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 20.

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 2 3 4/5/6/7	Write ? to STDOUT. . ignored ?=[A,B], write A with format B. . ignored Same as 0 with ? = . Same as 1 with ? = . Like 0/1/2/3 respectively, but it will only print at the end of the main predicate, meaning printed variables with those subscripts can be further constrained after the actual call to write in the program.
x	Xterminate	Default=0	? = [H|T], . is H with elements of T removed
y		Default
z	Zip	Default 0 1 2	. 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 Same as default but ensures that all elements of ? have the same length
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	. = -?
ȯ		Default
ṗ	Prime	Default	. = ? is a prime number
ṙ	Random number	Default 1 2	. is a random number in [0, ?] (if ? is an integer, then . is an integer; if ? is a float, then . is a float) (this holds for all subscripts) . 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.