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)
curried_flip match lambda g. lambda y x. g x y;
in ...
-The function `curry` takes as an argument a function `f` that expects its arguments *uncurried*, and returns instead a function `lambda x y. f (x, y)` a function that expects its arguments *curried* --- but then does with them whatever `f` does. Going in the other direction, the function `uncurry` takes a function `g` that expects its arguments *curried*, and returns instead a function that expects its arguments *uncurried* --- but then does with them whatever `g` does.
+The function `curry` takes as an argument a function `f` that expects its arguments *uncurried*, and returns instead `lambda x y. f (x, y)`, a function that expects its arguments *curried* --- but then does with them whatever `f` does. Going in the other direction, the function `uncurry` takes a function `g` that expects its arguments *curried*, and returns instead a function that expects its arguments *uncurried* --- but then does with them whatever `g` does.
The function `uncurried_flip` takes as an argument again an uncurried function `f`, and returns another function that also expects its arguments uncurried, but that expects them in the other order. `curried_flip` transforms a curried function `g` in the analogous way. These are both different from the function `swap` we defined in the [[course notes|topics/week1_kapulet_advanced#functions]] as: