X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=miscellaneous_lambda_challenges_and_advanced_topics.mdwn;h=ea7799c8892d9edb14e9b78963aabd4cfb2732a6;hp=0342fc64fcbbff3396aa304a4d5948670b671ba1;hb=76b230e153efac9e171508cd43b57156a7fa20fc;hpb=a23765ce50e30e655255b3eb24db91d4582cb68a diff --git a/miscellaneous_lambda_challenges_and_advanced_topics.mdwn b/miscellaneous_lambda_challenges_and_advanced_topics.mdwn index 0342fc64..ea7799c8 100644 --- a/miscellaneous_lambda_challenges_and_advanced_topics.mdwn +++ b/miscellaneous_lambda_challenges_and_advanced_topics.mdwn @@ -378,19 +378,19 @@ can use. ; and so on - Remarks: the `larger_computation_handler` should be supplied as both the + Remarks: the `larger_computation` handler should be supplied as both the `continue_leftwards_handler` and the `abort_handler` for the leftmost - application, where the head `5` is supplied to `f`. Because the result of this + application, where the head `5` is supplied to `f`; because the result of this application should be passed to the larger computation, whether it's a "fall off the left end of the list" result or it's a "I'm finished, possibly early" - result. The `larger_computation_handler` also then gets passed to the next + result. The `larger_computation` handler also then gets passed to the next rightmost stage, where the head `4` is supplied to `f`, as the `abort_handler` to use if that stage decides it has an early answer. Finally, notice that we don't have the result of applying `f` to `4` etc given as an argument to the application of `f` to `5` etc. Instead, we pass - (\result_of_fold_over_4321. f 5 result_of_fold_over_4321 one_handler another_handler) + (\result_of_fold_over_4321. f 5 result_of_fold_over_4321 ) *to* the application of `f` to `4` as its "continue" handler. The application of `f` to `4` can decide whether this handler, or the other, "abort" handler, should be @@ -402,8 +402,8 @@ can use. of the complex expression semantically depending only on this, not on that. A demon evaluator who custom-picked the evaluation order to make things maximally bad for you could ensure that all the semantically unnecessary computations got - evaluated anyway. At this stage, we don't have any way to prevent that. Later, - we'll see ways to semantically guarantee one evaluation order rather than + evaluated anyway. We don't have any way to prevent that. Later, + we'll see ways to *semantically guarantee* one evaluation order rather than another. Though even then the demonic evaluation-order-chooser could make it take unnecessarily long to compute the semantically guaranteed result. Of course, in any real computing environment you'll know you're dealing with a @@ -433,9 +433,6 @@ can use. ; here's the abort_handler larger_computation in let extract_tail = ; left as exercise - ;; for real efficiency, it'd be nice to fuse the apparatus developed - ;; in these v5 lists with the ideas from the v4 lists, above - ;; but that also is left as an exercise These functions are used like this: @@ -449,12 +446,47 @@ can use. your reach. And once you have followed it, you'll be well on your way to appreciating the full terrible power of continuations. - + Of course, like everything elegant and exciting in this seminar, [Oleg discusses it in much more detail](http://okmij.org/ftp/Streams.html#enumerator-stream). + *Comments*: + + 1. The technique deployed here, and in the v2 lists, and in our implementations + of pairs and booleans, is known as **continuation-passing style** programming. + + 2. We're still building the list as a right fold, so in a sense the + application of `f` to the leftmost element `5` is "outermost". However, + this "outermost" application is getting lifted, and passed as a *handler* + to the next right application. Which is in turn getting lifted, and + passed to its next right application, and so on. So if you + trace the evaluation of the `extract_head` function to the list `[5;4;3;2;1]`, + you'll see `1` gets passed as a "this is the head sofar" answer to its + `continue_handler`; then that answer is discarded and `2` is + passed as a "this is the head sofar" answer to *its* `continue_handler`, + and so on. All those steps have to be evaluated to finally get the result + that `5` is the outer/leftmost head of the list. That's not an efficient way + to get the leftmost head. + + We could improve this by building lists as left folds when implementing them + as continuation-passing style folds. We'd just replace above: + + let make_list = \h t. \f z continue_handler abort_handler. + f h z (\z. t f z continue_handler abort_handler) abort_handler + + now `extract_head` should return the leftmost head directly, using its `abort_handler`: + + let extract_head = \lst larger_computation. lst + (\hd sofar continue_handler abort_handler. abort_handler hd) + junk + larger_computation + larger_computation + + 3. To extract tails efficiently, too, it'd be nice to fuse the apparatus developed + in these v5 lists with the ideas from the v4 lists, above. + But that also is left as an exercise. 5. Implementing (self-balancing) trees