On 3/25/2014 11:18 AM, Steven D'Aprano wrote:
The thing is, we can't just create a ∑ function, because it doesn't work
the way the summation operator works. The problem is that we would want
syntactic support, so we could write something like this:
p = 2
∑(n, 1, 10, n**p)
Of course we can. If we do not insist on separating the dummy name from
the expression that contains it. this works.
def sigma(low, high, func):
sum = 0
for i in range(low, high+1):
sum += func(i)
return sum
p = 2
print(sigma(1, 10, lambda n: n**p))
>>>
385
which looks correct. This corresponds to a notation like so
10
∑ n: n**p
1
which, for ranges, is more sensible that the standard. Lambda is an
explicit rather than implicit quotation.
If you do insist on separating two things that belong together, you can
quote with quote marks instead and join within the function to get the
same answer.
def sig2(var, low, high, exp):
func = eval("lambda {}: {}".format(var, exp))
sum = 0
for i in range(low, high+1):
sum += func(i)
return sum
p = 2
print(sig2('n', 1, 10, 'n**p'))
>>>
385
To me, both these apis are 'something' like the api with implicit
quoting, which is impossible for function calls, but common in
statements. (This is one reason to make a construct a python statement
rather than function. Jumping is another) Using the same api, one could
instead expand the template to include the for loop and use exec instead
of eval.
def sig3(var, low, high, exp):
loca = {}
exec(
'''\
sum = 0
for {} in range({}, {}):
sum += {}\
'''.format(var, low, high+1, exp), globals(), loca)
return loca['sum']
print(sig3('n', 1, 10, 'n**p'))
This cannot be an ordinary function, because if it were, the n**p
expression would be evaluated before passing the result to the function.
So would the dummy parameter name n.
We want it to delay evaluation, like a list comp:
[n**p for n in range(1, 11)]
the expression n**p gets evaluated inside the list comp.
Which is to say, it is implicitly quoted
That cannot be written as a function either:
list_comp(n**p, n, range(1, 11)
It can be with explicit quoting, similar to how done for sigma. Some
lisps once and maybe still have 'special' functions that implicitly
quote certain arguments. One just has to learn which functions and which
parameters. I prefer having implicit quoting relegated to a limited set
of statements, where is it pretty clear what must be quoted for the
statement to make any sense. Assignment is one example, while, for, and
comprehensions are others.
--
Terry Jan Reedy
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