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Behavioural identity - a short discussion

 P: n/a In mathematics two functions can be considered equal when they represent the same function graph. This is nothing but a set-theoretical identity. It is a nice criterion in theory bad a bad one in practice because it is impossible to calculate all values of an arbitrary function and this is true not only in practice but also in theory. So mathematicians start to distinguish certain classes of functions e.q. polynomials or power-series and prove identity theorems about objects in those classes. But what can be said about the equality of two arbitrary Python-functions f and g? First of all not very much. If we define the trivial functions def f():pass def g():pass and we ask for equality the hash values will be compared and show us that f and g are different. On the other hand if we disassemble f and g we receive a completely different picture: dis.dis(f) 1 0 LOAD_CONST 0 (None) 3 RETURN_VALUE dis.dis(g) 1 0 LOAD_CONST 0 (None) 3 RETURN_VALUE This remains true if we add arguments to f: def f(x):pass dis.dis(f) 1 0 LOAD_CONST 0 (None) 3 RETURN_VALUE Inspecting a function using dis.dis() enables us to speak about it's "behavioural idenity". What is it good for? Answer: for using implementations as interfaces. Let's consider following classes: class NotImplemented(Exception): pass class A(object): def __init__(self): raise NotImplemented We can regard class A as a "pure abstract" class. It is impossible to create instances of A. Each subclass of A that wants to be instantiated must override __init__. This is clearly a property of A. But a client object that inspects A by checking the availability of methods and scanning argument signatures will remain insensitive to this simple fact. Thinking in Python makes live easier because we can not only check interfaces superficially but we can inspect the code and we can compare two code-objects on the behavioural level with a certain accuracy. We start with a function def not_implemented(): raise NotImplemented and we are not interested in the name or in the argument-signature that remains empty but in the implementation of not_implemented() as being prototypical for other functions. A variant of the dis.disassemble() function ( see [1]) deliveres: ['LOAD_GLOBAL', 'NotImplemented', 'RAISE_VARARGS', 'LOAD_CONST', None, 'RETURN_VALUE'] Analyzing A.__init__ will create exactly the same token stream. A client object that compares the token streams of __init__ and not_implemented holds a sufficient criterion for the abstractness of A. [1] Implementation of a stripped down variant of the dis.disassemble() function: def distrace(co): "trace a code object" code = co.co_code n = len(code) i = 0 extended_arg = 0 free = None while i < n: c = code[i] op = ord(c) yield opname[op] i = i+1 if op >= HAVE_ARGUMENT: oparg = ord(code[i]) + ord(code[i+1])*256 + extended_arg extended_arg = 0 i = i+2 if op == EXTENDED_ARG: extended_arg = oparg*65536L if op in hasconst: yield co.co_consts[oparg] elif op in hasname: yield co.co_names[oparg] elif op in hasjrel: yield (i,oparg) elif op in haslocal: yield co.co_varnames[oparg] elif op in hascompare: yield cmp_op[oparg] elif op in hasfree: if free is None: free = co.co_cellvars + co.co_freevars yield free[oparg] list(distrace(A.__init__.func_code)) ['LOAD_GLOBAL', 'NotImplemented', 'RAISE_VARARGS', 'LOAD_CONST', None, 'RETURN_VALUE'] Ciao, Kay Jul 18 '05 #1