Hakerh

Hakerh is an esolang by User:TBPO that imitates User:Hakerh400's esolangs. I made a timestamp below to mark where my transformation into Hakerh400 begun:

TBPO 11:32, 15 May 2025 (UTC)

Syntax

The program consists of function definitions:

f(X) = Y

Where uppercase letters (except T, F and N) are any expressions.

T, F and N are built-in functions that return themselves. f returns a function with name f. X(Y) calls function X with argument Y. X[Y] returns Y if X[Y] is T and N if isn't.

Syntactic sugar

There is some syntactic sugar to simplify and shorten the code. For example, let a, b is equivalement to:

a(x) = a
b(x) = b

f(X,Y) is equivalement to f(X)(Y), and f(X,Y) = Z is equivalement to:

f(X) = g
g(Y) = Z

f(X.Y) = Z:

f(X) = Z
f(Y) = Z

, has higher priority over ., so f(X.Y,Z) = W is:

f(X) = g
f(Y) = g
g(Z) = W

If a function isn't defined and isn't an argument of any function on the execution stack, it returns a unique function that returns itself.

Execution

Program execution:

• Take input.
• Check is it a valid Hakerh expression. If not, replace it with _(_).
• Evaluate input as Hakerh expression.
• Output the result.

A function call f(X) is evaluated by the following:

• Iterate through the function definitions, starting from the first.

Current definition will be written as g(Y) = Z.

• If g isn't f as the function, skip.
• If X evaluates to N and Y is N, return N.
• If X or Y evaluates to N, skip.
• Replace all instances of Y in Z with X and return

• If no definition is found, evaluate X and return unique function which returns itself.

Recursion is allowed.

Intention

There are two reasons why I created this language:

• To begin the transformation into User:Hakerh400,
• To explore the simulation of sets and types by functions. Set can be simulated by a function that returns T if value is in the set and F otherwise. Set defined in such way can also simulate type, because f[x] in function definition causes the definition to be used only if x is in f.

Examples

SKI Calculus

This proves it meta Turing-complete.

I(x) = x
K(x,y) = x
S(x,y,z) = x(z,y(z))

Basic relations

eq(x,x) = T
eq(x,y) = F
!(F) = T
!(x) = F
or(F,F) = F
or(x,y) = T
and(T,T) = T
and(x,y) = F
nor(x,y) = !(or(x,y))
nand(x,y) = !(and(x,y))
neq(x,y) = !(eq(x,y))
apply(x,y) = x(y)

Natural numbers

let 0
N(0) = T
N(S(N[x])) = T
P(S(N[x])) = x
N(P(0)) = F
eq(S(a),S(b)) = eq(a,b)
alt(0) = F
alt(S(alt[x]) = F
alt(x) = T
nat(alt[x]) = F