From: Jim Date: Sat, 31 Jan 2015 01:59:53 +0000 (-0500) Subject: begone evil tabs X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=2ab239e41e823b7338c5c90be884ee3471e2099d begone evil tabs --- diff --git a/assignment1.mdwn b/assignment1.mdwn index d6fdd9d3..f0d858d6 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.) @@ -28,7 +28,7 @@ let drop match lambda (n, xs). FILL_IN_THIS_PART - in drop + in drop What is the relation between `tail` and `drop`? @@ -51,39 +51,39 @@ 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 + 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 ... + 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: