25. We mentioned in the Encoding notes that `fold_left (flipped_cons, []) xs` would give us the elements of `xs` but in the reverse order. So that's how we can express `reverse` in terms of `fold_left`. How would you express `reverse` in terms of `fold_right`? As with problem 22, don't use `letrec`!
- See the [[hint|assignment2 hint]].
+ *Here is a boring, inefficient answer*
+ let
+ append (ys, zs) = fold_right ((&), zs) ys; # aka (&&)
+ f (y, prev) = append (prev, [y]);
+ reverse xs = fold_right (f, []) xs
+ in reverse
+
+ or (same basic idea, just written differently):
+
+ let
+ f (y, prev) = fold_right ((&), [y]) prev;
+ reverse xs = fold_right (f, []) xs
+ in reverse
+
+ *Here is an elegant, efficient answer following the [[hint|assignment2 hint]]*
+
+ Suppose the list we want to reverse is `[10, 20, 30]`. Applying `fold_right` to this will begin by computing `f (30, z)` for some `f` and `z` that we specify. If we made the result of that be something like `30 & blah`, or any larger structure that contained something of that form, it's not clear how we could, using just the resources of `fold_right`, reach down into that structure and replace the `blah` with some other element, as we'd evidently need to, since after the next step we should get `30 & (20 & blah)`. What we'd like instead is something like this:
+
+ 30 & < >
+
+ Where `< >` isn't some *value* but rather a *hole*. Then with the next step, we want to plug into that hole `20 & < >`, which contains its own hole. Getting:
+
+ 30 & (20 & < >)
+
+ And so on. That is the key to the solution. The questions you need to answer, to turn this into something executable, are:
+
+ 1. What is a hole? How can we implement it?
+
+ A hole is a bound variable. `30 & < >` is `lambda x. 30 & x`.
+
+ 2. What should `f` be, so that the result of the second step, namely `f (20, 30 & < >)`, is `30 & (20 & < >)`?
+
+ let
+ f (y, prev) = lambda x. prev (y & x)
+ in ...
+
+ 3. Given that choice of `f`, what should `z` be, so that the result of the first step, namely `f (30, z)` is `30 & < >`?
+
+ The identity function: `f (30, (lambda y. y))` will reduce to `lambda x. (lambda y. y) (30 & x)`, which will reduce to `lambda x. 30 & x`.
+
+ 4. At the end of the `fold_right`, we're going to end with something like `30 & (20 & (10 & < >))`. But what we want is `[30, 20, 10]`. How can we turn what we've gotten into what we want?
+
+ Supply it with `[]` as an argument.
+
+ 5. So now put it all together, and explain how to express `reverse xs` using `fold_right` and primitive syntax like `lambda`, `&`, and `[]`?
+
+ let
+ f (y, prev) = lambda x. prev (y & x);
+ id match lambda y. y;
+ reverse xs = (fold_right (f, id) xs) []
+ in reverse
Numbers
-------
> We posted [[answers to Week 1's homework|exercises/assignment1_answers]].
+(**Week 3**) Thursday 12 February 2015
+> Topics:
+More on Lists (in progress);
+Combinatorial Logic (in progress);
+Reduction Strategies and Normal Forms (in progress);
+Homework (in progress)
+
+> Also, by this point you should be able to handle all of *The Little Schemer* except for Chapters 9 and 10. Chapter 9 covers what is going on under the hood with `letrec`, and that will be our topic for next week.
+
+
<!--
We've added a [[Monad Library]] for OCaml.
We've posted a [[State Monad Tutorial]].
* [Introduction to Objective Caml](http://files.metaprl.org/doc/ocaml-book.pdf)
(284 pp. text from 2008, based on Jason Hickey's course at CalTech) <!-- also at http://www.cs.caltech.edu/courses/cs134/cs134b/book.pdf -->
* [Think OCaml](http://greenteapress.com/thinkocaml/thinkocaml.pdf) (142 pp. pdf)
-
+* [Real World OCaml](https://realworldocaml.org/v1/en/html/index.html) (510 pp. text from 2013)
+ * recommend reading [Chapters 1-4](https://realworldocaml.org/v1/en/html/a-guided-tour.html) when getting started (Chapter 4 is a bit more advanced)
+ * then [Chapter 6](https://realworldocaml.org/v1/en/html/variants.html) when learning types
+ * then [Chapter 8](https://realworldocaml.org/v1/en/html/imperative-programming-1.html) when learning about mutation (OCaml has what we call *explicit* mutation)
### Other ###
* OCaml-Tutorial [Glossary](http://mirror.ocamlcore.org/ocaml-tutorial.org/glossary.html)
* [Reddit's r/ocaml](https://www.reddit.com/r/ocaml)
* [Stack Overflow](https://stackoverflow.com/questions/tagged/ocaml?sort=faq) questions tagged "ocaml"
-* [Real World OCaml](https://realworldocaml.org/v1/en/html/index.html) (510 pp. text from 2013)
The values that are written `'true` and `'false` in Kapulet are written in Haskell as `True` and `False`, and in OCaml as just `true` and `false`. (It'd be more consistent with OCaml's other naming policies for them to have said True and False<!-- other value constructors must be capitalized -->, but they didn't.) These are written `#t` and `#f` in Scheme, but in Scheme in many contexts any value that isn't `#f` will behave as though it were `#t`, even values you might think are more "false-like", like `0` and the empty list.
<a id=truth-like></a> Thus `(if 0 'zero 'nope)` will evaluate to `'zero`.
-Some Scheme implementations, such as Racket, permit `#true` and `#false` as synonyms for `#t` and `#f`.
+Some Scheme implementations, such as Racket, permit `#true` and `#false` as synonyms for `#t` and `#f`. (These aliases are also mandated in "version 7", r7rs, of the Scheme standard.)
Scheme also recognizes the values `'true` and `'false`, but it treats `'false` as distinct from `#f`, and thus as a "truth-like" value, like all of its other values that aren't `#f`. Kapulet essentially took Scheme's `boolean` values and collapsed them into being a subtype of its `symbol` values.
<!-- This is also what it does with Scheme's `char`s ?? see [[below|rosetta1#chars]] -->
(+ 3 2)
-and the like. Moreover, in Scheme parentheses are never optional and never redundant. In contexts like this, the parentheses are necessary to express that the function is being applied; `+ 3 2` on its own is not a complete Scheme expression. And if the `+` were surrounded by its own parentheses, as in:
+and the like. Here is an example where the function to be applied is the result of evaluating a more complex expression:
+
+ ((if #t + *) 3 2)
+
+which will evaluate to `5`, not `6`.
+
+In Scheme the parentheses are never optional and never redundant. In expressions like `(+ 3 2)`, the parentheses are necessary to express that the function is being applied; `+ 3 2` on its own is not a complete Scheme expression. And if the `+` were surrounded by its own parentheses, as in:
((+) 3 2)