Function purity and idempotence

 Someone mentioned idempotence at work. I looked it up and noted that it too is a property of functions, like function purity.

I decided to see if I could write functions with combinations of those properties and embedded tests for those properties.

Running my resultant program produces this result:

Created on Fri Mar  3 18:04:09 2023

@author: Paddy3118

pure_idempotent.py

    Explores Purity and idempotence with Python examples

Definitions:

    Pure:

    * Answer relies solely on inputs. Same out for same in.

    I.E: `f(x) == f(x) == f(x) == ...`

    * No side-effects.

    Idempotent:

    * The first answer from any input, if used as input to

    subsequent runs of the function, will all yield the same answer.

    I.E: `f(x) == f(f(x)) == f(f(f(x))) == ...`

    * Any side effect of a first function execution is *preserved* on

    subsequent runs of the function using the previous answer.

    Side effect:

    * A function is said to have side effects if it relies apon or modifies

    state outside of that *given* by its arguments. Modifying mutable

    arguments is also a side effect.

#--------

def remove_twos(arg: list[int]) -> list[int]:

    "Returns a copy of the list with all twos removed."

    return [x for x in arg if x != 2]

Function is:

  Pure

  Idempotent

#--------

def return_first_int(arg: int) -> int:

    "Return the int given in its first call"

    global external_state

    if external_state is None:

        external_state = arg

    return external_state

Function is:

  Impure! External state changed

  Idempotent

#--------

def plus_one(arg: int) -> int:

    "Add one to arg"

    return arg + 1

Function is:

  Pure

  Non-idempotent! Output changes for nested calls

#--------

def epoc_plus_seconds(secs: float) -> float:

    "Return time since epoch + seconds"

    time.sleep(0.1)

    return time.time() + secs

Function is:

  Impure! Output changes for same input

  Non-idempotent! Output changes for nested calls

Code

The code that produces the above (but not its arbitrary colourising), is the following:

# -*- coding: utf-8 -*-

"""

Created on Fri Mar  3 18:04:09 2023

@author: Paddy3118

pure_idempotent.py

    Explores Purity and idempotence with Python examples

Definitions:

    Pure:

    * Answer relies solely on inputs. Same out for same in.

    I.E: `f(x) == f(x) == f(x) == ...`

    * No side-effects.

    Idempotent:

    * The first answer from any input, if used as input to

    subsequent runs of the function, will all yield the same answer.

    I.E: `f(x) == f(f(x)) == f(f(f(x))) == ...`

    * Any side effect of a first function execution is *preserved* on

    subsequent runs of the function using the previous answer.

    Side effect:

    * A function is said to have side effects if it relies apon or modifies

    state outside of that *given* by its arguments. Modifying mutable

    arguments is also a side effect.

"""

import inspect

print(__doc__)

# %% Pure, idempotent.

print('\n#--------')

def remove_twos(arg: list[int]) -> list[int]:

    "Returns a copy of the list with all twos removed."

    return [x for x in arg if x != 2]

print(f"\n{inspect.getsource(remove_twos)}")

arg0 = [1, 2, 3, 2, 4, 5, 2]

print('Function is:')

print('  Pure' if remove_twos(arg0.copy()) == remove_twos(arg0.copy())

      else '  Impure')

print('  Idempotent' if (answer1:=remove_twos(arg0)) == remove_twos(answer1)

      else 'Non-idempotent')

# %% Impure, idempotent.

print('\n#--------')

def return_first_int(arg: int) -> int:

    "Return the int given in its first call"

    global external_state

    if external_state is None:

        external_state = arg

    return external_state

print(f"\n{inspect.getsource(return_first_int)}")

# Purity

external_state = initial_state = None

arg0 = 1

same_output = (return_first_int(arg0)) == return_first_int(arg0)

same_state = external_state == initial_state

print('Function is:')

if same_output and same_state:

    print('  Pure')

else:

    if not same_output:

        print('  Impure! Output changes for same input')

    if not same_state:

        print('  Impure! External state changed')

# Idempotence

external_state = None

answer1, state1 = return_first_int(arg0), external_state

answer2, state2 = return_first_int(answer1), external_state

same_output = answer1 == answer2

same_state = state1 == state2

if same_output and same_state:

    print('  Idempotent')

else:

    if not same_output:

        print('  Non-idempotent! Output changes for nested calls')

    if not same_state:

        print('  Non-idempotent! External state changes for nested calls')

# %% Pure, non-idempotent.

print('\n#--------')

def plus_one(arg: int) -> int:

    "Add one to arg"

    return arg + 1

print(f"\n{inspect.getsource(plus_one)}")

# Purity

arg0 = 1

same_output = (plus_one(arg0)) == plus_one(arg0)

print('Function is:')

if same_output:

    print('  Pure')

else:

    print('  Impure! Output changes for same input')

# Idempotence

answer1 = plus_one(arg0)

answer2 = plus_one(answer1)

same_output = answer1 == answer2

if same_output:

    print('  Idempotent')

else:

    print('  Non-idempotent! Output changes for nested calls')

# %% Impure, non-idempotent.

print('\n#--------')

import time

def epoc_plus_seconds(secs: float) -> float:

    "Return time since epoch + seconds"

    time.sleep(0.1)

    return time.time() + secs

print(f"\n{inspect.getsource(epoc_plus_seconds)}")

# Purity

arg0 = 1

same_output = (epoc_plus_seconds(arg0)) == epoc_plus_seconds(arg0)

print('Function is:')

if same_output:

    print('  Pure')

else:

    print('  Impure! Output changes for same input')

# Idempotence

answer1 = epoc_plus_seconds(arg0)

answer2 = epoc_plus_seconds(answer1)

same_output = answer1 == answer2

if same_output:

    print('  Idempotent')

else:

    print('  Non-idempotent! Output changes for nested calls')

END.