Precedence chart

Each table lists operators with the same precedence, one table for each precedence level. They are ordered from lowest precedence to highest. For descriptions of each operator, see the operator list. There’s also a reasonably human-readable precedence table in operators.py.

Terminology

• Unary operators take one operand, binary operators take two, and ternary operators take three.
• Associativity determines how to parse an expression containing multiple operators with the same precedence. Left-associative operators break the tie in favor of the leftmost subexpression: x-y-z is equivalent to (x-y)-z. Right-associative operators break the tie in favor of the rightmost subexpression: x:y:z is equivalent to x:(y:z). Unary operators do not have an associativity.
• Chaining is a third type of associativity, used for comparison operators. For example, x<y=z isn’t equivalent to either (x<y)=z (left-associative) or x<(y=z) (right-associative) but rather to (x<y)&(y=z).
• Fold default is the value returned when folding an empty iterable on this operator. For example, $+[] returns 0, while $*[] returns 1. Unary operators cannot be folded and thus do not have a default value.
• Itemwise indicates whether the operator applies item-by-item to Lists, both Lists and Ranges, or neither.
• In lambda indicates whether the operator can be applied to functions (typically starting from the identity function _) to build bigger functions.

Output and yank

Unary

Symbol	Name	Itemwise?	In lambda?
O	Output	No	No
P	Print	No	No
Y	Yank	No	No
YO	YankOutput	No	No
YP	YankPrint	No	No

Assignment

Binary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
:	Assign	None	No	No
::	Swap	None	No	No

If-then-else

Ternary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
?	Ifte	None	No	No

Logical or

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
|	Or	0	No	No

Logical and

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
&	And	1	No	No

Logical not

Unary

Symbol	Name	Itemwise?	In lambda?
!	Not	No	No

Exact equality

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
==	ObjEqual	1	No	No

Functional operators

Unary

Symbol	Name	Itemwise?	In lambda?
V	Eval	No	No
FI	Filter	No	No
FN	FilterNot	No	No
FU	FilterUnpack	No	No
FX	FilterIndexes	No	No
FJ	FilterJoin	No	No
RE	Recurse	No	No

Binary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
M	Map	[]	No	No
MC	MapCoords	[]	No	No
ME	MapEnumerate	[]	No	No
MJ	MapJoin	""	No	No
MM	MapMap	[]	No	No
MP	MapPairs	[]	No	No
MS	MapSum	0	No	No
MU	MapUnpack	[]	No	No
MF	MapFlatten	[]	No	No
FI	Filter	[]	No	No
FN	FilterNot	[]	No	No
FE	FilterEnumerate	[]	No	No
FU	FilterUnpack	[]	No	No
FX	FilterIndexes	[]	No	No
FJ	FilterJoin	[]	No	No
SK	SortKeyed	[]	No	No
DK	DescendingKeyed	[]	No	No
V	Eval	None	No	No

Ternary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
MR	MapRegex	[]	No	No
MZ	MapZip	[]	No	No

If-then-else (for lambdas)

Ternary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
\?	Ifte	None	No	Yes

Logical or (for lambdas)

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
\|	Or	0	No	Yes

Logical and (for lambdas)

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
\&	And	1	No	Yes

Logical not (for lambdas)

Unary

Symbol	Name	Itemwise?	In lambda?
\!	Not	No	Yes

Comparison operators

Binary (chaining)

Symbol	Name	Fold default	Itemwise?	In lambda?
<	NumLess	1	No	Yes
>	NumGreater	1	No	Yes
=	NumEqual	1	No	Yes
<=	NumLessEq	1	No	Yes
>=	NumGreaterEq	1	No	Yes
!=	NumNotEqual	1	No	Yes
LT	StrLess	1	No	Yes
GT	StrGreater	1	No	Yes
Q	StrEqual	1	No	Yes
LE	StrLessEq	1	No	Yes
GE	StrGreaterEq	1	No	Yes
NE	StrNotEqual	1	No	Yes
#=	LenEqual	1	No	Yes
#<	LenLess	1	No	Yes
#>	LenGreater	1	No	Yes
~=	FullMatch	1	No	Yes

In and not in

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
N	In	None	No	Yes
NI	NotIn	None	No	Yes

String conversion

Unary

Symbol	Name	Itemwise?	In lambda?
RP	Repr	No	No
ST	Str	No	No

Low-precedence list operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
CB	Combinations	[]	No	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
M/MX	Max	No	Yes
N/MN	Min	No	Yes
RC	RandChoice	No	Yes
SH	Shuffle	No	Yes
SN	SortNum	No	Yes
SS	SortString	No	Yes
DN	DescendingNum	No	Yes
DS	DescendingString	No	Yes
UQ	Unique	No	Yes
EN	Enumerate	No	Yes
PM	Permutations	No	Yes
FL	Flatten	No	Yes
FA	FlattenAll	No	Yes

Append, push, and pop

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
AE	AppendElem	[]	No	Yes
AL	AppendList	[]	No	Yes
PE	PrependElem	[]	No	Yes
PU	Push	[]	No	Yes
PB	PushBack	[]	No	Yes
PK	Pick	[]	No	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
PO	Pop	No	Yes
DQ	Dequeue	No	Yes

High-precedence list operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
^	Split	[]	Both	Yes
^@	SplitAt	[]	No	Yes
@?	Find	None	No	Yes
@*	FindAll	[]	No	Yes
<>	Group	[]	No	Yes
CH	Chop	[]	No	Yes
J	Join	""	No	Yes
JW	JoinWrap	None	No	Yes
RL	RepeatList	[]	No	Yes
Z	Zip	[]	No	Yes
ZD	ZipDefault	[]	No	Yes
ZJ	ZipJoin	[]	No	Yes
H	Prefix	[]	No	Yes
S	Suffix	[]	No	Yes
WV	Weave	[]	No	Yes
UW	Unweave	[]	No	Yes
CP	CartesianProduct	[]	No	Yes
CG	CoordinateGrid	None	Both	Yes
ZG	ZeroGrid	None	Both	Yes
OG	OneGrid	None	Both	Yes
TD	ToDigits	[]	No	Yes
FD	FromDigits	[]	No	Yes

Ternary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
RA	ReplaceAt	None	No	Yes
TR	Transliterate	None	No	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
^	Split	Both	Yes
<>	Group	No	Yes
CH	Chop	No	Yes
J	Join	No	Yes
R/RV	Reverse	No	Yes
RF	Reflect	No	Yes
PZ	Palindromize	No	Yes
QR	QuadReflect	No	Yes
QP	QuadPalindromize	No	Yes
Z	Zip	No	Yes
ZD	ZipDefault	No	Yes
ZJ	ZipJoin	No	Yes
H	Prefix	No	Yes
S	Suffix	No	Yes
WV	Weave	No	Yes
UW	Unweave	No	Yes
CP	CartesianProduct	No	Yes
CG	CoordinateGrid	Both	Yes
ZG	ZeroGrid	Both	Yes
OG	OneGrid	Both	Yes
EY	IdentityMatrix	Both	Yes
TD	ToDigits	No	Yes
FD	FromDigits	No	Yes

Replace

Ternary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
R	Replace	None	No	No

Low-precedence string/regex operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
WR	Wrap	""	Yes	Yes
~	FirstMatch	""	Yes	Yes

Concatenate

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
.	Cat	""	Both	Yes

Regex modifiers

Unary

Symbol	Name	Itemwise?	In lambda?
X	Regex	No	Yes
.	Dot	List	Yes
K	KleeneStar	List	Yes

Remove

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
RM	Remove	""	No	Yes
DC	DeleteChars	""	Both	Yes

String repetition

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
X	StrMul	""	Both	Yes

Strip, trim, and case conversion

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
||	Strip	""	List	Yes
|>	LStrip	""	List	Yes
<|	RStrip	""	List	Yes
TM	Trim	""	List	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
||	Strip	List	Yes
|>	LStrip	List	Yes
<|	RStrip	List	Yes
TM	Trim	List	Yes
LC	Lowercase	List	Yes
UC	Uppercase	List	Yes
SC	Swapcase	List	Yes
TC	Titlecase	List	Yes
IC	InitialCaps	List	Yes

Range and to-base

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
,	Range	None	Both	Yes
\,	InclRange	None	Both	Yes
RR	RandRange	0	Both	Yes
TB	ToBase	0	Both	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
,	RangeTo	Both	Yes
\,	InclRangeTo	Both	Yes
RR	RandRangeTo	Both	Yes
TB	ToBase	Both	Yes

Low-precedence numeric operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
BA	BitwiseAnd	-1	Both	Yes
BO	BitwiseOr	0	Both	Yes
BX	BitwiseXor	0	Both	Yes
AT	Arctan	None	Both	Yes
CM	NumCmp	0	No	Yes
|<	Floor	0	Both	Yes
>|	Ceil	0	Both	Yes
RN	RoundNearest	0	Both	Yes
RZ	RoundZero	0	Both	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
BN	BitwiseNot	Both	Yes
SI	Sine	Both	Yes
CO	Cosine	Both	Yes
TA	Tangent	Both	Yes
SE	Secant	Both	Yes
CS	Cosec	Both	Yes
CT	Cotan	Both	Yes
AT	Arctan	Both	Yes
RD	Radians	Both	Yes
DG	Degrees	Both	Yes
BL	BitLength	Both	Yes
|<	Floor	Both	Yes
>|	Ceil	Both	Yes
RN	RoundNearest	Both	Yes
RZ	RoundZero	Both	Yes

Addition and subtraction

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
+	Add	0	List	Yes
-	Sub	0	List	Yes
AD	AbsoluteDiff	0	Both	Yes

Multiplication and division

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
*	Mul	1	Both	Yes
/	Div	1	Both	Yes
%	Mod	0	Both	Yes
//	IntDiv	1	Both	Yes

High-precedence numeric operators

Unary

Symbol	Name	Itemwise?	In lambda?
+	Pos	List	Yes
-	Neg	Both	Yes
/	Invert	Both	Yes
%	Mod2	Both	Yes
E/**	Pow	Both	Yes
EE	PowerOfTen	Both	Yes
RT	Sqrt	Both	Yes
SQ	Square	Both	Yes
HV	Halve	Both	Yes
HU	HalveUp	Both	Yes
DB	Double	Both	Yes
EX	Exponential	Both	Yes
LN	NaturalLog	Both	Yes
LB	BinaryLog	Both	Yes
LD	DecimalLog	Both	Yes

Binary (right-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
E/**	Pow	1	Both	Yes
EE	PowerOfTen	1	Both	Yes
RT	Root	1	Both	Yes

Very high-precedence operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
FB	FromBase	0	Both	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
U	Inc	List	Yes
D	Dec	List	Yes
#	Len	No	Yes
A	Asc	Both	Yes
C	Chr	Both	Yes
AB	Abs	Both	Yes
SG	Sign	Both	Yes
FB	FromBase	Both	Yes

Highest-precedence operators

Binary (left-associative)

Symbol	Name	Fold default	Itemwise?	In lambda?
@	At	None	No	Yes
@<	LeftOf	None	No	Yes
@>	RightOf	None	No	Yes

Unary

Symbol	Name	Itemwise?	In lambda?
@	At	No	Yes
@<	LeftOf	No	Yes
@>	RightOf	No	Yes
++	Inc	List	Yes
--	Dec	List	Yes