Zilde

Zilde (⍬), or Zero-tilde (which the common name is a portmanteau of), is the empty numeric vector. It shares its name with the glyph used to represent it, a zero overstruck with a tilde. It is the shape of any scalar, although its own shape is <syntaxhighlight lang=apl inline>,0</source>. This is because, as a vector, it has exactly one axis, and this axis has length 0. Zilde is equivalent to <syntaxhighlight lang=apl inline>⍳0</source> and <syntaxhighlight lang=apl inline>⍴0</source> and <syntaxhighlight lang=apl inline>0⍴0</source>. Being numeric, Zilde's prototype is 0.

The glyph Zilde is notable in that it represents an array rather than a primitive function or primitive operator. This usage was introduced in NARS and included in Dyalog APL and many other dialects influenced by these. In most of these APLs it is the only array literal which is produced using its own token rather than being part of a family of array literals like numeric literals, strings, or system constants. A similar special literal is SHARP APL's nil (<syntaxhighlight lang=apl inline>∘</source>), which corresponds to <syntaxhighlight lang=apl inline>⊂⍬</source>, and Dyalog APL's namespace reference to the root of the workspace (<syntaxhighlight lang=apl inline>#</source>).

It should be noted that the empty numeric vector (<syntaxhighlight lang=apl inline>⍬</source>) is distinct from the empty character vector (<syntaxhighlight lang=apl inline></source>) even though they have the same shape and the same elements: <syntaxhighlight lang=apl>

     ∧/⍬=

1

     ⍬≡

0 </source> This is because <syntaxhighlight lang=apl inline>⍬=</source> itself returns an empty numeric vector, and reducing an empty vector with the Logical And function (<syntaxhighlight lang=apl inline>∧</source>) yields the identity element of Logical And, which is 1. However, match takes empty array prototypes into account as well as shapes and elements, so it indicates that the arrays are different.

Zilde can be used to concisely produce other empty arrays, for example:

<syntaxhighlight lang=apl inline>⍬⊤⍬</source> gives a 0-row 0-column numeric matrix, identical to <syntaxhighlight lang=apl inline>0 0⍴0</source>.
<syntaxhighlight lang=apl inline>⍪⍬</source> gives a 0-row 0-column numeric matrix, identical to <syntaxhighlight lang=apl inline>0 1⍴0</source>.
<syntaxhighlight lang=apl inline>,¨⍬</source> gives an empty vector of 1-element numeric vectors, identical to <syntaxhighlight lang=apl inline>0⍴⊂,0</source>.
<syntaxhighlight lang=apl inline>⍪¨⍬</source> gives an empty vector of 1-by-1 numeric matrices, identical to <syntaxhighlight lang=apl inline>0⍴⊂,0</source>.

APL built-ins [edit]
Primitives (Timeline)	Functions
Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

APL glyphs [edit]
Information	Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics ∙ Overstrikes ∙ Migration level
Individual glyphs	Jot (`∘`) ∙ Right Shoe (`⊃`) ∙ Up Arrow (`↑`) ∙ Zilde (`⍬`) ∙ High minus (`¯`) ∙ Dot (`.`) ∙ Del (`∇`)

Zilde

Navigation menu

Search