miniapl

miniapl is an APL calculator for mathematics, with an interactive terminal and a Python API. Work with whole arrays, define functions, and combine them with operators. Numbers include approximate reals, complex numbers and exact rationals.

+/⍳10                  ⍝ 55
avg←+/÷≢ ⋄ avg 2 4 9   ⍝ 5
1r3+1r6                ⍝ 1r2

Using miniapl

Getting started: install and try a calculation.
REPL: type glyphs, edit input and display arrays/functions.
Command line: expressions, files and pipes.
Python: sessions, arrays, NumPy and callable APL functions.
Process interfaces: JSON lines and interruptible workers.
Language rules: evaluation, numbers, agreement, axes and fill.

Glyph reference

Each name below links to its definitions and examples. Examples show an equivalent APL value after ⍝. A monad takes one argument; a dyad takes two. Operators take functions or arrays and derive functions.

Functions

Glyph	Monad	Dyad
`+` Plus	Conjugate	Add
`-` Minus	Negate	Subtract
`×` Times	Direction	Multiply
`÷` Divide	Reciprocal	Divide
`⌊` Floor	Floor	Minimum
`⌈` Ceiling	Ceiling	Maximum
`\\|` Stile	Magnitude	Residue
`*` Star	Exponential	Power
`⍟` Log	Natural log	Logarithm
`○` Circle	Pi times	Circular functions
`!` Factorial	Factorial	Binomial
`ℙ` Prime	Nth prime (one-based)	Prime operations
`Ⓠ` Factor	Prime factors	Exponents / factor table
`Ⓟ` Polynomial	Roots / coefficients	Evaluate
`?` Question	Roll	Deal
`∨` Or	—	OR / GCD
`∧` And	—	AND / LCM
`⍲` Nand	—	NAND
`⍱` Nor	—	NOR
`~` Tilde	NOT	Without
`=` Equal	—	Equal
`≠` Not equal	Unique mask	Not equal
`<` Less	—	Less
`≤` Less or equal	—	Less or equal
`>` Greater	—	Greater
`≥` Greater or equal	—	Greater or equal
`≡` Match	Depth	Match
`≢` Tally	Tally	Not match
`⍴` Rho	Shape	Reshape
`,` Comma	Ravel	Catenate
`⍪` Table	Table	Catenate first
`⌽` Reverse	Reverse last	Rotate last
`⊖` Reverse first	Reverse first	Rotate first
`⍉` Transpose	Transpose	Reorder / diagonal axes
`↑` Take	Mix	Take
`↓` Drop	Split	Drop
`↕` Windows	—	Full leading-axis windows
`⊂` Enclose	Enclose	Partitioned enclose
`⊆` Nest	Nest	Partition
`⊃` Disclose	First / disclose	Pick
`⌷` Squad	Identity	Index
`⍳` Iota	Index generator	Index of
`⍸` Where	Where	Interval index
`∊` Member	Enlist	Membership
`∪` Union	Unique	Union
`∩` Intersection	—	Intersection
`⍷` Find	—	Find
`⍋` Grade up	Grade up	Grade with collation
`⍒` Grade down	Grade down	Grade with collation
`/` Slash	—	Replicate last
`⌿` Slash bar	—	Replicate first
`\` Backslash	—	Expand last
`⍀` Backslash bar	—	Expand first
`⊤` Encode	—	Encode
`⊥` Decode	—	Decode
`⌹` Domino	Matrix inverse	Matrix divide
`⊣` Left	Identity	Left
`⊢` Right	Identity	Right
`⍎` Execute	Execute	Execute in current scope (`''⍎Y`)
`⍕` Format	Format	Format by specification

Operators

f, g are functions; a, n, r are arrays or numbers.

Glyph	Form	Meaning
`/` Slash	`f/`	Reduce / n-wise reduce last
`⌿` Slash bar	`f⌿`	Reduce / n-wise reduce first
`\` Backslash	`f\`	Scan / seeded scan last
`⍀` Backslash bar	`f⍀`	Scan / seeded scan first
`¨` Each	`f¨`	Each
`⍨` Commute	`f⍨`, `a⍨`	Self / commute / constant
`∘` Compose	`f∘g`, `a∘f`, `f∘a`	Compose / bind
`⍤` Rank	`f⍤g`, `f⍤r`	Atop / rank
`⍥` Over	`f⍥g`	Over
`⍛` Behind	`f⍛g`	Behind
`.` Dot	`f.g`	Inner product
`⌝` Outer	`g⌝`	Outer product
`⌸` Key	`f⌸`	Key
`⍣` Power	`f⍣n`, `f⍣g`	Iterate / invert / repeat until
`⍣\` History	`f⍣\n`, `f⍣\g`	Iteration states, including initial state
`⇄` Inverse pair	`f⇄g`	Attach an explicit inverse
`⌾` Under	`f⌾g`	Transform, apply, inverse-transform
`∂` Derivative	`f∂`	Gradient / vector–Jacobian product
`◶` Agenda	`selector◶cases`	Select and call one function
`@` At	`f@a`, `a@g`	Functional amend
`⌺` Stencil	`f⌺a`	Stencil

Syntax and literals

Form	Meaning
`‿` Strand	Form a vector of values: `1‿+‿'abc'`
`←` Assign	Assignment, including modified/indexed/selective forms
`(…)` Parentheses	Grouping / nested array literals / trains
`[…]` Brackets	Array literals, indexing and axes
`;` Semicolon	Index-axis separator
`{…}` Braces	Defined function or operator
`⍺` Alpha, `⍵` Omega	Left / right argument
`⍺⍺` Alpha alpha, `⍵⍵` Omega omega	Left / right operand
`∇` Nabla, `∇∇` Nabla nabla	Function / operator self-reference
`:` Colon, `::` Error guard	Boolean / error guard
`⋄` Diamond	Statement or literal separator
`⍝` Comment	Comment
`⎕←` Quad	Explicit output
`⍬` Zilde	Empty numeric vector
`'…'` Quote	Character literal
`¯` Overbar	Negative literal sign
`∞` Infinity	Real infinity

Numeric notation x, r, j, E: see numbers.

System names

Names are case-insensitive. •A and •D are constant arrays; •C and •UCS are functions, usable with operators and composition.

Name	Meaning
`•A` Alphabet	Uppercase Latin alphabet
`•D` Digits	Decimal digits
`•C` Case	Unicode case conversion
`•UCS` Unicode	Unicode code points / encodings

Index origin: 1. Comparison tolerance: 1E¯14.

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