September Morn Update

Task/Filter/Python/filter-4.py

@@ -0,0 +1,95 @@
+'''Functional filtering - by descending generality and increasing brevity'''
+
+from functools import (reduce)
+from itertools import (chain)
+import inspect
+import re
+
+
+def f1(xs):
+    '''Catamorphism: fold / reduce.
+       See [The expressiveness and universality of fold]
+       (http://www.cs.nott.ac.uk/~pszgmh/fold.pdf)'''
+    return reduce(lambda a, x: a + [x] if even(x) else a, xs, [])
+
+
+def f2(xs):
+    '''List monad bind/inject operator (concatMap combined with
+       an (a -> [b]) function which wraps its result in a
+       possibly empty list). This is the universal abstraction
+       which underlies list comprehensions.'''
+    return concatMap(lambda x: [x] if even(x) else [])(xs)
+
+
+def f3(xs):
+    '''Built-in syntactic sugar for list comprehensions.
+       Convenient, and encouraged as 'Pythonic',
+       but less general and expressive than a fold.'''
+    return (x for x in xs if even(x))
+
+
+def f4(xs):
+    '''Built-in filter function'''
+    return filter(even, xs)
+
+
+def main():
+    '''Tests'''
+    xs = enumFromTo(0)(10)
+    print(
+        tabulated(showReturn)(
+            'By descending generality and increasing brevity:\n'
+        )(
+            lambda f: list(f(xs))
+        )([f1, f2, f3, f4])
+    )
+
+
+# GENERIC -------------------------------------------------
+
+
+# concatMap :: (a -> [b]) -> [a] -> [b]
+def concatMap(f):
+    '''Concatenated list over which a function has been mapped.
+       The list monad can be derived by using a function of the type
+       (a -> [b]) which wraps its output in list
+       (using an empty list to represent computational failure).'''
+    return lambda xs: list(
+        chain.from_iterable(
+            map(f, xs)
+        )
+    )
+
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# even :: Int -> Bool
+def even(x):
+    '''Predicate'''
+    return 0 == x % 2
+
+
+# showReturn :: (a -> b) -> String
+def showReturn(f):
+    '''Stringification of final (return) expression in function body.'''
+    return re.split('return ', inspect.getsource(f))[-1].strip()
+
+
+# tabulated :: (a -> String) -> String -> (a -> b) -> [a] -> String
+def tabulated(fShow):
+    '''heading -> function -> input List -> tabulated output string'''
+    def go(s, f, xs):
+        w = max(len(fShow(x)) for x in xs)
+        return s + '\n' + '\n'.join([
+            fShow(x).rjust(w, ' ') +
+            ' -> ' + str(f(x)) for x in xs
+        ])
+    return lambda s: lambda f: lambda xs: go(s, f, xs)
+
+
+if __name__ == '__main__':
+    main()