Glossary
- Array
- The fundamental data structure in APL. A rectangular collection of scalars with a shape.
- Axis
- One dimension of an array. A matrix has two axes (rows and columns).
- Cell
- A subarray formed by trailing axes. A k-cell uses the last k axes. See Leading-Axis Theory.
- Catenate
- The
, function used dyadically. Joins two arrays along the last axis.
- Compress
- Dyadic
/ with a boolean left argument. Selects elements where the mask is 1.
- Dfn
- Direct function. A function defined with
{body} syntax, using ⍵ and ⍺ for arguments.
- Dop
- Direct operator. Like a dfn but takes function operands (
⍺⍺, ⍵⍵).
- Dyadic
- A function called with two arguments (left and right).
- Fill element
- The value used for padding: 0 for numbers, space for characters.
- Frame
- The leading axes that organise cells. If cells are k-cells, the frame is the first
rank-k axes.
- From
- The
⌷ function. Selects major cells along the leading axis.
- Grade
⍋ (grade up) and ⍒ (grade down). Return the indices that would sort an array.- Guard
- Conditional expression in a dfn:
condition : result.
- I-Beam
- The
⌶ operator. Calls a Python function from APL.
- Index origin
- The starting index for arrays, controlled by
⎕IO. MARPLE defaults to 1.
- Inner product
f.g applied to two arrays. Generalises matrix multiplication (+.×).- Iota
⍳n. Generates the integers from ⎕IO to n.- Major cell
- The largest cells of an array -- subarrays along the first axis.
- Monadic
- A function called with one argument (right only).
- Operator
- A higher-order construct that takes a function (and sometimes a value) and produces a derived function. Examples:
/ (reduce), ⍤ (rank).
- Outer product
∘.f applied to two arrays. Applies f to every combination of elements.- Pervasive
- A scalar function that applies element-by-element, penetrating through array structure.
- Rank (of an array)
- The number of dimensions. Scalar = 0, vector = 1, matrix = 2.
- Rank (operator)
- The
⍤ operator. Applies a function at a specified cell rank.
- Ravel
- Monadic
,. Flattens an array into a vector.
- Reduce
- The
/ operator applied to a function. Folds the function across the elements of an array.
- Replicate
- Dyadic
/ with a non-boolean left argument. Repeats each element the specified number of times.
- Reshape
- Dyadic
⍴. Creates an array with the specified shape, cycling the data.
- Scalar
- A single value (number or character). Rank 0.
- Scalar extension
- When a scalar is paired with each element of an array in a dyadic scalar function.
- Scan
- The
\ operator applied to a function. Running reduction producing all intermediate results.
- Shape
- A vector of integers giving the length along each axis. Monadic
⍴ returns the shape of its argument.
- Strand
- Numbers (or names) separated by spaces forming a vector:
1 2 3.
- Vector
- A one-dimensional array. Rank 1.
- Workspace
- A saved collection of variables and functions, stored as a directory of
.apl files.