 Main article: Comparison function
Less than or Equal to (≤
) is a comparison function which tests whether the left argument is tolerantly less than or equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the negation of Less than (<
), and in fact was called Not greater in APL\360.
Boolean function
When the arguments to Less than or Equal to are Boolean, it is the material implication Boolean function, also known as the IMPLY gate:
In the context of logic, it can be read as implies.
Less than or Equal to Scan is an occasionally used pattern related to Less than Scan. While <\
changes all 1s after the first to 0, ≤\
changes all 0s after the first to 1. Thus ≤\A
$\Leftrightarrow$ ~<\~A
.
≤\ 1 0 1 0 0 0 1 0
1 0 1 1 1 1 1 1
≤\
appears in the FinnAPL idiom library as entry 350, "Not first zero".
External links
Documentation
APL builtins [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

NonScalar

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 ∙ IBeam ∙ 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
