--- language: BQN filename: learnbqn.bqn contributors: - ["Raghu Ranganathan", "https://github.com/razetime"] --- BQN is a modern array language (similar to APL) that aims to eliminate burdensome aspects of the APL tradition. It is recommended to try these code examples out in a REPL. The [online REPL](https://mlochbaum.github.io/BQN/try.html) is recommended for quick start, since it comes with keyboard and easy to access help. You can try building [CBQN](https://github.com/dzaima/CBQN) for a local install, but it will need keyboard setup. ```bqn # This is a comment. # The characters ',' and `⋄` are statement separators. ################## # Main datatypes # ################## # Numbers 1,2,3,4 ¯1,¯2,¯3 # Negative numbers are written with a high minus π,∞,¯π,¯∞ # Pi and Infinity are defined constants 1_234_456 # You can add underscores in between numbers # This does not change their value 1.3E4 # Scientific notation is supported # Characters 'a','⥊' ' ' # Yes, you can put *any* character in a character literal @ # Null character ('\0' in C) # Arrays 1‿2‿3 # Stranding, good for simple lists ⟨1,2,3⟩ # General list notation ⟨1‿2,2‿3⟩ # Both can be mixed [1‿2,2‿3] # Array notation # An array is multidimensional, as opposed to containing sublists. # It must be rectangular in shape (a grid structure rather than a tree structure) [1‿2‿3,4‿5] # This is hence invalid # May be familiar coming from Numpy, MATLAB and similar languages. "asdf" # Character array (String) "newline separated" # Allows newlines "quo""tes" # Escape a double quote by typing it twice # Functions 1{𝕨+𝕩}3 # All functions are infix # 𝕨 is left argument, 𝕩 is right argument {-𝕩}5 # 𝕨 can be omitted 1+3 # Same as the above {𝕊𝕩} # 𝕊 is a recursive call # (this function will loop forever) {𝕨 𝕊 𝕩: 𝕨+𝕩} # Functions can have headers (too many cases to discuss here) # Headers can define arity {𝕊 a‿b: a}1‿2 # and also do basic pattern matching # (returns 1) # Modifiers (higher order functions) {𝕗,𝔽,𝕘,𝔾} # 𝔽 and 𝔾 are the operands as callable functions # 𝕗 and 𝕘 are the operands as values {𝔽𝕩} # 1-modifiers use 𝔽/𝕗 ONLY ˜,˘,¨,⁼,⌜ # primitive 1-modifiers are superscripts {𝕨𝔽𝔾𝕩} # 2-modifiers MUST use both 𝔽/𝕗 and 𝔾/𝕘 in body or header ⊸,∘,○,⟜ # primitive 2-modifiers all have circles +{⟨𝕗⟩} # returns ⟨ + ⟩ 1-{𝔽 𝕨 𝔾 𝕩 }×2 # returns ¯2 (operators are *also* infix) # (same as 1 -○× 2) # Trains (Special form of function composition) (+´÷≠) # Average (but how?) # The above train is an F G H train, where # (F G H) 𝕩 → (F 𝕩) G (H 𝕩) # F ← +´, G ← ÷, H ← ≠ # In explicit form, this is {(+´𝕩)÷≠𝕩} # The second pattern is (f g) 𝕩 → f g 𝕩. # longer trains are complex arrangements of these patterns, involving constants and Nothing (·). # Read more about trains at https://mlochbaum.github.io/BQN/doc/train.html # Evaluation order: # BQN evaluates functions right to left with no precedence rules governing *functions*. Functions are what # one would call operators in a mainstream language. 1÷2+3 # 1÷(2+3) = 0.2 (1÷2)+3 # ((1÷2)+3) = 1.5 # Modifiers: # Modifiers are higher order functions, and bind tighter than functions. Modifiers execute left to right. # Modifiers can take non-function arguments e.g. Constant (`˙`) + 1+˜2+○-∘×3 # 1(+˜)(2((+○-)∘×)3) # Variables # Since the case of a variable matters to determine what it means, BQN variables are *case insensitive* # The case that a variable is written in can change the way it is interpreted by BQN. # Eg. `F` refers to a value as a callable function, whereas `f` refers to the same variable as just a value. # Variable assignment is done with `←`. Variables have naming conventions based on their value: subject ← 1‿2‿3 # Arrays, single values, namespaces come under this # name must start with with a lowercase letter Function ← {𝕨+𝕩} # Primitive and user defined functions come under this, both monadic and dyadic # Starts with an uppercase letter _1modifier ← {𝕨𝔽𝕩} # Starts with an underscore _2modifier_ ← {𝔽𝕨𝔾𝕩} # Starts and ends with an underscore # Variable modification is done with `↩`. An existing name cannot be reassigned with `←`. Func ↩ {"Hello"∾𝕩} array_or_atom +↩ 2 # You can use a dyadic function for modification #≡ 3‿4‿5 array_or_atom -↩ # Or a monadic function. #≡ ¯3‿¯4‿¯5 # Due to all functions being infix, you can use your own functions for modification as well: array_or_atom {2⋆𝕩}↩ #≡ ⟨ 0.125, 0.0625, 0.03125 ⟩ ################## # BQN Primitives # ################## # All of BQN's base primitives are a single character long. Refer to https://mlochbaum.github.io/BQN/help/index.html for # examples. # Here we will look at a few primitives from each section. You will want to consult the docs for detailed explanations. # Primitive Functions # All BQN functions are variadic, and can take one or two arguments. The base functions have both monadic and dyadic overloads. # Usually the two overloads for a function are related. ## Arithmetic Functions +, -, ×, ÷ # Add, Subtract, Signum/Multiply, Reciprocal/Divide , '*' does NOT do multiplication # ⌊∘÷ does floor division √, ⋆ # Square root/Nth root, e^x/Power # All Arithmetic functions vectorize: 1 + 2‿3‿4 #≡ 3‿4‿5 1‿2‿3 + 2‿3‿4 #≡ 3‿5‿7 # Character arithmetic(+ and - only): "abc"+3 #≡ "def" 'a'-'d' #≡ ¯3 ## Logic Functions ∧, ∨, ¬ # For Booleans, retrun 1 or 0 ≤, <, >, ≥, = # Vectorizing comparisons ≡, ≢ # Nonvectorizing comparisons ## Array manipulation Functions ↕ # Make a range ∾, ≍, ⋈ # Joining arrays together a←1‿2‿3,b←4‿5 # Let us take a and b. a∾b #≡ 1‿2‿3‿4‿5 a≍b # Same as previous, since a and b are not multidimensional # Adds an extra dimension, similar to a ⋈ for multidimensional arrays. a⋈b #≡ ⟨1‿2‿3, 4‿5⟩ ⊑, ⊏ # Indexing 1⊑1‿2‿3 #≡ 2 (BQN is 0-indexed) 1‿2⊏1‿2‿3 #≡ 2‿3 (for multiple indices) ↑, ↓ # Getting a prefix, suffix of an array. # together they can be used for slicing ⥊ # Reshape/repeat items to create a new array # Primitive 1-Modifiers ## Looping combinators ¨, ˘, ⌜ # Mapping/Zipping ´, ˝ # Fold from right ` # Scan from left ## General combinators ˜ # duplicate argument/swap args - Very useful! ˙ # Create constant function 1 -˜ 2 #≡ 2 - 1 +˜ 2 #≡ 2 + 2 # Primitive 2-modifiers ## Control Flow ◶ # Choose from a list of funcs ⍟ # Repeat n times ## General Combinators ⊸, ⟜ # hook, hookf ∘, ○ # simple function composition ########## # Blocks # ########## # Code delimited by {} # Lexically scoped # For more info: https://mlochbaum.github.io/BQN/doc/block.html # Can have headers, which are ways to explicitly define what a block should be. # A block without headers is automatically inferred from its special variables (𝕨, 𝕩, ...). # Function blocks # Implicit variables(Capitals are functions): # - 𝕨, 𝕎 left argument # - 𝕩, 𝕏 right argument # - 𝕤, 𝕊 represent the block itself # Optional: one or more headers that trigger based on # - pattern match (':') o # - condition ('?') (similar to if-then-else) { # A factorial using headers: 𝕊 0: 1; 𝕊 𝕩: 𝕩×𝕊 𝕩-1 } { # Factorial with predicates 𝕩<2 ? 1; # Similar to an if-else pattern. 𝕩×𝕊 𝕩-1 } # Modifier blocks # create 1-modifiers and 2-modifiers, which have separate types # Implicit variables(Capitals are functions): # - has 𝕨 and 𝕩 if needed # - 𝕗, 𝔽 left operand # - 𝕘, 𝔾 right operand (only in 2-modifiers) # - 𝕣 represents the block itself* (requires underscores as per convention) # Same header rules as functions. { 𝕨=0 ? 𝔽 𝕩; 𝔾 𝕩 } # execute 𝔽 or 𝔾 based on whether left argument is 0. # Namespace blocks # Create immutable namespaces with fields # Require exports (`⇐`) for accessible fields. # Use '.' for field access n←{ A←+ b⇐4 } n.b #≡ 4 n.a # ERROR # Immediate Blocks # No arguments taken # Run the code inside and return the last statement # Often responsible for strange errors. # Can be mistaken for other blocks easily # Good for avoiding scoping issues { 1‿2‿3 } {+} # Trick for returning a function as a value #################### # Basic constructs # #################### # Functional programming # `¨` is used for mapping, as discussed before: {𝕩∾2}¨1‿2‿3 #≡ ⟨1‿2,2‿2,3‿2⟩ # ⋈¨ is a plain zip, which produces pairs. # `¨` acts as a zipWith when used with two arguments: 1‿2‿3 {⟨𝕩+2,2⥊𝕨⟩} 4‿5‿6 #≡ ⟨⟨6,1‿1⟩,⟨7,2‿2⟩,⟨8,3‿3⟩⟩ # `/` is replicate, which serves several purposes *including* filtering. # elements in 𝕩 are repeated by the corresponding number in 𝕨. 1‿2‿3‿0/4‿5‿6‿7 #≡ 4‿5‿5‿6‿6‿6 # a simple filter idiom is F⊸/: {2|𝕩}⊸/67‿42‿83 # keep the odd elements #≡ 67‿83 # Conditionals # There are two main ways to define a conditional. ## Predicate headers { 𝕩 > 2: "greater than 2"; 𝕩 < 2: "lesser than 2"; "equal to 2" } ## Choose (function-based) # - 2-modifier # - 𝔾: list of functions that serve as bodies # - 𝔽: condition function that specifies which function from 𝔾 to select # The same conditional as above would be: {⊑/⟨𝕩>2, 𝕩<2, 𝕩=2⟩}◶⟨ {𝕊: "greater than 2"} {𝕊: "lesser than 2"} {𝕊: "equal to 2"} ⟩ ## Some helpers for conditionals If ← {𝕏⍟𝕎@}´ # Used as If ⟨Condition, Block⟩ IfElse ← {c‿T‿F: c◶F‿T@} # Used as IfElse ⟨Condition, Block, ElseBlock⟩ # Looping # The primary form of unbounded looping is recursion (performed with 𝕊). # BQN does not eliminate tail calls, but the while idiom can be used to work around this: While ← {𝕩{𝔽⍟𝔾∘𝔽_𝕣_𝔾∘𝔽⍟𝔾𝕩}𝕨@}´ # While 1‿{... to run forever DoWhile ← {𝕏@ ⋄ While 𝕨‿𝕩}´ # A For loop can be done with ¨, functions need not be pure. ``` ## Ready for more? - [Quickstart guide](https://mlochbaum.github.io/BQN/doc/quick.html) - [Full length, explained documentation](https://mlochbaum.github.io/BQN/doc/index.html) - [Short docs](https://mlochbaum.github.io/BQN/help/index.html) - [BQN community!](https://mlochbaum.github.io/BQN/community/index.html)