
Any
 is
 
[Inherited from  Type]
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

§
:
Any
 is
 
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
§(a num_option.type.T)
:
Any
 is
 
[Redefinition of monad.type.return]
return function

redefines:

§
:
Any
 is
 
[Inherited from  Any]
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`.
last changed: 2024-09-18