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
• Part 6: Tests, Docs, Each
• Part 7: Quads, Key, Index

Documentation is available here

Features

Marked features are supported, unmarked features are planned

• Types
  • [x] Arrays
    • [x] complex numbers
    • [x] unicode characters
    • [x] boxes (nested arrays)
  • [x] Functions
  • [x] Monadic Operators ("Adverbs")
  • [x] Dyadic Operators ("Conjunctions")
• Syntax
  • [x] number literals
    • [x] decimal point .
    • [x] negative sign ¯
    • [x] exponent notation ⏨
    • [x] complex notation ᴊ
    • [ ] complex phase notation? ∠
    • [ ] infinities ∞
  • [x] character literals '
  • [x] string literals "
    • [x] escapes with ⍘
      • [x] ⍘⍘ -> ⍘
      • [x] ⍘" -> "
      • [x] ⍘n -> newline
      • [x] ⍘r -> carriage return
      • [x] ⍘t -> tab
      • [ ] ⍘{22be} -> unicode?
  • [x] names
    • [x] array names (abc)
    • [x] function names (Abc)
    • [x] monadic operator names (_Abc)
    • [x] dyadic operator names (_Abc_)
  • [x] assignment ←
  • [x] dfns/dops
    • [x] multiple statements ⋄
    • [x] guards :
    • [x] early return ■
    • [x] dfns {...}, dadvs _{...}, dconjs _{...}_
    • [x] refer to arguments and operands: ⍺ left argument, ⍵ right argument, ⍺⍺ left array operand, ⍶⍶ left function operand, ⍵⍵ right array operand, ⍹⍹ right function operand
    • [x] recursion: ∇ recurse function, _∇ recurse adverb, _∇_ recurse conjunction
  • [ ] comments ⍝
    • [x] inline comments? ⟃/⟄
  • [x] console I/O with ⎕ and ⍞
  • [x] array notation ⟨/⋄/⟩ and [/⋄/]
• primitives
  • arrays
    • [x] ⍬
  • number functions
    • [x] + conjugate
    • [x] + add
    • [x] - negate
    • [x] - subtract
    • [x] × direction
    • [x] × multiply
    • [x] ÷ reciprocal
    • [x] ÷ divide
      • 0÷0 is 1
      • x÷0 is an error
    • [x] * exponential
    • [x] * power
    • [x] ⍟ ln
    • [x] ⍟ log
      • 1⍟1 is 1
      • 1⍟y is an error
      • x⍟0 is an error
    • [x] ○ pi times
    • [x] ○ 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 $e^{iy}$
    • [x] √ square root
    • [x] √ root
    • [x] ⌊ floor
    • [x] ⌊ minimum
    • [x] ⌈ ceiling
    • [x] ⌈ maximum
    • [x] ⸠ round
    • [ ] ⸠ average?
    • [ ] ⌹ matrix inverse
    • [ ] ⌹ matrix divide
    • [ ] ! factorial/gamma
    • [ ] ! binomial
    • [x] | magnitude
    • [x] | remainder
    • [x] ∨ greatest common divisor
    • [x] ∧ least common multiple
    • [x] ⊕ cartesian (x⊕y is $x + iy$)
    • [x] ⊕ pure imaginary (⊕y is $iy$)
    • [x] ⊗ polar (x⊗y is $xe^{iy}$)
    • [x] ⊗ unit polar (⊗y is $e^{iy}$)
    • [x] ∡ phase
    • [ ] ∡ atan2
    • [x] ℜ real part
    • [x] ℑ imaginary part
    • [ ] ⊥ decode
    • [ ] ⊥ base 2 decode
    • [ ] ⊤ encode
    • [ ] ⊤ base 2 encode
  • boolean functions
    • [x] = equals
    • [x] ≠ not equals
    • [x] < less
    • [x] ≤ less or equal
    • [x] ≥ greater or equal
    • [x] > greater
    • [x] ≡ match
    • [x] ≢ not match
    • [x] ∧ and
    • [x] ∨ or
    • [x] ⍲ nand
    • [x] ⍱ nor
    • [x] ~ not
  • set functions
    • [x] ∪ unique
    • [x] ∪ union
    • [x] ∩ intersection
    • [x] ~ difference
    • [x] § symmetric difference
    • [x] ≠ nub sieve
    • [ ] multisets?
  • property functions
    • [ ] ⍳ index of
    • [ ] ⍸ interval index
    • [ ] ∊ element of
    • [ ] ⍷ find
    • [ ] ⍷ type? depends on if prototypes are added or not
    • [ ] ⋷ histogram (inverse of where)
    • [ ] ⋷ count
    • [ ] ≡ depth
    • [x] ⍴ shape
    • [x] ≢ tally
    • [ ] ϼ rank
  • array creation functions
    • [x] ⍳ index generator
    • [x] ? roll
    • [ ] ? deal
    • [ ] … range?
    • [x] ⍮ pair
    • [x] ⍮ half pair
  • array manipulation functions
    • [x] ↑ take
    • [x] ↓ drop
    • [ ] ↑ mix
    • [ ] ↓ major cells (split is ⊂⍤1)
    • [x] ⊂ enclose
    • [ ] ⊆ nest
    • [ ] ⊂ partitioned enclose
    • [ ] ⊆ group (not partition!)
    • [ ] ⍋ grade up
    • [ ] ⍒ grade down
    • [ ] ⍋ sort by up?
    • [ ] ⍒ sort by down?
    • [ ] ≤ sort up? useless with sort by (⍋⍨)
    • [ ] ≥ sort down? as above
    • [x] ⍸ where
    • [x] ∊ enlist
    • [x] ⌿ replicate
    • [ ] ⍀ expand? (might not make much sense without prototypes)
    • [x] , ravel
    • [ ] ⍪ table
    • [ ] ⍪ catenate
    • [x] ⍴ reshape
    • [ ] ϼ rerank (generalized version of promote/demote: introduce leading length-1 axes or combine leading axes)
    • [x] ⊖ reverse
    • [x] ⊖ rotate
    • [ ] ⍉ transpose
    • [ ] ⍉ reorder axes
    • [ ] ∧ promote (introduce leading axis)
    • [ ] ∨ demote (combine two leading axes)
    • [ ] , laminate
  • array lookup functions
    • [x] ⊃ first
    • [x] ⊇ last
    • [x] ⊇ from
    • [x] ⌷ index
    • [ ] ⊃ pick
  • misc functions
    • [x] ⊢/⊣ same
    • [x] ⊢ right
    • [x] ⊣ left
    • [ ] ⍎ execute
    • [ ] ⍕ format
    • [ ] ↗ raise?
  • operators
    • [x] ⍆ reduce left-to-right
    • [ ] ⍆ windowed reduce left-to-right
    • [x] ⍅ reduce right-to-left
    • [ ] ⍅ windowed reduce right-to-left
    • [x] ↟ on prefixes
    • [x] ↡ on suffixes
    • [x] ¨ each
    • [x] ᐵ each-left
    • [x] ᑈ each-right
    • [ ] ⍣ repeat (with inverses?)
    • [ ] ⍣ until
    • [ ] ∙ inner product
    • [ ] ∙ alternant?
    • [ ] ⊞ outer product
    • [ ] ⍤ at rank
    • [ ] ⍥ at depth
    • [ ] @ at
    • [x] ⌸ key
    • [ ] ⌸ key with vocabulary
    • [ ] ⍁ diagonals?
    • [ ] ⌺ stencil
    • [ ] ⁖ valences (call left if monad and right if dyad)
    • [ ] ⍢ strucutral under
  • combinators
    • [x] ⍨ constant
    • [x] ⍨ commute
    • [x] ⍨ duplicate
    • [x] ∘ bind argument
    • [x] ∘ after
    • [x] ⍛ default argument (uses operand if called monadically, and argument if called dyadically)
    • [x] ⍛ before (not a hook!)
    • [x] ⊸ left hook
    • [x] ⟜ right hook
    • [x] ⍤ atop
    • [x] ⍥ over
    • [ ] ⸚ mirror (_{(⍵ ⍹⍹ ⍺)⍶⍶(⍺ ⍹⍹ ⍵)}_)
    • [ ] «/» fork?
• system names (quad names)
  • [x] support for system names in parsing and interpreting
  • system arrays (nilads, i guess)
    • [x] ⎕u (constant) the uppercase alphabet
    • [x] ⎕l (constant) the lowercase alphabet
    • [x] ⎕d (constant) the digits
    • [ ] ⎕ts current Unix timestamp
    • [x] ⎕io (constant) 1
    • [x] ⎕ct (constant) 1⏨¯14
    • [x] ⎕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
    • [x] ⎕Exists does a variable exist?
    • [ ] ⎕C/⎕Case case fold/uppercase/lowercase
    • [ ] ⎕Partition convert Partition representation to Group representation (so that Partition is ⎕Partition⍛⊆)
    • [x] ⎕Repr convert an array to a representation that can be read with Execute
    • [ ] ⎕Assert assertions
  • system adverbs
    • [ ] ⎕_BinFile read/write binary files, with format chosen from the operand
  • system conjunctions