The Z Programming Language

Z is a functional, Turing-complete programming language that uses paradigms of lambda calculus.

Generic Types

Integer

Set

Built-in Constructs

S (Global Stack)

S is the only global variable in the whole Z program code. It is mainly to use as an outout buffer.

Z (Z-combinator)

Grammar: Z <lambda-decl>

Z is used to recursively call lambda functions. As there are no iterative loops in Z, recursive calls are the way we do iteration :)

K (Kombine)

Grammar: K <lambda-identifier|lambda-decl|Z-expression|K-expression>+ <int|set|S>

Lambda function bodies in Z consists of exactly one expression. So, we need to 'kombine' the expressions as a chain. The K combinator does this.

K f g h t x == f(g(h(t x)))

Lambda

Lambda functions are what the Z language is built on. Lambda functions,

• Can be anonymous
• Can have zero number of parameters
• Can only be passed integer, set type of constant or variables, or the S as arguments.

Built-in Functions

' (Put one char)

Grammar: ' <constant|integer|set|S>

Puts the ASCII character equivalent of the given integer argument's value to standard output. If the given argument is of set type or S, puts the ASCII character equivalent of the top/first element.

If S is given as argument, this function pops the top item from S. No such action is taken if a set is given.

Usage:

' S
\? (x) (' x)
\? () (' 10)

^ (Peek)

Grammar: ^ <integer|set|S>

Returns the first element of given set. If the given argument is S, returns the top item. Otherwise, returns the value of the integer argument itself.

Usage:

^ S
\y (x) ((!= 0 (^ x)) (' x))

<< (Pop from && push to)

Grammar: <integer|set|S> << <constant|integer|set|S>

Pops one item from y and pushes it to x. If y is of type integer, takes its value and pushes it to x. If x is type integer, sets its value to taken integer value.