Revision as of 15:30, 15 November 2019 by Miraheze>Adám Brudzewsky
High minus (¯) or Negative is the character used in numeric literals to indicate that a number is negated. APL syntax dicatetes that it be distinct from the function Negate in order to allow all numbers to be expressed as numeric literals. This ability is particularly useful in stranding or vector notation, since a number obtained from function application is harder to use in a strand—depending on the type of stranding available, it must either be parenthesized or cannot be stranded at all. It also allows negative numbers to be used as left arguments to functions, or as operands.
Examples
Using a high minus in a vector of numbers allows one number to be negated. With an ordinary minus, the expression is instead parsed as subtraction, where 2 3 is subtracted from 1. In both cases, APL expresses negative results using the high minus.
1 ¯2 3
1 ¯2 3
1 -2 3
¯1 ¯2
Because the high minus is part of a number and not a separate operation, it can be used as the left argument to a function without parenthesizing it. An ordinary minus will instead apply the function to the positive number and Negate the final result.
¯2 ↓ 3 4 5
3
-2 ↓ 3 4 5
¯5
In langauges which allow array operands, a negative number can be passed directly as an operand without parenthesizing it. Using an ordinary minus in the right operand will cause the minus alone to be used as the operand, while the number is not. In the expression below, it is passed as the left argument of Right (⊢), causing it to be discarded.
+∘¯1 ⊢3
2
+∘-1 ⊢3
¯3
| APL built-ins [edit]
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| Primitives (Timeline) |
Functions
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| Scalar
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| Monadic
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Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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| Dyadic
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Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
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| Non-Scalar
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| Structural
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Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
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| Selection
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First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
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| Selector
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Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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| Computational
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Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
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| Operators |
Monadic
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Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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| Dyadic
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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)
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| Quad names
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Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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