= 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 FOLDOC<<FootNote(''FOLDOC:'' see [[http://foldoc.org/|The Free On-Line Dictionary Of Computing]], Editor Denis Howe)>>.
||'''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.||
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-- PhilLast <<DateTime(2009-10-05T14:55:22Z)>>
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