Grammar
The following one-line grammar describes the essence of k syntax[1]:
E:E;e|e e:nve|te| t:n|v v:tA|V n:t[E]|(E)|{E}|N
or in more verbose form:
<Exprs> ::= <Exprs> ";" <expr> | <expr>
<expr> ::= <noun> <verb> <expr> | <term> <expr> | empty
<term> ::= <noun> | <verb>
<verb> ::= <term> <Adverb> | <Verb>
<noun> ::= <term> "[" <Exprs> "]" | "(" <Exprs> ")" | "{" <Exprs> "}" | <Noun>
Further, <Adverb> <Verb> <Noun> can be defined, with minor variations between dialects, as:
<Adverb> ::= "'" | "/" | "\" | "':" | "/:" | "\:"
<Verb> ::= <Verb1> | <Verb1> ":"
<Verb1> ::= ":" | "+" | "-" | "*" | "%" | "!" | "&" | "|" | "<" | ">" | "=" | "~" | "," |
"^" | "#" | "_" | "$" | "?" | "@" | "." | <Digit> ":"
<Noun> ::= <Names> | <Ints> | <Floats> | <String> | <Symbols>
<Names> ::= <Names> "." <Name> | <Name>
<Name> ::= <Letter> | <Name> <Letter> | <Name> <Digit>
<Ints> ::= <Int> | <Ints> " " <Int>
<Int> ::= "-" <Digits> | <Digits>
<Floats> ::= <Float> | <Floats> " " <Float>
<Float> ::= <Int> | <Int> "." <Digits> | <Int> "." <Digits> "e" <Int>
<String> ::= '"' <Chars> '"' | "0x" <Bytes>
<Chars> ::= <Chars> <Char> | empty
<Char> ::= "\0" | "\t" | "\n" | "\r" | '\"' | "\\" | any
<Bytes> ::= <Bytes> <Hex> <Hex> | empty
<Symbols>::= <Symbols> <Symbol> | <Symbol>
<Symbol> ::= "`" | "`" <Name> | "`" <String>
<Digits> ::= <Digit> | <Digits> <Digit>
<Digit> ::= "0" | .. | "9"
<Hex> ::= <Digit> | "a" | .. | "f"
<Letter> ::= "A" | .. | "Z" | "a" | .. | "z"
An important property of k syntax is it's static parsability - a parse tree can be built just by looking at the source code, without any knowledge of the values variables have at runtime.
Note that a k expression could have the syntactic role of a <noun> in the source code and evaluate to a function at runtime, for instance {1+x} or (+). A bare + would be a verb, but enclosing anything in parentheses marks it as a noun - this is called nominalization ("turning into a noun").
Examples of nouns:
0 1 2 "a" 3.14 ``a`bc {1+2*x} (+) -[;1]
Examples of verbs:
+ 0: -: */: ","\' 2*