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python lambda functions behavior

I am having a hard time understanding the behavior of these lambda functions in python 3.10.0

I am trying to define the NOT logical operator from lambda calculus (see, e.g., the definition on wikipedia The following implementation is correct:

In [1]: TRUE  = lambda a: lambda b: a
   ...: FALSE = lambda a: lambda b: b
   ...: NOT = lambda a: a(FALSE)(TRUE)
   ...: assert NOT(FALSE) == TRUE

However, when I try and do a literal substitution either for FALSE or TRUE, the code fails

In [2]: NOT1 = lambda a: a(FALSE)(lambda a: lambda b: a)
   ...: assert NOT1(FALSE) == TRUE
---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
Cell In[2], line 2
      1 NOT1 = lambda a: a(FALSE)(lambda a: lambda b: a)
----> 2 assert NOT1(FALSE) == TRUE

AssertionError:

Can anybody explain me why this happens?

Solution

  • Python function == works by object identity. (Trying to implement it any other way ranges from "painfully inconsistent" to "plain impossible".) You have created another function with the same behavior as your NOT function, but it is not the same function object, so == says they're not equal.