Isomorphism

This is still a work in progress. It may be changed in the future.

Isomorphism

Designed by	PSTF
Appeared in	2024
Computational class	High-level, Pseudonatural
Reference implementation	Unimplemented
File extension(s)	.ism

Isomorphism is an esoteric programming language that was invented by User:PrySigneToFry upon reading Isomorphism: The mathematics in programming.

Syntax

Assignment, variables and constants

Assign a variable to a specified value:

var -> type = value

Change the value of variable:

var = value

Initialization:

Constant

data name -> type = value, const = true

Variable

data name -> type = value, const = false

Number

You can define the number like these:

zero
one
two
...
ten
eleven
...

And you can use succ to get a successor of any data, and use pre to get a previous of any data.

So you can define the set ℕ by these code:

data Nat -> int = zero \\ succ Nat

I/O

Input

Normal

input(var)

With prompt

input(var, __prompt = "")

Output

Normal

print(*args)

With end sign

print(*args, end = "")

Another unique way (output variables only)

Take only one variable

output var

Take an element from a list

list !! elem_num

Take a part from a list

take (start, )end(, step) from list

If-state

Only if state

if expr then:
    code
fi

If-else state

if expr then:
    code1
else:
    code2
fi

If-elif-else state

if expr1 then:
    code1
elif expr2 then:
    code2
--snip--
else:
    codeN+1
fi

Loops

For loop

for(init; cond; incr)
    code
fi

While loop

while(expr)
    code
fi

Function

Define a function

type func name(*args, **kwargs)
    function_body
end

Object

Define an object and invoke it

class objName(superclass)
    attrib
    void static __init__(self)
        initialization
    end
    other statics
end

data var -> objName
var.staticName()

Mathematical and Logical

Mathematics

Define the mathematical calculations

a + zero = a
a + succ b = succ a + b
a * zero = zero
a * succ b = a * b + a
a ^ zero = one
a ^ succ b = a ^ b * a
a - b = a + negate(b)
a / b = a * recipr(b)
a // b = floor(a / b)
a% of b = b / 100 * a
mod(a, b) = a - (b * (a // b))
root(a, b) = a ^ recipr(b)
sqrt(a) = root(a, two)
cbrt(a) = root(a, three)
qdrt(a) = root(a, four)
log(a, b) = x if a ^ x == b
log(a, a) = one
log(a, one) = zero
log(a, zero) = negate(infinity)
negate(zero) = zero
negate(succ a) = pre negate(a)
recipr(a) = a ^ negate(1)
max(a, b) = a if a > b else b
min(a, b) = a if a < b else b

LOGICAL

Define logical and binary calculation

p = {0, 0, 1, 1}
q = {0, 1, 0, 1}
p and q = {0, 0, 0, 1}
# The result is true only if both logical values are true.
p or q = {0, 1, 1, 1}
# As long as one of the two logical values is true, the result is true.
not p = {1, 1, 0, 0}
# When a logical value is negated (NOT gate), the true becomes false and the false becomes true.
yes p = {0, 0, 1, 1}
# A logical value will remain as it is and output after passing through the YES gate.
p nand q = not (p and q)
p nor q = not (p or q)
p xor q = {0, 1, 1, 0}
# When two logical values are DIFFERENT, the result is true.
p nxor q = not (p xor q)

Define comparison

a > b if succ a > succ b
a < b if b > a
a == b if succ a == succ b
a ~= b if not (a == b)
a >= b if not (a < b)
a <= b if not (a > b)

More syntax

See Isomorphism/More Syntax for more details.

Example

Hello, world!

print("Hello, world!")

A+B Problem

data a -> int
data b -> int
input(a)
input(b)
data c -> int = a + b
output c