Differences between revisions 15 and 24 (spanning 9 versions)

Glossary of APL terms

APL literature includes many terms whose meanings, though rigorous, differ slightly from elsewhere. Terms used but not defined here follow normal usage or are defined at FOLDOC¹.

Term	Description
adverb	monadic operator, taking its single operand on the left.
ambivalent	(of a dyadic function) permitting its left argument to be elided; nomadic²; either monadic or dyadic.
argument	value or reference passed to a function or operator.
array	data valued object of zero or more orthogonal dimensions in row-major order in which each item is a primitive scalar or another (enclosed) array; variable; noun.
cell	(of an array) sub-array whose dimensions are a suffix of those of the whole. The 2-cells of a 3D array are the planes whose dimensions are the numbers of rows and columns of the 3D array.
conjunction	dyadic operator, taking its two operands on the left and right.
define	create an operation by lexical assignment³ or association⁴ or in an editor⁵.
depth	(of an array) the number of levels of nesting.
derive	create a function by juxtaposition as a combination of existing arrays or functions with an operator or as a train.⁶.
dyadic	accepting or requiring two arguments or operands: left and right; having valence of two; binary.
element	(of an array) sub-array being a simple scalar at whatever depth. The elements of a simple array are also its items.
empty	(of an array) having one or more dimensions of length zero; null.
enclose	(of an array) convert into a scalar preserving all the original structure within. An enclosed array can occupy a single position in another array.
frame	(of an array) prefix of the dimensions of the array being the shape of the collection of cells of a given rank. The frame of the 2-cells of a 3D array is its first dimension; the numbers of planes.⁷
function	primitive, defined, derived or system operation or mapping that takes zero, one (right) or two (left & right) array valued arguments and may return an array valued result; verb.
item	(of an array) sub-array, which may be enclosed, occupying a single position in the outer structure of the array. The items of a simple array are also its elements.
matrix	(of an array) having two dimensions. (of a function) applying to matrices.
monadic	accepting or requiring one argument or operand; on the right for a function; on the left for an operator; having valence of one; unary
nested	(of an array) having one or more enclosed items or a prototype which is not a primitive scalar.
niladic	accepting no arguments; having valence of zero; nullary⁸.
operand	argument to an operator.
operator	primitive or defined operation or mapping that takes one (left) or two (left & right) function or array valued arguments (operands) and derives a function.
pervasive	(of a function) applying equally to scalars at any depth.
prototype	(of an array) the type of its first item.
rank	(of an array) number of dimensions. (of a function) ranks of arguments to which it applies.
reduction	application of a function between the items or cells of its right argument thus reducing the rank by removal of the dimension along which the items or cells are counted or the last dimension of the frame.
scalar	(of an array) having zero dimensions. (of a function) applying equally to or between all scalars in its argument(s).
scalar extension	replication of a scalar argument to the shape of the other. Performed implicitly by dyadic scalar functions and by the application of the primitive "each" operator to any dyadic function.
shape	(of an array) length of each dimension.
simple	(of a scalar) a single primitive datum. (of an array) composed entirely of primitive scalars.
strand	lexical juxtaposition of array valued names or expressions to form a larger, possibly nested, array⁹.
train	lexical juxtaposition of functions to form a new function of one of two kinds depending on the parity of the number of functions.¹⁰
type	(of an array) array of identical structure in which all numbers are zero and all characters are blanks.
valence	degree or number of arguments or operands of an operation.
vector	(of an array) having one dimension. (of a function) applying to vectors.
workspace	area of computer memory containing arrays and defined &/or derived operations or a file containing a preserved binary image of such.

-- PhilLast 2009-10-05 14:55:22

CategoryAboutApl

FOLDOC: see The Free On-Line Dictionary Of Computing, Editor Denis Howe (1)
nomadic: see APLX concepts (2)
define by lexical assignment: assigned←{expression in terms of ⍺ and/or ⍵} (3)
define by lexical association: ⎕FX 'r←a associated w' 'r←expression in terms of a and/or w' (4)
define in an editor: ∇edited or )EDIT edited (5)
derive: derived←∘.,/∘(⍳¨) (6)
frame: see J: Frame and Cell (7)
nullary: see Wikipedia: Nullary (8)
strand: stranded←0(1 2)('three' 'four')'five' (9)
train: mean←+⌿ ÷ ≢ see Dyalog: Function Trains (10)

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-||<rowclass="odd">'''Term'''    ||'''Description'''||
||<rowclass="even">''ambivalent''||(or nomadic<<FootNote(''nomadic:'' see [[http://www.microapl.co.uk/APL/apl_concepts_chapter6.html|APLX concepts]])>>)(of a ''dyadic'' ''function'') permitting its left ''argument'' to be elided.||
||<rowclass="odd">''argument''  ||value or reference passed to a ''function'' or ''operator''.||
||<rowclass="even">''array''     ||(or variable) data valued object of zero or more orthogonal dimensions in row-major order in which each item is a primitive ''scalar'' or another ''array''.||
||<rowclass="odd">''define''    ||create by lexical assignment<<FootNote(''define by lexical assignment:'' {{{assigned←{expression in terms of ⍺ and/or ⍵} }}})>> or association<<FootNote(''define by lexical association:'' {{{⎕FX 'r←a associated w' 'r←expression in terms of a and/or w'}}})>> or in an editor<<FootNote(''define in an editor:'' {{{∇edited}}} or {{{)EDIT edited}}})>>.||
||<rowclass="even">''depth''     ||(of an ''array'') the number of levels of ''nesting''.||
||<rowclass="odd">''derive''    ||create by juxtaposition as a combination of one or two existing ''arrays'' or ''functions'' with an ''operator''<<FootNote(''derive:'' {{{derived←∘.,/∘(⍳¨)}}})>>.||
||<rowclass="even">''dyadic''    ||accepting or requiring two ''arguments'' or ''operands'': left and right; having ''valence'' of two.||
||<rowclass="odd">''empty''     ||(or null)(of an ''array'') having one or more dimensions of length zero.||
||<rowclass="even">''function''  ||primitive, ''defined'', ''derived'' or system operation or mapping that takes zero, one (right) or two (left & right) ''array'' valued ''arguments'' and may return an ''array'' valued result.||
||<rowclass="odd">''matrix''    ||(of an ''array'') having two dimensions.<<BR>>(of a ''function'') applying to ''matrices''.||
||<rowclass="even">''monadic''   ||accepting or requiring one ''argument'' or ''operand''; on the right for a ''function''; on the left for an ''operator''; having ''valence'' of one.||
||<rowclass="odd">''nested''    ||(of an ''array'') having one or more items or a ''prototype'' which is not a primitive ''scalar''.||
||<rowclass="even">''niladic''   ||accepting no ''arguments''; having ''valence'' of zero.||
||<rowclass="odd">''operand''   ||''argument'' to an ''operator''.||
||<rowclass="even">''operator''  ||primitive or ''defined'' operation or mapping that takes one (left) or two (left & right) ''function'' or ''array'' valued ''arguments'' (''operands'') and ''derives'' a ''function''.||
||<rowclass="odd">''pervasive'' ||(of a ''function'') applying equally to ''scalars'' at any ''depth''.||
||<rowclass="even">''prototype'' ||(of an ''array'') the ''type'' of its first item.||
||<rowclass="odd">''rank''      ||(of an ''array'') number of dimensions.<<BR>>(of a ''function'') ''ranks'' of ''arguments'' to which it applies.||
||<rowclass="even">''reduction'' ||application of a ''function'' between the items of its right ''argument'' thus ''reducing'' the ''rank'' by one.||
||<rowclass="odd">''scalar''    ||(of an ''array'') having zero dimensions.<<BR>>(of a ''function'') applying to ''scalars''.<<BR>>(- extension) replication of a ''scalar'' ''argument'' to the ''shape'' of the other.||
||<rowclass="even">''shape''     ||(of an ''array'') length of each dimension.||
||<rowclass="odd">''simple''    ||(of a ''scalar'') a single primitive datum.<<BR>>(of an ''array'') composed entirely of primitive ''scalars''.||
||<rowclass="even">''strand''    ||lexical juxtaposition of ''array'' valued names or expressions to form a larger, possibly ''nested'', ''array''<<FootNote(''strand:'' {{{stranded←0(1 2)('three' 'four')'five'}}})>>.||
||<rowclass="odd">''type''      ||(of an ''array'') ''array'' of identical structure in which all numbers are zero and all characters are blanks.||
||<rowclass="even">''valence''   ||degree or number of ''arguments'' or ''operands'' of an operation.||
||<rowclass="odd">''vector''    ||(of an ''array'') having one dimension.<<BR>>(of a ''function'') applying to vectors.||
||<rowclass="even">''workspace'' ||area of computer memory containing ''array''s and ''defined'' &/or ''derived'' operations or a file containing a preserved binary image of such.||
+||'''Term'''    ||'''Description'''||
||''adverb''||''monadic operator'', taking its single ''operand'' on the left.||
||''ambivalent''||(of a ''dyadic'' ''function'') permitting its left ''argument'' to be elided; nomadic<<FootNote(''nomadic:'' see [[http://www.microapl.co.uk/APL/apl_concepts_chapter6.html|APLX concepts]])>>; either ''monadic'' or ''dyadic''.||
||''argument''  ||value or reference passed to a ''function'' or ''operator''.||
||''array''     ||data valued object of zero or more orthogonal dimensions in row-major order in which each ''item'' is a primitive ''scalar'' or another (''enclosed'') ''array''; variable; noun.||
||''cell''      ||(of an ''array'') sub-array whose dimensions are a suffix of those of the whole. The 2-cells of a 3D array are the planes whose dimensions are the numbers of rows and columns of the 3D ''array''.||
||''conjunction''||''dyadic operator'', taking its two ''operands'' on the left and right.||
||''define''    ||create an operation by lexical assignment<<FootNote(''define by lexical assignment:'' {{{assigned←{expression in terms of ⍺ and/or ⍵} }}})>> or association<<FootNote(''define by lexical association:'' {{{⎕FX 'r←a associated w' 'r←expression in terms of a and/or w'}}})>> or in an editor<<FootNote(''define in an editor:'' {{{∇edited}}} or {{{)EDIT edited}}})>>.||
||''depth''     ||(of an ''array'') the number of levels of ''nesting''.||
||''derive''    ||create a function by juxtaposition as a combination of existing ''arrays'' or ''functions'' with an ''operator'' or as a ''train''.<<FootNote(''derive:'' {{{derived←∘.,/∘(⍳¨)}}})>>.||
||''dyadic''    ||accepting or requiring two ''arguments'' or ''operands'': left and right; having ''valence'' of two; binary.||
||''element''   ||(of an ''array'') sub-array being a ''simple scalar'' at whatever ''depth''. The ''elements'' of a ''simple array'' are also its ''items''.||
||''empty''     ||(of an ''array'') having one or more dimensions of length zero; null.||
||''enclose''   ||(of an ''array'') convert into a ''scalar'' preserving all the original structure within. An ''enclosed array'' can occupy a single position in another ''array''.||
||''frame''||(of an ''array'') prefix of the dimensions of the array being the ''shape'' of the collection of ''cells'' of a given ''rank''. The frame of the 2-cells of a 3D array is its first dimension; the numbers of planes.<<FootNote(''frame:'' see [[http://www.jsoftware.com/primer/frame_and_cell.htm|J: Frame and Cell]])>>||
||''function''  ||primitive, ''defined'', ''derived'' or system operation or mapping that takes zero, one (right) or two (left & right) ''array'' valued ''arguments'' and may return an ''array'' valued result; verb.||
||''item''      ||(of an ''array'') sub-array, which may be ''enclosed'', occupying a single position in the outer structure of the ''array''. The ''items'' of a ''simple array'' are also its ''elements''.||
||''matrix''    ||(of an ''array'') having two dimensions.<<BR>>(of a ''function'') applying to ''matrices''.||
||''monadic''   ||accepting or requiring one ''argument'' or ''operand''; on the right for a ''function''; on the left for an ''operator''; having ''valence'' of one; unary||
||''nested''    ||(of an ''array'') having one or more ''enclosed items'' or a ''prototype'' which is not a primitive ''scalar''.||
||''niladic''   ||accepting no ''arguments''; having ''valence'' of zero; nullary<<FootNote(''nullary:'' see [[http://en.wikipedia.org/wiki/Arity#Nullary|Wikipedia: Nullary]])>>.||
||''operand''   ||''argument'' to an ''operator''.||
||''operator''  ||primitive or ''defined'' operation or mapping that takes one (left) or two (left & right) ''function'' or ''array'' valued ''arguments'' (''operands'') and ''derives'' a ''function''.||
||''pervasive'' ||(of a ''function'') applying equally to ''scalars'' at any ''depth''.||
||''prototype'' ||(of an ''array'') the ''type'' of its first ''item''.||
||''rank''      ||(of an ''array'') number of dimensions.<<BR>>(of a ''function'') ''ranks'' of ''arguments'' to which it applies.||
||''reduction'' ||application of a ''function'' between the ''items'' or ''cells'' of its right ''argument'' thus ''reducing'' the ''rank'' by removal of the dimension along which the items or cells are counted or the last dimension of the ''frame''.||
||''scalar''    ||(of an ''array'') having zero dimensions.<<BR>>(of a ''function'') applying equally to or between all ''scalars'' in its ''argument(s)''.||
||''scalar extension''||replication of a ''scalar'' ''argument'' to the ''shape'' of the other. Performed implicitly by ''dyadic scalar functions'' and by the application of the primitive "each" ''operator'' to any dyadic function.||
||''shape''     ||(of an ''array'') length of each dimension.||
||''simple''    ||(of a ''scalar'') a single primitive datum.<<BR>>(of an ''array'') composed entirely of primitive ''scalars''.||
||''strand''    ||lexical juxtaposition of ''array'' valued names or expressions to form a larger, possibly ''nested'', ''array''<<FootNote(''strand:'' {{{stranded←0(1 2)('three' 'four')'five'}}})>>.||
||''train''     ||lexical juxtaposition of ''functions'' to form a new function of one of two kinds depending on the parity of the number of functions.<<FootNote(''train'': {{{mean←+⌿ ÷ ≢}}} see [[http://help.dyalog.com/14.0/Content/Language/Introduction/Trains.htm#Function_Trains|Dyalog: Function Trains]])>>||
||''type''      ||(of an ''array'') ''array'' of identical structure in which all numbers are zero and all characters are blanks.||
||''valence''   ||degree or number of ''arguments'' or ''operands'' of an operation.||
||''vector''    ||(of an ''array'') having one dimension.<<BR>>(of a ''function'') applying to vectors.||
||''workspace'' ||area of computer memory containing ''array''s and ''defined'' &/or ''derived'' operations or a file containing a preserved binary image of such.||