TinyAPL

TinyAPL (read like tiny apple) is a tiny APL dialect and interpreter in Haskell. It is being implemented as a series of articles available here.

• Part 1: Introduction & Arrays
• Part 2: Functions & Operators
• Part 3: More Primitives
• Part 4: Finally, Parsing!
• Part 5: Array Notation and Reductions

Features

Marked features are supported, unmarked features are planned

• Types
  • Arrays
    • complex numbers
    • unicode characters
    • boxes (nested arrays)
  • Functions
  • Monadic Operators ("Adverbs")
  • Dyadic Operators ("Conjunctions")
• Syntax
  • number literals
    • decimal point .
    • negative sign ¯
    • exponent notation ⏨
    • complex notation ᴊ
    • complex phase notation? ∠
    • infinities ∞
  • character literals '
  • string literals "
    • escapes with ⍘
      • ⍘⍘ -> ⍘
      • ⍘" -> "
      • ⍘n -> newline
      • ⍘r -> carriage return
      • ⍘t -> tab
      • ⍘{22be} -> unicode?
  • names
    • array names (abc)
    • function names (Abc)
    • monadic operator names (_Abc)
    • dyadic operator names (_Abc_)
  • assignment ←
  • dfns/dops
    • multiple statements ⋄
    • guards :
    • early return ■
    • dfns {...}, dadvs _{...}, dconjs _{...}_
    • refer to arguments and operands: ⍺ left argument, ⍵ right argument, ⍺⍺ left array operand, ⍶⍶ left function operand, ⍵⍵ right array operand, ⍹⍹ right function operand
    • recursion: ∇ recurse function, _∇ recurse adverb, _∇_ recurse conjunction
  • comments ⍝
    • inline comments? ⟃/⟄
  • console I/O with ⎕ and ⍞
  • array notation ⟨/⋄/⟩ and [/⋄/]
• primitives
  • arrays
    • ⍬
  • number functions
    • + conjugate
    • + add
    • - negate
    • - subtract
    • × direction
    • × multiply
    • ÷ reciprocal
    • ÷ divide
      • 0÷0 is 1
      • x÷0 is an error
    • * exponential
    • * power
    • ⍟ ln
    • ⍟ log
      • 1⍟1 is 1
      • 1⍟y is an error
      • x⍟0 is an error
    • ○ pi times
    • ○ circular
      • 0○y is $\sqrt{1 - y^2}$
      • 1○y is $\sin y$
      • ¯1○y is $\arcsin y$
      • 2○y is $\cos y$
      • ¯2○y is $\arccos y$
      • 3○y is $\tan y$
      • ¯3○y is $\arctan y$
      • 4○y is $\sqrt{1 + y^2}$
      • ¯4○y is $\sqrt{y^2 - 1}$
      • 5○y is $\sinh y$
      • ¯5○y is $\mathop{\text{arsinh}} y$
      • 6○y is $\cosh y$
      • ¯6○y is $\mathop{\text{arcosh}} y$
      • 7○y is $\tanh y$
      • ¯7○y is $\mathop{\text{artanh}} y$
      • 8○y is $\sqrt{-1 - y^2}$
      • ¯8○y is $-\sqrt{-1 - y^2}$
      • 9○y is $\mathop{\text{Re}} y$
      • ¯9○y is $y$
      • 10○y is $\left|y\right|$
      • ¯10○y is $\overline y$ (conjugate of $y$)
      • 11○y is $\mathop{\text{Im}} y$
      • ¯11○y is $iy$
      • 12○y is $\mathop{\text{Arg}} y$
      • ¯12○y is $e^{iy}$
    • √ square root
    • √ root
    • ⌊ floor
    • ⌊ minimum
    • ⌈ ceiling
    • ⌈ maximum
    • ⸠ round
    • ⸠ average?
    • ⌹ matrix inverse
    • ⌹ matrix divide
    • ! factorial/gamma
    • ! binomial
    • | magnitude
    • | remainder
    • ∨ greatest common divisor
    • ∧ least common multiple
    • ⊕ cartesian (x⊕y is $x + iy$)
    • ⊕ pure imaginary (⊕y is $iy$)
    • ⊗ polar (x⊗y is $xe^{iy}$)
    • ⊗ unit polar (⊗y is $e^{iy}$)
    • ∡ phase
    • ∡ set phase ((|y)⊗x)
    • ℜ real part
    • ℜ set real part
    • ℑ imaginary part
    • ℑ set imaginary part
    • ⊥ decode
    • ⊥ base 2 decode
    • ⊤ encode
    • ⊤ base 2 encode
  • boolean functions
    • = equals
    • ≠ not equals
    • < less
    • ≤ less or equal
    • ≥ greater or equal
    • > greater
    • ≡ match
    • ≢ not match
    • ∧ and
    • ∨ or
    • ⍲ nand
    • ⍱ nor
    • ~ not
  • set functions
    • ∪ unique
    • ∪ union
    • ∩ intersection
    • ~ difference
    • § symmetric difference
    • ≠ nub sieve
    • multisets?
  • property functions
    • ⍳ index of
    • ⍸ interval index
    • ∊ element of
    • ⍷ find
    • ⍷ type? depends on if prototypes are added or not
    • ≡ depth
    • ⍴ shape
    • ≢ tally
    • ϼ rank
  • array creation functions
    • ⍳ index generator
    • ? roll
    • ? deal
    • … range?
    • ⍮ pair
    • ⍮ half pair
  • array manipulation functions
    • ↑ take
    • ↓ drop
    • ↑ prefixes (mix is ⊃⍤0)
    • ↓ suffixes (split is ⊂⍤1)
    • ⊂ enclose
    • ⊆ nest
    • ⊂ partitioned enclose
    • ⊆ partition
    • ⍋ grade up
    • ⍒ grade down
    • ⍋ sort by up?
    • ⍒ sort by down?
    • ≤ sort up? useless with sort by (⍋⍨)
    • ≥ sort down? as above
    • ⍸ where
    • ∊ enlist
    • ⌿ replicate
    • ⍀ expand? (might not make much sense without prototypes)
    • / replicate last
    • \ expand last?
    • , ravel
    • ⍪ table
    • ⍪ catenate
    • , catenate last
    • ⍴ reshape
    • ϼ rerank (generalized version of promote/demote: introduce leading length-1 axes or combine leading axes)
    • ⊖ reverse
    • ⊖ rotate
    • ⌽ reverse last
    • ⌽ rotate last
    • ⍉ transpose
    • ⍉ reorder axes
  • array lookup functions
    • ⊃ first
    • ⊇ last
    • ⊇ from
    • ⌷ index
    • ⊃ pick
  • misc functions
    • ⊢/⊣ same
    • ⊢ right
    • ⊣ left
    • ⍎ execute
    • ⍕ format
    • ↗ raise?
  • operators
    • ⤈ reduce top-to-bottom (first)
    • ⤈ windowed reduce top-to-bottom (first)
    • ⤉ reduce bottom-to-top (first)
    • ⤉ windowed reduce bottom-to-top (first)
    • ⇸ reduce left-to-right (last)
    • ⇸ windowed reduce left-to-right (last)
    • ⇷ reduce right-to-left (last)
    • ⇷ windowed reduce right-to-left (last)
    • ⇟ scan (on prefixes) top-to-bottom (first)
    • ⇞ scan (on suffixes) bottom-to-top (first)
    • ⇻ scan (on prefixes) left-to-right (last)
    • ⇺ scan (on suffixes) right-to-left (last)
    • ¨ each
    • ᐵ each-left?
    • ᑈ each-right?
    • ⍣ repeat (with inverses?)
    • ⍣ until
    • ∙ inner product
    • ∙ alternant?
    • ⊞ outer product
    • ⍤ at rank
    • ⍥ at depth
    • @ at
    • ⌸ key
    • ⌸ key with vocabulary
    • ⍁ diagonals?
    • ⌺ stencil
    • ⁖ valences (call left if monad and right if dyad)
    • ⍢ strucutral under
  • combinators
    • ⍨ constant
    • ⍨ commute
    • ⍨ duplicate
    • ∘ bind argument
    • ∘ after
    • ⍛ default argument (uses operand if called monadically, and argument if called dyadically)
    • ⍛ before (not a hook!)
    • ⊸ left hook
    • ⟜ right hook
    • ⍤ atop
    • ⍥ over
    • ⸚ mirror (_{(⍵ ⍹⍹ ⍺)⍶⍶(⍺ ⍹⍹ ⍵)}_)
    • «/» fork?
• system names (quad names)
  • support for system names in parsing and interpreting
  • system arrays (nilads, i guess)
    • ⎕u (constant) the uppercase alphabet
    • ⎕l (constant) the lowercase alphabet
    • ⎕d (constant) the digits
    • ⎕ts current Unix timestamp
    • ⎕io (constant) 1
    • ⎕ct (constant) 1⏨¯14
    • ⎕seed (set only) seed the random number generator
  • system functions
    • ⎕File read/write files
    • ⎕DateTime (or ⎕DT maybe?) convert between time formats
    • ⎕HTTP http requests
    • ⎕CSV convert from/to CSV
    • ⎕JSON convert from/to JSON
    • ⎕Unicode convert between unicode representations
    • ⎕Exists does a variable exist?
    • ⎕C/⎕Case case fold/uppercase/lowercase
  • system adverbs
    • ⎕_BinFile read/write binary files, with format chosen from the operand
  • system conjunctions