8.1) Built in Predicates

All built-in predicates act like user-defined predicates as described in the previous section: they have one Input variable ? and one Output variable .. However, built-in predicates also have a subscript, which is an additional parameter which can change the behavior of the predicate.

For example, the built-in predicate +, by default, applies the constraint that the sum of the elements of ? must result in .. In that case, the input is necessarily a list. However, the built-in predicate +₁, with subscript ₁, applies the constraint that ? + 1 = . (i.e. incrementation).

It is possible to indicate that a value of ? must be used as a subscript for the predicate, using ₍ and ₎ (first and last). For example, in ["test",2]∋₎, 2 (the last element of the Input) will be used as subscript for ∋.

A lack of subscript means that the predicate uses its default behavior (which may be the same as the behavior for a specific subscript, see the list below).

↙ Subscript arrow

You can use the subscript arrow ↙ to pass the immediately following variable as a subscript to a predicate (like ₍ and ₎, in a shorter way that does not require the input to contain that variable).

For example, 13+↙7 will output 14.

List of built-in predicates

Symbol	Name	Subscript	Description
≤	Less-equal	Default=0 1	? ≤ . ? is a non-decreasing list
≥	Greater-equal	Default=0 1	? ≥ . ? is a non-increasing list
∈	Contains	Default I	. contains ? . contains ? at index I
∋	In	Default I	. is an element of ? . is the Ith element of ?
⊆	Superset	Default=0	? is an ordered subset of .
⊇	Subset	Default=0	. is an ordered subset of ?
↔	Reverse	Default=0	. is the reverse of ?
↰	Call predicate	Default I	Call the current predicate recursively Call the Ith predicate
↺	Cyclically permute counterclockwise	Default=1 I	Cyclically permute ccw once Cyclically permute ccw I times
↻	Cyclically permute clockwise	Default=1 I	Cyclically permute cw once Cyclically permute cw I times
√	Root	Default=2 I	. × . = ? Ith root
⌉	Ceil	Default=0 1	. is the max of ? . = ceil(?)
⌋	Floor	Default=0 1	. is the min of ? . = floor(?)
⟦	Range ascending	Default=0 1 2 3 4 5 6	. = [0, …, ?] . = [1, …, ?] . = [?⌋, …, ?⌉] . = [?⌋, …, ?⌉ - 1] . = [?⌋ + 1, …, ?⌉] . = [0, …, ? - 1] . = [1, …, ? - 1]
⟧	Range descending	Default=0 1 2 3 4 5 6	. = [?, …, 0] . = [?, …, 1] . = [?⌉, …, ?⌋] . = [?⌉ - 1, …, ?⌋] . = [?⌉, …, ?⌋ + 1] . = [? - 1, …, 0] . = [? - 1, …, 1]
ℕ	Natural integer	Default=0 I	? = . ≥ 0 ? = . ≥ I
ℤ	Integer	Default I	? = . is any integer ? = . ≤ -I
ℝ	Float	Default I	? = . is a float Convert ? from int to float .
≠	Different	Default	All elements of ? = . are different
≡	Identity	Default	. = ?
÷	Integer division	Default=0 I	? = [A,B], . = floor(A/B) . = floor(?/I)
×	Multiply	Default I	. is the product of element of ? . = ? × I
%	Modulo	Default=0 I	? = [A,B], . = A mod B . = ? mod I
*	Exp	Default=0 1 2 3 4 5 6 7 8 9 10 11 12 13	. = exp(?) . = ln(?) . = cos(?) . = sin(?) . = tan(?) . = arccos(?) . = arcsin(?) . = arctan(?) . = cosh(?) . = sinh(?) . = tanh(?) . = arcosh(?) . = arsinh(?) . = artanh(?)
+	Plus	Default=0 I	. is the sum of elements of ? . = ? + I
-	Minus	Default=0 I	. is the difference of elements of ? . = ? - I
/	Divide	Default=0 1 I	? = [A,B], . = A/B . = 1/? . = ?/I
<	Less	Default=0 1	? < . ? is an increasing list
=	Equal	Default X	All elements of ? are equal All elements of ? are X
>	Greater	Default=0 1	? > . ? is a decreasing list
\	Transpose	Default=0	. = ?ᵀ
^	Power	Default I	? = [A,B], . = A^B . = ?^I
a	Adfix	Default 0 1	. is an adfix of ? . is a prefix of ? . is a suffix of ?
b	Behead	Default=1 I	. = ? minus the head . = ? minus the first I elements
c	Concatenate	Default=0 I	Concatenate ? into . Concatenate ? into ., length(?) = I
d	Duplicates	Default=0	. is ? without duplicates
e		Default
f	Factors	Default	. is the list of factors of ?
g	Group	Default=1 I	. = [?] . = […[?]…] (nested I times)
h	Head	Default I	. is the first element of ? . is the first I elements of ?
i	Index	Default 1	. = [E,I], E is the Ith element of ? Same as default but 1-indexed
j	Juxtapose	Default=2 I	. is ? concatenated with ? . is ? concatenated I times
k	Knife	Default=1 I	. = ? minus the tail . = ? minus the last I elements
l	Length	Default I	. is the length of ? . = ? has length I
m		Default
n		Default
o	Order	Default=0 1	. is ? sorted in ascending order . is ? sorted in descending order
p	Permute	Default=0	. is a permutation of ?
q		Default
r		Default
s	Substring	Default I	. is a sublist of consecutive elements of ? . is a sublist of I consecutive elements of ?
t	Tail	Default I	. is the last element of ? . is the last I elements of ?
u		Default
v		Default
w	Write	Default=0 1	Write ? to STDOUT. . ignored ? = [A,B], write A with format B
x	Xterminate	Default=0	? = [H|T], . is H with elements of T removed
y		Default
z	Zip	Default 0 1	. is elements of ? zipped together, cycles on elements shorter than the longest one . is elements of ? zipped together, stops once the shortest element is depleted . is elements of ? zipped together, does not cycle on short elements
ạ	To codes	Default	. is the list of char codes of string ?
ḅ	Blocks	Default	. concatenated is ?. All elements of elements of . are equal
ḍ	Dichotomize	Default=2 I	. is ? splitted in half . is ? splitted in I equal parts
ẹ	Elements	Default	. is the list of elements of ?. Automatically vectorizes
ḥ		Default
ị	To number	Default	. is the number represented by the string ?
ḳ		Default
ḷ	Lowercase	Default	. is ? lowercased
ṃ		Default
ṇ	Split lines	Default 1 2 3	. is the list of lines in the string ? . is ? splitted on spaces . is ? splitted on spaces and lines ? ṇṇ₁ᵐ .
ọ	Occurences	Default	. is a list of couples [E∈?, number of E in ?]
ṛ	Random element	Default	. is a random element of ?
ṣ	Shuffle	Default	. is a random permutation of ?
ṭ		Default
ụ	Uppercase	Default	. is ? uppercased
ṿ		Default
ẉ	Writeln	I	Like w followed by a linebreak
ỵ		Default
ẓ		Default
ȧ	Absolute value	Default	. = abs(?)
ḃ	Base	Default=2 I	. is the list of digits of ? in base 2 . is the list of digits of ? in base I
ċ	Coerce	Default 1 2	.= ? is a list . = ? is an integer . = ? is a string
ḋ	Prime decomposition	Default	. is the list of prime factors of ?
ė		Default
ḟ	Factorial	Default	. is the factorial of ?
ġ	Groups	Default I	. is ? splitted into groups of equal length (except maybe the last one) . is ? splitted into groups of length I (except maybe the last one)
ḣ		Default
ṁ	Matrix	Default I	. = ? is a square matrix . = ? is a I×I matrix
ṅ	Negate	Default	. = -I
ȯ		Default
ṗ	Prime	Default	. = ? is a prime number
ṙ	Random number	Default 1 2	. is a random number in [0, ?] . is a random number in [0, 1] . is a random number in [A,B] = ?
ṡ	Sign	Default	. is the sign of ?
ṫ	To string	Default	. is the number ? cast as a string
ẇ		Default
ẋ	Cartesian product	Default	. is the cartesian product of elements of ?
ẏ		Default
ż		Default
≜	Label	Default=0 1	Affects an integer to . = ? (or their elements) that matches their constraints Same as Default but in a random order.