Close composition
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In SHARP APL and J, a close composition is one of the operators Atop, Over, or Under, defined so that the overall result has function rank equal to the right operand. In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most modern APLs) are provided.
| Operator | SHARP | J close | J non-close | Modern |
|---|---|---|---|---|
| Atop | ⍥ |
@ |
@: |
⍤
|
| Over | ⍤ |
& |
&: |
⍥
|
| Under | ¨ |
&. |
&.: |
⍢
|
| APL features [edit] | |
|---|---|
| Built-ins | Primitives (functions, operators) ∙ Quad name |
| Array model | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |
| Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |
| Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function |
| Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |