I-Beam

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I-Beam (⌶) is a primitive ambivalent function or monadic operator that takes a numeric code as an argument/operand and provides a range of ad-hoc operations. This range covers non-primitive functions, for example experimental features, interpreter-level control, access to the environment, and information about APL itself.

History

I-Beam was introduced in APL\360 as an ambivalent function for implementers to execute IBM System/360 (I-Beam being pronounced very similarly to IBM) instructions from program control. The convenience of this lead to I-Beam becoming directly available for use by anyone.[1] However, modern IBM-derived APLs replace all I-Beams with quad names. For example, 5⌶ became ⎕DL (Delay) while changing time unit from jiffies of 1⁄300th of a second to a whole second.

Later, after it became common to use arrays as operands, Dyalog APL began using the glyph as an operator where the operand selects functionality. It is used for testing experimental features, some of which may eventually become primitives or quad names. For example, 819⌶ became ⎕C (Case Convert), while introducing distinction between case folding (for case insensitive comparisons) and case mapping (for human presentation forms).

Mnemonics

In general, I-Beam's numeric operand isn't intended to be easily recalled. But some are given meaningful names.

One method is to devise a name from the Roman numeral letters I, V, X, L, C, D, and M:[2]

I-Beam Numeral
Colour Coding CC (200)
Colour Coding Information CCI (201)
Called Monadically CM (900)
Line Count LC (50100)

External links

References

  1. ↑ The Design of APL
  2. ↑ I-Beam Mnemonics
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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