+1. Define a function `zero?` that expects a single number as an argument, and returns `'true` if that number is `0`, else returns `'false`. Your solution should have a form something like this:
+
+ let
+ zero? match lambda x. FILL_IN_THIS_PART
+ in zero?
+
+ You can use the `if...then...else` construction if you like, but it will make it easier to generalize to later problems if you use the `case EXPRESSION of PATTERN1 then RESULT1; PATTERN2 then RESULT2; ... end` construction instead.
+
+2. Define a function `empty?` that expects a sequence of values as an argument (doesn't matter what type of values), and returns `'true` if that sequence is the empty sequence `[]`, else returns `'false`. Here your solution should have a form something like this:
+
+ let
+ empty? match lambda xs. case xs of
+ FILL_IN_THIS_PART
+ end
+ in empty?
+
+3. Define a function `tail` that expects a sequence of values as an argument (doesn't matter what type of values), and returns that sequence with the first element (if any) stripped away. (Applying `tail` to the empty sequence `[]` can just give us back the empty sequence.)
+
+4. Define a function `drop` that expects two arguments, in the form (*number*, *sequence*), and works like this:
+
+ drop (0, [10, 20, 30]) # evaluates to [10, 20, 30]
+ drop (1, [10, 20, 30]) # evaluates to [20, 30]
+ drop (2, [10, 20, 30]) # evaluates to [30]
+ drop (3, [10, 20, 30]) # evaluates to []
+ drop (4, [10, 20, 30]) # evaluates to []
+
+ Your solution should have a form something like this:
+
+ let
+ drop match lambda (n, xs). FILL_IN_THIS_PART
+ in drop
+
+ What is the relation between `tail` and `drop`?
+
+5. Define a function `take` that expects two arguments, in the same form as `drop`, but works like this instead:
+
+ take (0, [10, 20, 30]) # evaluates to []
+ take (1, [10, 20, 30]) # evaluates to [10]
+ take (2, [10, 20, 30]) # evaluates to [10, 20]
+ take (3, [10, 20, 30]) # evaluates to [10, 20, 30]
+ take (4, [10, 20, 30]) # evaluates to [10, 20, 30]
+
+6. Define a function `split` that expects two arguments, in the same form as `drop` and `take`, but this time evaluates to a pair of results. It works like this:
+
+ split (0, [10, 20, 30]) # evaluates to ([], [10, 20, 30])
+ split (1, [10, 20, 30]) # evaluates to ([10], [20, 30])
+ split (2, [10, 20, 30]) # evaluates to ([10, 20], [30])
+ split (3, [10, 20, 30]) # evaluates to ([10, 20, 30], [])
+ split (4, [10, 20, 30]) # evaluates to ([10, 20, 30], [])
+
+ Here's a way to answer this problem making use of your answers to previous questions:
+
+ let
+ drop match ... ; # as in problem 4
+ take match ... ; # as in problem 5
+ split match lambda (n, xs). let
+ ys = take (n, xs);
+ zs = drop (n, xs)
+ in (ys, zs)
+ in split
+
+ However, we want you to instead write this function from scratch.
+
+7. Write a function `filter` that expects two arguments. The second argument will be a sequence `xs` with elements of some type *t*, for example numbers. The first argument will be a function `p` that itself expects arguments of type *t* and returns `'true` or `'false`. What `filter` should return is a sequence that contains exactly those members of `xs` for which `p` returned `'true`. For example, helping ourself to a function `odd?` that works as you'd expect:
+
+ filter (odd?, [11, 12, 13, 14]) # evaluates to [11, 13]
+ filter (odd?, [11]) # evaluates to [11]
+ filter (odd?, [12, 14]) # evaluates to []
+
+8. Write a function `partition` that expects two arguments, in the same form as `filter`, but this time evaluates to a pair of results. It works like this:
+
+ partition (odd?, [11, 12, 13, 14]) # evaluates to ([11, 13], [12, 14])
+ partition (odd?, [11]) # evaluates to ([11], [])
+ partition (odd?, [12, 14]) # evaluates to ([], [12, 14])
+
+9. Write a function `double` that expects one argument which is a sequence of numbers, and returns a sequence of the same length with the corresponding elements each being twice the value of the original element. For example:
+
+ double [10, 20, 30] # evaluates to [20, 40, 60]
+ double [] # evaluates to []
+
+10. Write a function `map` that generalizes `double`. This function expects a pair of arguments, the second being a sequence `xs` with elements of some type *t*, for example numbers. The first argument will be a function `f` that itself expects arguments of type *t* and returns some type *t'* of result. What `map` should return is a sequence of the results, in the same order as the corresponding original elements. The result should be that we could say:
+
+ let
+ map match lambda (f, xs). FILL_IN_THIS_PART;
+ double match lambda xs. map ((lambda x. 2*x), xs)
+ in ...
+
+11. Write a function `map2` that generalizes `map`. This function expects a triple of arguments: the first being a function `f` as for `map`, and the second and third being two sequences. In this case `f` is a function that expects *two* arguments, one from the first of the sequences and the other from the corresponding position in the other sequence. The result should behave like this:
+
+ map2 ((lambda (x,y). 10*x + y), [1, 2, 3], [4, 5, 6]) # evaluates to [14, 25, 36]
+
+
+EXTRA CREDIT PROBLEMS
+
+*Will post shortly*
+
+<!-- take_while, drop_while, split_while -->
+
+<!-- unmap2 (g, xs) where g x \mapsto (y,z), and unmap2 (g, [x1, x2, x3]) \mapsto ([y1, y2, y3], [z1, z2, z3]) -->
+