add assignment2

Signed-off-by: Jim Pryor <profjim@jimpryor.net>

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+We'll assume the "Version 3" implementation of lists and numbers throughout. So:
+
+<pre><code>zero &equiv; \s z. z
+succ &equiv; \n. \s z. s (n s z)
+iszero &equiv; \n. n (\x. false) true
+add &equiv; \m \n. m succ n
+mul &equiv; \m \n. \s. m (n s)</code></pre>
+
+And:
+
+<pre><code>empty &equiv; \f z. z
+make-list &equiv; \hd tl. \f z. f hd (tl f z)
+isempty &equiv; \lst. lst (\hd sofar. false) true
+extract-head &equiv; \lst. lst (\hd sofar. hd) junk</code></pre>
+
+The `junk` in `extract-head` is what you get back if you evaluate:
+
+       extract-head empty
+
+As we said, the predecessor and the extract-tail functions are harder to define. We'll just give you one implementation of these, so that you'll be able to test and evaluate lambda-expressions using them in Scheme or OCaml.
+
+<pre><code>predecesor &equiv; (\shift n. n shift (make-pair zero junk) get-second) (\pair. pair (\fst snd. make-pair (successor fst) fst))
+extract-tail &equiv; (\shift lst. lst shift (make-pair empty junk) get-second) (\hd pair. pair (\fst snd. make-pair (make-list hd fst) fst))</code></pre>
+
+The `junk` is what you get back if you evaluate:
+
+       predecessor zero
+
+       extract-tail empty
+
+Alternatively, we might reasonably declare the predecessor of zero to be zero (this is a common construal of the predecessor function in discrete math), and the tail of the empty list to be the empty list.
+ 
+
+For these exercises, assume that `LIST` is the result of evaluating:
+
+       (make-list a (make-list b (make-list c (make-list d (make-list e empty)))))
+
+
+1.     What would be the result of evaluating:
+
+               LIST make-list empty
+
+2.     Based on your answer to question 1, how might you implement the **map** function? Expected behavior:
+
+       <pre><code>map f LIST <~~> (make-list (f a) (make-list (f b) (make-list (f c) (make-list (f d) (make-list (f e) empty)))))</code></pre>
+
+3.     Based on your answer to question 1, how might you implement the **filter** function? The expected behavior is that:
+
+               filter f LIST
+
+       should evaluate to a list containing just those of `a`, `b`, `c`, `d`, and `e` such that `f` applied to them evaluates to `true`.
+
+4. How would you implement map using the either the version 1 or the version 2 implementation of lists?
+
+5. Our version 3 implementation of the numbers are usually called "Church numerals". If `m` is a Church numeral, then `m s z` applies the function `s` to the result of applying `s` to ... to `z`, for a total of *m* applications of `s`, where *m* is the number that `m` represents or encodes.
+
+       Given the primitive arithmetic functions above, how would you implement the less-than-or-equal function? Here is the expected behavior, where `one` abbreviates `succ zero`, and `two` abbreviates `succ (succ zero)`.
+
+               less-than-or-equal zero zero ~~> true
+               less-than-or-equal zero one ~~> true
+               less-than-or-equal zero two ~~> true
+               less-than-or-equal one zero ~~> false
+               less-than-or-equal one one ~~> true
+               less-than-or-equal one two ~~> true
+               less-than-or-equal two zero ~~> false
+               less-than-or-equal two one ~~> false
+               less-than-or-equal two two ~~> true
+
+       You'll need to make use of the predecessor function, but it's not important to understand how the implementation we gave above works. You can treat it as a black box.
+