Less than or Equal to: Difference between revisions

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== Boolean function ==
== Boolean function ==
{{Main|Boolean function}}
{{Main|Boolean function}}
When used as a [[Boolean function]] (that is, with argument consisting entirely of 0s and 1s), it represents [[wikipedia:Material conditional|material implication]], also known as the [[wikipedia:IMPLY gate|IMPLY gate]]:
When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Material conditional|material implication]] function, also known as the [[wikipedia:IMPLY gate|IMPLY gate]]:
{|class=wikitable
{|class=wikitable
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
Line 15: Line 15:
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|}
|}
In the context of logic, it can be read as ''implies''.  
In the context of logic, it can be read as ''implies''.
 
== External links ==
== External links ==


Revision as of 08:42, 29 March 2020

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

Main article: Boolean function

When the arguments to Equal to are Boolean, it is the material implication function, also known as the IMPLY gate:

≤ 0 1
0 1 1
1 0 1

In the context of logic, it can be read as implies.

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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