X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=ea8f2511992e97ff0caed2f8f002426dd2bc053b;hp=d6fdd9d3c2cc459ffda685e411fb8e4ce46ea0ce;hb=513394b4086fc02f9f8214c52d3e8bbaa9cdfd27;hpb=2785fd4e7ca1a59261905831b1454099992d75c2

diff --git a/assignment1.mdwn b/assignment1.mdwn
index d6fdd9d3..ea8f2511 100644
--- a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ -2,7 +2,7 @@
 
         let
           zero? match lambda x. FILL_IN_THIS_PART
-	in zero?
+        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.
 
@@ -10,9 +10,9 @@
 
         let
           empty? match lambda xs. case xs of
-	                             FILL_IN_THIS_PART
-				  end
-	in empty?
+                                     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.)
 
@@ -26,9 +26,9 @@
 
     Your solution should have a form something like this:
 
-        let
+        letrec
           drop match lambda (n, xs). FILL_IN_THIS_PART
-	in drop
+        in drop
 
     What is the relation between `tail` and `drop`?
 
@@ -50,51 +50,69 @@
 
     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
+        letrec
+          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
+                                        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 []
+        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])
+        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 []
+        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 ...
+        letrec
+          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
+###Extra credit problems###
+
+*   In class I mentioned a function `&&` which occupied the position *between* its arguments, rather than coming before them (this is called an "infix" function). The way that it works is that `[1, 2, 3] && [4, 5]` evaluates to `[1, 2, 3, 4, 5]`. Define this function, making use of `letrec` and the simpler infix operation `&`.
+
+*   Write a function `unmap2` that is something like the inverse of `map2`. This function expects two arguments, the second being a sequence of elements of some type *t*. The first is a function `g` that expects a single argument of type *t* and returns a *pair* of results, rather than just one result. We want to collate these results, the first into one list, and the second into a different list. Then `unmap2` should return those two lists. Thus if:
+
+        g z1  # evaluates to [x1, y1]
+        g z2  # evaluates to [x2, y2]
+        g z3  # evaluates to [x3, y3]
+
+    Then `unmap2 (g, [z1, z2, z3])` should evaluate to `([x1, x2, x3], [y1, y2, y3])`.
+
+*   Write a function `takewhile` that expects a `p` argument like `filter`, and also a sequence. The result should behave like this:
+
+        takewhile ((lambda x. x < 10), [1, 2, 20, 4, 40]) # evaluates to [1, 2]
+
+    Note that we stop "taking" once we reach `20`, even though there are still later elements in the list that are less than `10`.
+
+*   Write a function `dropwhile` that expects a `p` argument like `filter`, and also a sequence. The result should behave like this:
 
-*Will post shortly*
+        dropwhile ((lambda x. x < 10), [1, 2, 20, 4, 40]) # evaluates to [20, 4, 40]
 
-<!-- take_while, drop_while, split_while -->
+    Note that we stop "dropping" once we reach `20`, even though there are still later elements in the list that are less than `10`.
 
-<!-- unmap2 (g, xs) where g x \mapsto (y,z), and unmap2 (g, [x1, x2, x3]) \mapsto ([y1, y2, y3], [z1, z2, z3]) -->
+*   Write a function `reverse` that returns the reverse of a sequence. Thus, `reverse [1, 2, 3, 4]` should evaluate to `[4, 3, 2, 1]`.