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copied!<p>I will add another answer in order not to overload my first one and because this one includes both my initial idea and the valuable input from <a href="https://stackoverflow.com/users/355230/martineau">@martineau</a> (and this time hopefully PEP-8 compliant).</p> <p>Let's define a function like this and let's try to guess its arity:</p> <pre><code>import inspect import operator class UnguessableArityException(Exception): pass class Function: def __init__(self, f, arity = ...): self.f = f self.arity = arity if arity == ...: argspec = inspect.getfullargspec(f) if argspec.varargs or argspec.kwonlyargs: raise UnguessableArityException() self.arity = len(argspec.args) def __call__(self, *args): return self.f(*args) def op(self, g, op): if isinstance(g, Function): return Function(lambda *args: op(self.f(*args[:self.arity]), g.f(*args[self.arity:])), self.arity + g.arity) return Function(lambda *args: op(self.f(*args), g), self.arity) def rop(self, g, op): return Function(lambda *args: op(g, self.f(*args)), self.arity) def __add__(self, g): return self.op(g, operator.add) def __radd__(self, g): return self.rop(g, operator.add) def __mul__(self, g): return self.op(g, operator.mul) def __rmul__(self, g): return self.rop(g, operator.mul) def __truediv__(self, g): return self.op(g, operator.truediv) def __rtruediv__(self, g): return self.rop(g, operator.truediv) </code></pre> <p>Now we basically just need to define identity:</p> <pre><code>#define identity i = Function(lambda x: x) # λx.x </code></pre> <p>And using the identity you can start to build your "growing" ("appending") functions.</p> <pre><code>#now you can start building your function f = i * i # λxy.x*y print(f(3, 2)) #later in your code you need to "append" another term λxy.x*y f = f + f # λxyza.x*y+z*a print(f(3,2,1,4)) #even later, you need to "append" a term λxy.x/y f = f + i / i # λxyzabc.x*y+z*a+b/c print(f(3,2,1,4,14,2)) #works also with constants f = 2 * f # λxyzabc.2*(x*y+z*a+b/c) print(f(3,2,1,4,14,2)) </code></pre>

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