Range

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… ..

Range (…, ..) or Sequence is a dyadic primitive function which creates a vector of consecutive integers based on the start and end values given by its arguments. It serves as an index origin-agnostic alternative to Index Generator for creating a range of numbers. Range is currently implemented in NARS2000 (using the digraph ..), Extended Dyalog APL, and dzaima/APL.

Basic usage

If both arguments are scalar integers, Range creates the consecutive range between the two arguments inclusive. If the left argument is greater than the right argument, the result becomes a decreasing sequence. 

      3…8
3 4 5 6 7 8
      4…4
4
      5…¯5
5 4 3 2 1 0 ¯1 ¯2 ¯3 ¯4 ¯5
Works in: NARS2000, Extended Dyalog APL, dzaima/APL

It should be noted that, since the exact definition of Range has never been standardised, a different implementation might as well choose to return ⍬ or even throw a DOMAIN ERROR for X…Y when X>Y.

Extensions

NARS2000 supports step size and multi-dimensional range (giving the result similar to multi-dimensional Index Generator): 

      3 2..10  ⍝ Start, step, and end values
3 5 7 9
      (⊂3 4)..6  ⍝ Two start values, so the result is two-dimensional and nested
┌───┬───┬───┐
│3 4│3 5│3 6│
├───┼───┼───┤
│4 4│4 5│4 6│
├───┼───┼───┤
│5 4│5 5│5 6│
├───┼───┼───┤
│6 4│6 5│6 6│
└───┴───┴───┘
      (6 7)2..2  ⍝ Two start values with step size; the sign of step size is ignored
┌───┬───┬───┐
│6 7│6 5│6 3│
├───┼───┼───┤
│4 7│4 5│4 3│
├───┼───┼───┤
│2 7│2 5│2 3│
└───┴───┴───┘
Works in: NARS2000

In Extended Dyalog APL, the extension is focused on making it easier to produce integer or character vector constants: 

      1…10 20…100 80…0
1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 80 60 40 20 0
      'a'…'zA'…'Z'
abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ
Works in: Extended Dyalog APL

External links

Documentation


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)
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
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