should be stable now

diff --git a/rosetta1.mdwn b/rosetta1.mdwn
index 6cd0ab1..4e37427 100644 (file)
--- a/rosetta1.mdwn
+++ b/rosetta1.mdwn
@@ -1,13 +1,10 @@
 [[!toc levels=2]]
 
 [[!toc levels=2]]
 

-** *This page is still being written!* **
-
-

 ## Can you summarize the differences between your made-up language and Scheme, OCaml, and Haskell? ##
 
 The made-up language we wet our toes in in week 1 is called Kapulet. (I'll tell you the story behind its name sometime.) The purpose of starting with this language is that it represents something of a center of gravity between Scheme, OCaml, and Haskell, and also lacks many of their idiosyncratic warts. One downside is that it's not yet implemented in a form that you can run on your computers. So for now, if you want to try out your code on a real mechanical evaluator, you'll need to use one of the other languages.
 
 ## Can you summarize the differences between your made-up language and Scheme, OCaml, and Haskell? ##
 
 The made-up language we wet our toes in in week 1 is called Kapulet. (I'll tell you the story behind its name sometime.) The purpose of starting with this language is that it represents something of a center of gravity between Scheme, OCaml, and Haskell, and also lacks many of their idiosyncratic warts. One downside is that it's not yet implemented in a form that you can run on your computers. So for now, if you want to try out your code on a real mechanical evaluator, you'll need to use one of the other languages.
 

-Also, if you want to read code written outside this class, or have others read your code, for these reasons too you'll need to make the shift over to one of the established languages.
+Also, if you want to read code written outside this seminar, or have others read your code, for these reasons too you'll need to make the shift over to one of the established languages.

 
 We hope, though, that learning Kapulet first puts you in a position to make that shift more effortlessly, and also to more quickly see the places where there's underlying unity to Scheme, OCaml, and Haskell, despite their diverse syntaxes. (And idiosyncratic warts.)
 
 
 We hope, though, that learning Kapulet first puts you in a position to make that shift more effortlessly, and also to more quickly see the places where there's underlying unity to Scheme, OCaml, and Haskell, despite their diverse syntaxes. (And idiosyncratic warts.)
 


@@ -58,7 +55,11 @@ In OCaml and Kapulet, some variables made of letters also have infix syntax, suc
 
 The relation that's written `==` in Kapulet is also written that way in Haskell. That symbol means something else in OCaml, having to do with mutable reference cells; to get the same notion in OCaml one writes just a single `=`. The negation of this relation is written `!=` in Kapulet, `/=` in Haskell, and `<>` in OCaml. (Again, `!=` means something else in OCaml.)
 
 
 The relation that's written `==` in Kapulet is also written that way in Haskell. That symbol means something else in OCaml, having to do with mutable reference cells; to get the same notion in OCaml one writes just a single `=`. The negation of this relation is written `!=` in Kapulet, `/=` in Haskell, and `<>` in OCaml. (Again, `!=` means something else in OCaml.)
 

-FIXME 3 and Scheme Equalities
+These comparison operators are "polymorphic". This is a notion we'll discuss later when we get to types, but in the present context it means that you can apply `==` to two numbers, or to two booleans, and so on. In Kapulet, OCaml, and Haskell, however, you cannot apply that comparison to a number and a boolean at the same time. That will fail as a type error, instead of evaluating to `'false`.
+
+Also, these languages (and Scheme too) behave in idiosyncratic ways if you try to compare two function values for equality. The equivalence of function values is not in general recursively decidable; it may be possible in some specific cases to give you a definite yes-or-no answer, but you'll have to look up the specific rules for (each implementation of) each language. I recommend that you in general just avoid comparing function values for equality.
+
+Scheme has a whole bunch of equality functions. First, there are functions restricted to specific kinds of values: `=` for numbers, `symbol=?` for symbolic atoms, `boolean=?` for booleans (this is more familiar to us as "iff"), and so on. Those functions fail if called with arguments that aren't of the expected types. Scheme also has a couple of unrestricted equality functions, which can take arguments of any type, and the arguments need not even be of the same type (but if they're not, they'll always be counted as unequal). The two most fundamental of these are `eqv?` and `equal?`. They behave the same for numbers (at least, for "exact" numbers like integers), for symbols, for booleans, and the like. As we'll discuss [[below|rosetta1#mlists]], containers in Scheme (lists, pairs, vectors, strings) are generally "mutable", so there's a choice when comparing two such containers whether we're asking if the containers merely *happen now to contain corresponding values* (including, if their elements are themselves containers, they too containing corresponding values). Or whether we're asking if the containers *occupy the same mutable location in memory*, so that it'd be impossible for them to become unequal at any stage in the program's evaluation. The first comparison is expressed by `equal?`; the second by `eqv?`. (You may also see Scheme programs that use the predicate `eq?`. This is a variant of `eqv?` that may sometimes be more efficient.)

 
 The relations that are written `and`, `or`, and `not` in Kapulet are written the same way in Scheme. Note that in Scheme the first two can take zero or more arguments:
 
 
 The relations that are written `and`, `or`, and `not` in Kapulet are written the same way in Scheme. Note that in Scheme the first two can take zero or more arguments:
 


@@ -72,12 +73,13 @@ As you'd expect `(and bool1)` evaluates the same as plain `bool1`; similarly wit
 
 These relations are written in Haskell and OCaml as `&&`, `||`, and `not`. (Haskell uses `and` and `or` to express other functions, which compute the joint conjunction or disjunction of every `Bool` value in a List of such. OCaml permits `or` as an old synonym for `||`, but discourages using that spelling. OCaml also permits `&` as an old, discouraged synonym for `&&`.)
 
 
 These relations are written in Haskell and OCaml as `&&`, `||`, and `not`. (Haskell uses `and` and `or` to express other functions, which compute the joint conjunction or disjunction of every `Bool` value in a List of such. OCaml permits `or` as an old synonym for `||`, but discourages using that spelling. OCaml also permits `&` as an old, discouraged synonym for `&&`.)
 

-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, 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.
+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`.
 
 <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`.
 

-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. FIXME also with chars.
+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]] -->

 
 
 
 
 
 


@@ -110,7 +112,7 @@ and the like. Moreover, in Scheme parentheses are never optional and never redun
 
     ((+) 3 2)
 
 
     ((+) 3 2)
 

-what that would mean is that `+` is first being applied to *zero* arguments, which is different from not applying it all. (In Kapulet, OCaml, and Haskell, one would write that `f` is being applied to "zero arguments" like this: `f ()`. We will discuss FIXME) Scheme helpfully defines the result of applying `+` to zero arguments to be `0`. So `((+) 3 2)` would evaluate to whatever `(0 3 2)` does, and that's an error, because `0` is not a function.
+what that would mean is that `+` is first being applied to *zero* arguments, which is different from not applying it all. (In Kapulet, OCaml, and Haskell, one would write that `f` is being applied to "zero arguments" like this: `f ()`; see [[below|rosetta1#void]]. We will discuss functions that "take zero arguments" a few weeks into the seminar.) Scheme helpfully defines the result of applying `+` to zero arguments to be `0`. So `((+) 3 2)` would evaluate to whatever `(0 3 2)` does, and that's an error, because `0` is not a function.

 
 Note that `(0 3 2)`, although it *is*, qua expression, a list of numbers, does not evaluate to a list. To get an expression that *evaluates to* that list, you'd have to use `(list 0 3 2)` or `'(0 3 2)`. (Notice the initial `'`.) More on this [[below|rosetta1#writing-scheme-lists]].
 
 
 Note that `(0 3 2)`, although it *is*, qua expression, a list of numbers, does not evaluate to a list. To get an expression that *evaluates to* that list, you'd have to use `(list 0 3 2)` or `'(0 3 2)`. (Notice the initial `'`.) More on this [[below|rosetta1#writing-scheme-lists]].
 


@@ -135,7 +137,7 @@ In Scheme, the common idiom would be to define `add` like this:
 
     (define add (lambda (x y) (+ x y)))
 
 
     (define add (lambda (x y) (+ x y)))
 

-(We'll explain `define` [[below#define]].) After this, you cannot say `(add 2)`, because `add` will be expecting two arguments, but you only supplied one. You can however define curried functions in Scheme, it's just more laborious:
+(We'll explain `define` [[below|rosetta1#define]].) After this, you cannot say `(add 2)`, because `add` will be expecting two arguments, but you only supplied one. You can however define curried functions in Scheme, it's just more laborious:

 
     (define curried_add (lambda (x) (lambda (y) (+ x y))))
     (define add2 (curried_add 2))
 
     (define curried_add (lambda (x) (lambda (y) (+ x y))))
     (define add2 (curried_add 2))


@@ -174,7 +176,8 @@ like this:
 
 There are just minor differences between these languages. First, OCaml doesn't have the `( + 10)` or `(10 + )` forms, but only the `( + )`.
 
 
 There are just minor differences between these languages. First, OCaml doesn't have the `( + 10)` or `(10 + )` forms, but only the `( + )`.
 

-Second, as a special case, OCaml doesn't permit you to do this with its list cons-ing operator `::`. You have to write `fun x xs -> x :: xs`, not `( :: )`. Whereas in Kapulet `( & )`, `(x & )`, and `( & xs)` are all sections using its sequence cons-ing operator `&`; and in Haskell, `( : )`, `(x : )`, and `( : xs)` are the same.
+Second, as a special case, OCaml doesn't permit you to do this with its list cons-ing operator `::`. You have to write `fun x xs -> x :: xs`, not `( :: )`. <!-- Syntax error -->
+Whereas in Kapulet `( & )`, `(x & )`, and `( & xs)` are all sections using its sequence cons-ing operator `&`; and in Haskell, `( : )`, `(x : )`, and `( : xs)` are the same.

 
 Third, as [[mentioned above|rosetta1#pre-curried]], OCaml's and Haskell's `( + )` and the like evaluate to *curried* functions.
 
 
 Third, as [[mentioned above|rosetta1#pre-curried]], OCaml's and Haskell's `( + )` and the like evaluate to *curried* functions.
 


@@ -202,7 +205,7 @@ I know all these languages fairly well, and I still find this fourth issue diffi
 
 
 
 
 
 

-### Sequences, Lists, and Tuples
+### Sequences and Lists

 
 In Kapulet, we have a notion I called a "sequence" which has an empty form `[]` and a cons-ing operator `&`, so that:
 
 
 In Kapulet, we have a notion I called a "sequence" which has an empty form `[]` and a cons-ing operator `&`, so that:
 


@@ -237,7 +240,7 @@ Here are some list functions in Kapulet:
     length
     (&&)
     # the following were defined in homework
     length
     (&&)
     # the following were defined in homework

-    empty?
+    empty?       # can also use ([] == ) or pattern-match against []

     tail
     drop
     take
     tail
     drop
     take


@@ -266,7 +269,7 @@ Here are the corresponding functions in Haskell:
 
     length
     (++)
 
     length
     (++)

-    null
+    null     -- can also use ([] == ) or pattern-match against []

     tail     -- compare head, which fails on []
     drop     {- but these are curried functions, so you write `drop n xs`
                 not `drop (n, xs)` as in Kapulet -}
     tail     -- compare head, which fails on []
     drop     {- but these are curried functions, so you write `drop n xs`
                 not `drop (n, xs)` as in Kapulet -}


@@ -295,17 +298,18 @@ Here they are in OCaml:
 
     List.length
     (@)          (* or List.append *)
 
     List.length
     (@)          (* or List.append *)

-    (* no function corresponding to empty? *)
+    (* no function predefined for empty?
+       can use fun xs -> [] == xs, or function [] -> true | _ -> false *)

     List.tl      (* compare List.hd, which fails on [] *)
     List.tl      (* compare List.hd, which fails on [] *)

-    (* no function corresponding to drop or take *)
-    (* no function corresponding to split; OCaml uses List.split to mean something else *)
+    (* no function predefined for drop or take *)
+    (* no function predefined for split; OCaml uses List.split to mean something else *)

     List.filter  (* also List.find_all *)
     List.partition
     List.map
     List.map2    (* compare List.combine, like Haskell's zip
                     both map2 and combine fail if the lists are different lengths *)
     List.split   (* like Haskell's unzip, doesn't take an f argument *)
     List.filter  (* also List.find_all *)
     List.partition
     List.map
     List.map2    (* compare List.combine, like Haskell's zip
                     both map2 and combine fail if the lists are different lengths *)
     List.split   (* like Haskell's unzip, doesn't take an f argument *)

-    (* no function corresponding to takewhile or dropwhile *)
+    (* no function predefined for takewhile or dropwhile *)

     List.rev
     List.concat  (* also List.flatten, which still only "joins" a single layer of []s *)
     List.mem     (* not infix syntax *)
     List.rev
     List.concat  (* also List.flatten, which still only "joins" a single layer of []s *)
     List.mem     (* not infix syntax *)


@@ -313,16 +317,34 @@ Here they are in OCaml:
     List.for_all p xs
     List.exists p xs
 
     List.for_all p xs
     List.exists p xs
 

+Recall that in addition to sequences/lists, Kapulet also has a notion of *sets*, which can be literally expressed using notation like this:
+
+    {'x, x}
+
+That set contains the atomic symbol `'x`, and whatever symbol value the variable `x` is bound to (which need not, but may, be the symbol `'x`). Or:
+
+    {1, 2, x}
+
+That set contains the numbers `1` and `2`, and whatever number the variable `x` is bound to. Sets in Kapulet, like sequences, must have elements of all the same type.
+
+OCaml and Haskell also have set values (in the `Set` and `Data.Set` libraries, respectively), but these are harder to use and can't be literally expressed. In particular, the `{ ... }` notation in these languages has different meanings. <!-- In addition to Haskell block syntax, also expressed *records* in both languages, which roughly correspond to multivalues-with-keys in Kapulet. -->
+
+
+

 
 <a id=scheme-lists></a>
 How does all this look in Scheme? Well, Scheme has a notion they call a (proper) `list`, and also a notion they call a `vector`. There are also what Scheme calls "improper" `list`s, with `(cons 1 'nonlist)` or `'(1 . nonlist)`, where `'nonlist` is any non-list (here it's a `symbol`) being a limiting case. Let's ignore the improper `list`s. Scheme's (proper) `list`s and `vector`s each have a claim to correspond to Kapulet's sequences / Haskell's Lists / OCaml's `list`s. But they also differ from those. The main differences are:
 
 
 <a id=scheme-lists></a>
 How does all this look in Scheme? Well, Scheme has a notion they call a (proper) `list`, and also a notion they call a `vector`. There are also what Scheme calls "improper" `list`s, with `(cons 1 'nonlist)` or `'(1 . nonlist)`, where `'nonlist` is any non-list (here it's a `symbol`) being a limiting case. Let's ignore the improper `list`s. Scheme's (proper) `list`s and `vector`s each have a claim to correspond to Kapulet's sequences / Haskell's Lists / OCaml's `list`s. But they also differ from those. The main differences are:
 

+<a id=mlists></a>
+

 1.  these structures in Scheme can contain heterogenously-typed elements, including further `list`s and `vector`s in some positions but not in others
 2.  in the official Scheme standard, `list`s and `vector`s are both *mutable* containers, that is, one and the same persisting `list` structure can have different
 elements at different stages in a program's evaluation
 
 Many Scheme implementations also provide immutable versions of `list`s and `vector`s, more closely approximating the sequences/lists in Kapulet, Haskell, and OCaml. With some configurations, Racket even makes the immutable versions the defaults. But none of these are yet part of the official Scheme standard. Also, difference 1 is present in all Scheme implementations. This makes Scheme's `list`s and `vector`s in some ways more akin to *tuples* in the other languages (to "proper" tuples in Kapulet) (see [[below|rosetta1#tuples]]).
 
 1.  these structures in Scheme can contain heterogenously-typed elements, including further `list`s and `vector`s in some positions but not in others
 2.  in the official Scheme standard, `list`s and `vector`s are both *mutable* containers, that is, one and the same persisting `list` structure can have different
 elements at different stages in a program's evaluation
 
 Many Scheme implementations also provide immutable versions of `list`s and `vector`s, more closely approximating the sequences/lists in Kapulet, Haskell, and OCaml. With some configurations, Racket even makes the immutable versions the defaults. But none of these are yet part of the official Scheme standard. Also, difference 1 is present in all Scheme implementations. This makes Scheme's `list`s and `vector`s in some ways more akin to *tuples* in the other languages (to "proper" tuples in Kapulet) (see [[below|rosetta1#tuples]]).
 

+(OCaml does have `Array` values, and Haskell has `Data.Array.MArray` values, both of which are similar to Scheme's mutable `vector`s. But they are more difficult to use.)
+

 <a id=writing-scheme-lists></a>
 There are also some differences in how `list`s are specified in Scheme versus the other languages. In Scheme, one writes the empty list like this:
 
 <a id=writing-scheme-lists></a>
 There are also some differences in how `list`s are specified in Scheme versus the other languages. In Scheme, one writes the empty list like this:
 


@@ -356,41 +378,74 @@ Here are the `list` functions in Scheme corresponding to the functions listed in
     cdr               ; corresponds to Kapulet's and Haskell's tail
     (list-tail xs k)  ; corresponds to Kapulet's drop (k, xs)
                       ; fails if the list has length < k
     cdr               ; corresponds to Kapulet's and Haskell's tail
     (list-tail xs k)  ; corresponds to Kapulet's drop (k, xs)
                       ; fails if the list has length < k

-    ; no official function corresponding to take or split or filter or partition
+    ; no official function predefined for take or split or filter or partition

     map               ; corresponds to Kapulet's map and map2
                       ; can take one or more list arguments
     map               ; corresponds to Kapulet's map and map2
                       ; can take one or more list arguments

-    ; no official function corresponding to unmap2 or takewhile or dropwhile
+    ; no official function predefined for unmap2 or takewhile or dropwhile

     reverse
     reverse

-    ; no official function corresponding to join/concat
-    member            ; corresponds to Kapulet's (mem) and Haskell's elem  FIXME: eqv? version
+    ; no official function prefefined for join/concat
+    memv, member      ; correspond to Kapulet's (mem) and Haskell's elem
+                      ; memv compares elements using eqv?, member using equal?

     (list-ref xs k)   ; corresponds to Kapulet's `nth xs k`
                       ; fails if the index k is out of bounds
     (list-ref xs k)   ; corresponds to Kapulet's `nth xs k`
                       ; fails if the index k is out of bounds

-    ; no official function corresponding to all or any
+    ; no official function predefined for all or any
+
+<!-- memv, member return the first tail headed by the matching element, or #f -->

 
 All of the functions listed as missing from the official Scheme standard can be found in various add-on libraries, or you could define them yourself if you had to.
 
 
 All of the functions listed as missing from the official Scheme standard can be found in various add-on libraries, or you could define them yourself if you had to.
 

+
+
+

 <a id=tuples></a>
 <a id=tuples></a>

-FIXME tuples
+### Tuples

 
 

+The course notes [[already mentioned|topics/week1#lightweight]] that Kapulet has a "lightweight" notion of tuples, called multivalues and written `(10, x)`, as well as a heavier notion written `Pair (10, x)`. The latter is what corresponds to the tuples in Haskell and OCaml. They don't have any explicit notation for Kapulet's "lightweight" tuples (though they exist behind the scenes in OCaml and explain some of its otherwise puzzling behavior). There are good reasons for introducing this additional complexity in Kapulet, but this is not the place to explain them.

 
 

+All of these languages have notions of zero-length tuples, as well as pairs, triples, and the like. (In Kapulet's case, there are both the 0-length multivalue `()` and heavier counterparts.)

 
 

-LATER
-### Other functions
+Probably the closest approximation to tuples in Scheme is its notion of `vector`s, though in the case of pairs, Scheme's `pair`s---which it identifies with short, possibly "improper" `list`s---are arguably also contenders. The fact that these Scheme structures permit elements of heterogenous type is not a problem, because that is also true for tuples in the other languages. However, Scheme's `vector`s and `pair`s are officially mutable, but tuples in the other languages are not. (As mentioned above, many Scheme implementations do also provide immutable versions of these structures.)
+
+<a id=void></a>
+What corresponds to the zero-length tuples in Kapulet, OCaml, and Haskell? Perhaps the zero-length `vector`. Or perhaps a different Scheme value, called *void*. Different Scheme implementations display this value in different ways. For example, Racket and Chicken may display it as `#<void>` or as `#<unspecified>` or may just display nothing. This is the value returned, for example, by a `case` or a `cond` construction if there is no `else` clause and none of the provided clauses successfully match. In many respects, this value more closely approximates in Scheme the behavior that `()` has in Kapulet, OCaml, and Haskell.
+
+
+
+
+<a id=chars></a>
+### Chars and Strings
+
+Scheme, OCaml, and Haskell all have values they call "characters", and sequences of such characters they call "strings". Haskell and OCaml write the first character of the word "false" like this:

 
 

-Same in all: `succ`, `pred`, `fst`, `snd`.
+    'f'

 
 

-Same in Kapulet and Haskell (modulo the differences between multivalues and tuples), aren't predefined in OCaml: `id`, `const`, `flip`, `curry`, `uncurry`.
+whereas Scheme writes it like this:

 
 

-Kapulet's `(comp)` is Haskell's `( . )`; isn't predefined in OCaml.
+    #\f

 
 

-Kapulet and Haskell both have `( $ )`; OCaml expresses as `( @@ )`. (OCaml also has `|>` to express the converse operation: `f x`, `f @@ x` and `x |> f` all mean the same.)
+(Note the difference between the *character* `#\f` and the *boolean* `#f`.) Scheme gives special characters like `#\space` funny names.
+
+Sequences of characters are called "strings". All of these languages write the string "false" like this:
+
+    "false"
+
+This is not the same as the truth-value, nor is it the same as the atomic symbol `'false` (which Kapulet but not Scheme identifies with the truth-value). In Haskell, strings are strictly equivalent to Lists of `Char`s. In OCaml and Scheme, they are not equivalent to lists (nor to vectors) but merely isomorphic to them. In OCaml and Scheme, some strings are mutable, like Scheme's vectors.
+
+
+
+
+### Other functions

 
 

-Kapulet's `odd?` and `even?` are Haskell's `odd`, `even`; aren't predefined in OCaml.
+These functions are roughly the same in Kapulet, OCaml, and Haskell: `succ`, `pred`, `fst`, `snd`. The official Scheme standard doesn't include any `succ` or `pred` functions, but Racket and Chicken both have `add1` and `sub1`. Depending on what Scheme values you take to correspond to tuples in the other languages, `fst` and `snd` may correspond to `car` and `cdr`. (These also correspond to `head` and `tail` when applied to lists.)

 
 

-Kapulet's `swap` (defined in homework) is Haskell's `Data.Tuple.swap`.
+Kapulet's `(comp)`, `odd?`, `even?`, and `swap` (defined in homework) are Haskell's `( . )`, `odd`, `even`, and `Data.Tuple.swap`. None of these are predefined in OCaml.

 
 Kapulet's `dup` isn't predefined in Haskell but can be easily expressed as `\x -> (x, x)`.
 
 
 Kapulet's `dup` isn't predefined in Haskell but can be easily expressed as `\x -> (x, x)`.
 

+These are the same in Kapulet and Haskell (modulo the differences between [[Kapulet's multivalues|topics/week1#lightweight]] or "lightweight tuples" and Haskell's tuples), aren't predefined in OCaml: `id`, `const`, `flip`, `curry`, `uncurry`. None of these are predefined in OCaml.
+
+Kapulet and Haskell both have `( $ )`, which was explained [[in the course notes|topics/week1_advanced_notes#dollar]]. OCaml expresses this as `( @@ )`. (OCaml also uses `|>` to express the converse operation: `f x`, `f @@ x` and `x |> f` all mean the same.)
+

 
 
 
 
 
 


@@ -408,16 +463,18 @@ The complex expression that's written like this in Kapulet:
 is written very similarly in Haskell:
 
     -- Haskell
 is written very similarly in Haskell:
 
     -- Haskell

-    case some_expression {
+    case some_expression of {

       0 -> result0;
       1 -> result1;
       x -> resultx
     }
 
 <a id=haskell-whitespace></a>
       0 -> result0;
       1 -> result1;
       x -> resultx
     }
 
 <a id=haskell-whitespace></a>

-Unlike the other languages we're discussing, Haskell pays special attention to the whitespace/indentation of what you write. This permits you to omit the `{`, `;`, and `}`s in the above, if you've got the indentation right. And that's how you will often see Haskell code displayed. On this website, though, I propose to always include the `{`s and so on when displaying Haskell code, because the indentation rules aren't 100% intuitive. It's easy to read properly-indented Haskell code, but until you've learned and practiced the specific rules, it's not always easy to write it.
+Unlike the other languages we're discussing, Haskell pays special attention to the whitespace/indentation of what you write. If you've got the indentation right, you can omit the `{`, `;`, and `}`s in the above. And that's how you will often see Haskell code displayed. On this website, though, I propose to always include the `{`s and so on when displaying Haskell code, because the indentation rules aren't 100% intuitive. It's easy to read properly-indented Haskell code, but until you've learned and practiced the specific rules, it's not always easy to write it.
+
+<!-- In OCaml, separating expressions with `;` has a different meaning, concerning the sequencing of effects. To bracket a block of code in the way Haskell does with `{...; ...}`, in OCaml you'd use parentheses or `begin ... end`. -->

 
 

-This is written only a little bit differently in OCaml:
+The `case` construction is written only a little bit differently in OCaml:

 
     (* OCaml *)
     match some_expression with
 
     (* OCaml *)
     match some_expression with


@@ -445,7 +502,7 @@ The syntax for [[guards|topics/week1_advanced_notes#guards]] and [[as-patterns|t
 <a id=haskell-guards></a>
 
     -- Haskell
 <a id=haskell-guards></a>
 
     -- Haskell

-    case some_expression {
+    case some_expression of {

       pat1 | guard              -> result1;
            | different_guard    -> result2;
       (var@(complex_pat), pat4) -> result3
       pat1 | guard              -> result1;
            | different_guard    -> result2;
       (var@(complex_pat), pat4) -> result3


@@ -467,9 +524,9 @@ The official Scheme standard only provides for a limited version of this. There
       ((2 3 5) 'smallprime)
       (else 'toobig))
 
       ((2 3 5) 'smallprime)
       (else 'toobig))
 

-The results can be complex expressions; I just used bare symbols here for illustration. Note that the literal patterns in the first two clauses are surrounded by an extra pair of parentheses than you might expect. The reason is shown in the third clause, which begins `(2 3 5)`. This does not mean to match a list containing the values `2` `3` and `5`. Instead it means to match the simple value `2` *or* the simple value `3` *or* the simple value `5`. The final `else` clause is optional. FIXME no match?
+The results can be complex expressions; I just used bare symbols here for illustration. Note that the literal patterns in the first two clauses are surrounded by an extra pair of parentheses than you might expect. The reason is shown in the third clause, which begins `(2 3 5)`. This does not mean to match a list containing the values `2` `3` and `5`. Instead it means to match the simple value `2` *or* the simple value `3` *or* the simple value `5`. The final `else` clause is optional. If it's omitted, and none of the other clauses match, the result is Scheme's [[special void value|rosetta1#void]].

 
 

-The patterns here can be any literal value (what the Scheme standards call a "datum"). Numbers are permitted, as are boolean literals (`#t` and `#f`) and symbolic atoms (`'alpha` and the like, though inside a pattern position in a `case`-construction, you omit the initial `'`). You can also use the list literal `'()` (again, omit the initial `'` when writing it as a pattern). Some implementations of Scheme allow more complex list patterns, matching literal lists like `'(alpha 0 () #t)`; others don't.
+The patterns here can be any literal value (what the Scheme standards call a "datum"). Numbers are permitted, as are boolean literals (`#t` and `#f`) and symbolic atoms (`'alpha` and the like, though inside a pattern position in a `case` construction, you omit the initial `'`). You can also use the list literal `'()` (again, omit the initial `'` when writing it as a pattern). Some implementations of Scheme allow more complex list patterns, matching literal lists like `'(alpha 0 () #t)`; others don't.

 
 There are various add-on libraries to Scheme that will permit you to pattern-match in more ambitious ways, approximating what you can do in Kapulet, OCaml, and Haskell. We will explain some of these later in the course, after we've introduced you to the notion of *datatypes*.
 
 
 There are various add-on libraries to Scheme that will permit you to pattern-match in more ambitious ways, approximating what you can do in Kapulet, OCaml, and Haskell. We will explain some of these later in the course, after we've introduced you to the notion of *datatypes*.
 


@@ -486,7 +543,7 @@ What programmers using standard Scheme tend to do instead is to use *predicates*
       (test3 'result3)
       (else  'somethingelse))
 
       (test3 'result3)
       (else  'somethingelse))
 

-The tests tend to use predicates like `null?` (are you the empty list?), `pair?` (are you a non-empty list, whether proper or improper?), `list?` (are you a proper list, whether empty or not?), `symbol?`, `boolean?`, `number?`, `zero?` (you get the idea). The *Little Schemer* books use their own predicates they call `atom?` (are you a non-list?) and `lat?` (are you a list all of whose members are atoms?)
+The tests tend to use predicates like `null?` (are you the empty list?), `pair?` (are you a non-empty list, whether proper or improper?), `list?` (are you a proper list, whether empty or not?), `symbol?`, `boolean?`, `number?`, `zero?` (you get the idea). The *Little Schemer* books use their own predicates they call `atom?` (are you a non-list?) and `lat?` (are you a list all of whose members are atoms?) <!-- They seem to only use `symbol`s, `number`s, and `boolean`s as atoms. -->

 
 You can also use more complex tests you write on the spot, or your own antecedently-defined functions:
 
 
 You can also use more complex tests you write on the spot, or your own antecedently-defined functions:
 


@@ -527,7 +584,7 @@ Scheme standards after r5rs also provide two further conditional constructions,
     (unless test-expression
        result-expression2...)
 
     (unless test-expression
        result-expression2...)
 

-If the test-expression evaluates to `#f`, then the `when` expression evaluates to a special "void" value; mutatis mutandis for the `unless` expression. This is analogous to `()` in OCaml, Haskell, and Kapulet. FIXME
+If the test-expression evaluates to `#f`, then the `when` expression evaluates to Scheme's [[special void value|rosetta1#void]]; mutatis mutandis for the `unless` expression. This is analogous to `()` in OCaml, Haskell, and Kapulet.

 
 In the last three languages, the expressions in the then-branch and the else-branch of a conditional have to have the same type. You can't say `if test-expression then 0 else []`. Also, they expect the test-expression to evaluate specifically to a boolean value, not merely to `'false` versus "anything else". They are stricter about types here than Scheme is.
 
 
 In the last three languages, the expressions in the then-branch and the else-branch of a conditional have to have the same type. You can't say `if test-expression then 0 else []`. Also, they expect the test-expression to evaluate specifically to a boolean value, not merely to `'false` versus "anything else". They are stricter about types here than Scheme is.
 


@@ -539,14 +596,14 @@ instead of
 
      if test_expression then then_result else ()
 
 
      if test_expression then then_result else ()
 

-This is similar to Scheme's `when`-construction. Kapulet and Haskell have no analogue.
+This is similar to Scheme's `when` construction. Kapulet and Haskell have no analogue.

 
 
 
 
 ### Lambda expressions
 
 
 
 
 
 ### Lambda expressions
 

-In Kapulet you write &lambda;-expressions (sometimes called "anonymous functions") with a prefix of either &lambda; or the spelled-out `lambda`. That's followed by one or more patterns, separated by spaces, then a period, then a single expression which makes up the body of the function. When there are multiple patterns, the function expressed is *curried*, thus:
+In Kapulet you write &lambda; expressions (sometimes called "anonymous functions") with a prefix of either &lambda; or the spelled-out `lambda`. That's followed by one or more patterns, separated by spaces, then a period, then a single expression which makes up the body of the function. When there are multiple patterns, the function expressed is *curried*, thus:

 
     lambda (x, y) z. result
 
 
     lambda (x, y) z. result
 


@@ -566,7 +623,7 @@ and in OCaml you'd write:
     (* OCaml *)
     fun (x, y) z -> result
 
     (* OCaml *)
     fun (x, y) z -> result
 

-You may sometimes see &lambda;-expressions in OCaml written using `function` instead of `fun`. These overlap somewhat in their usage. The difference is that `function` only allocates a position for *one* argument pattern, so can't straightforwardly define curried functions. (You can however embed `function` expressions inside other `function` expressions.) On the other hand, `function` can take multiple *variant* patterns for that single position. Thus with `function` you can say:
+You may sometimes see &lambda; expressions in OCaml written using `function` instead of `fun`. These overlap somewhat in their usage. The difference is that `function` only allocates a position for *one* argument pattern, so can't straightforwardly define curried functions. (You can however embed `function` expressions inside other `function` expressions.) On the other hand, `function` can take multiple *variant* patterns for that single position. Thus with `function` you can say:

 
     (* OCaml *)
     function []    -> result1 |
 
     (* OCaml *)
     function []    -> result1 |


@@ -584,7 +641,7 @@ In Scheme, lambda expressions are written like this:
     ; Scheme
     (lambda (vars...) body-expressions...)
 
     ; Scheme
     (lambda (vars...) body-expressions...)
 

-Scheme only permits simple variables as its argument patterns, and the lambda-expression can be defined to take zero or more arguments:
+Scheme only permits simple variables as its argument patterns, and the lambda expression can be defined to take zero or more arguments:

 
     ; Scheme
     (lambda () ...)
 
     ; Scheme
     (lambda () ...)


@@ -592,7 +649,7 @@ Scheme only permits simple variables as its argument patterns, and the lambda-ex
     (lambda (x y) ...)
     (lambda (x y z) ...)
 
     (lambda (x y) ...)
     (lambda (x y z) ...)
 

-We will discuss functions that "take zero arguments" a few weeks into the semester.
+As I said before, we will discuss functions that "take zero arguments" a few weeks into the seminar.

 
 There is special syntax for defining functions that may take *varying* numbers of arguments (recall `and` and `+`), where Scheme binds a single variable to a list containing all of the received arguments (or all of the arguments after the *n*th...). I won't explain that syntax here.
 
 
 There is special syntax for defining functions that may take *varying* numbers of arguments (recall `and` and `+`), where Scheme binds a single variable to a list containing all of the received arguments (or all of the arguments after the *n*th...). I won't explain that syntax here.
 


@@ -654,6 +711,22 @@ Haskell has both of the syntactic forms that Kapulet does, though like OCaml, it
 
 Also, in Haskell `let` always means `letrec`. There is no term in Haskell that means what simple `let` does in Kapulet and OCaml.
 
 
 Also, in Haskell `let` always means `letrec`. There is no term in Haskell that means what simple `let` does in Kapulet and OCaml.
 

+Haskell also has another form, roughly synonymous with its `let ... in ...`. It looks like this:
+
+    -- Haskell
+    result where {
+      pat1  = expr1;
+      pat2  = expr2;
+      pat3  = expr3
+    }
+
+Here all the new bindings introduced for the variables in the `pat`s are in effect for the evaluation of the `expr`s (this works like `letrec` too), and also for the evaluation of `result`.
+
+There are a few places where you can use `let ... in ...` but not `... where ...`, and a few places where the inverse is true.
+
+<!-- (1) `let pat = expr` has a use inside do-blocks and guards; (2) `let ... in ...` is an expression, and so can occur within other expressions; (3) `where` can bind multiple guard-clauses in a `case` block: in `case expr of { pat | g1 -> e1 | g2 -> e2 where { ... }; another_pat -> ... }`, the `where` bindings govern free variables in all of `g1`, `e1`, `g2`, `e2`. -->
+
+

 <a id=five-lets></a>
 Scheme has *four (or five)* syntactic forms here, including `let`, `let*`, `letrec`, and `letrec*`. The difference between the last two [is subtle](http://stackoverflow.com/questions/13078165) and only arises in the presence of continuations; you can just use `letrec` for ordinary purposes. I won't try to explain the difference between `let` and `let*` here, except to say this:
 
 <a id=five-lets></a>
 Scheme has *four (or five)* syntactic forms here, including `let`, `let*`, `letrec`, and `letrec*`. The difference between the last two [is subtle](http://stackoverflow.com/questions/13078165) and only arises in the presence of continuations; you can just use `letrec` for ordinary purposes. I won't try to explain the difference between `let` and `let*` here, except to say this:
 


@@ -679,7 +752,7 @@ Notice that this form ends with `end`, not with `in result`. The above is roughl
       ...
     in ... # rest of program or library
     
       ...
     in ... # rest of program or library
     

-That is, the bindings initiated by the clauses of the `let`-construction remain in effect until the end of the program or library. They can of course be "hidden" by subsequent bindings to new variables spelled the same way. The program:
+That is, the bindings initiated by the clauses of the `let` construction remain in effect until the end of the program or library. They can of course be "hidden" by subsequent bindings to new variables spelled the same way. The program:

 
     # Kapulet
     let
 
     # Kapulet
     let


@@ -732,7 +805,7 @@ to be written more concisely as:
       g pat2 pat3 = body2
     in ...
 
       g pat2 pat3 = body2
     in ...
 

-OCaml and Haskell permit that same shorthand. And what Haskell permits at the toplevel of *files* are just the bare binding clauses of such expressions, that is, without the surrounding `let` and `in`. That is, a Haskell file can look like this:
+OCaml and Haskell permit that same shorthand. And Haskell additionally permits the bare binding clauses of such expressions (that is, without the surrounding `let` and `in`) to occur at the toplevel of files. In other words, a Haskell file can look like this:

 
     -- Haskell file.hs
     f pat1      = body1
 
     -- Haskell file.hs
     f pat1      = body1


@@ -740,13 +813,20 @@ OCaml and Haskell permit that same shorthand. And what Haskell permits at the to
     g pat2 pat3 = body2
     ...
 
     g pat2 pat3 = body2
     ...
 

-Note there are no semicolons here. These are called "toplevel declarations" of the functions `f` and `g`. A single function can have multiple declarations (within a single scoping context), using different patterns:
+Note there are no semicolons here. These are called "toplevel declarations" of the functions `f` and `g`. A single function name can have multiple declarations (within a single scoping context), using different patterns:

 
     -- Haskell file.hs
     f [] = 0
     f (x:xs) = 1 + f xs
 
 
     -- Haskell file.hs
     f [] = 0
     f (x:xs) = 1 + f xs
 

-defines `f` as a function that returns the length of a single List argument. (You can also do that *inside* Haskell's `let`-constructions, too.) This is what corresponds *in Haskell files* to `let ... end` in Kapulet.
+defines `f` as a function that returns the length of a single List argument. (You can also do that *inside* Haskell's `let` constructions, too.) This is what corresponds *in Haskell files* to `let ... end` in Kapulet.
+
+Haskell also permits multiple declarations of this sort inside its `let` and `where` constructs, too. Moreover, there declarations can also have [[pattern guards|rosetta1#haskell-guards]], as in:
+
+    -- Haskell file.fs
+    f [] = 0
+    f (x:xs) | odd x = 1 + f xs
+             | otherwise = f xs

 
 <a id=define></a>
 Scheme has a version of `letrec ... end`, which it writes as `define`. Thus in Scheme this:
 
 <a id=define></a>
 Scheme has a version of `letrec ... end`, which it writes as `define`. Thus in Scheme this:


@@ -781,22 +861,6 @@ There is no analogue to this in the other languages.
 
 
 
 
 
 

-
-### More to come ...
-
-(This page is being worked on...)
-
-
-FIXME
-
-symbol=?
-
-characters: #\c  #\xff  #\space  #\newline
-
-
-
-
-

 ### Further Installments ...
 
 We will expand these comparisons (on separate web pages) as we introduce additional ideas in the course, such as types and monads and continuations.
 ### Further Installments ...
 
 We will expand these comparisons (on separate web pages) as we introduce additional ideas in the course, such as types and monads and continuations.


@@ -804,20 +868,15 @@ We will expand these comparisons (on separate web pages) as we introduce additio
 
 
 
 
 
 

-
-
-FIXME
-
-

 ## Offsite Readings comparing Scheme, OCaml, and Haskell ##
 
 ## Offsite Readings comparing Scheme, OCaml, and Haskell ##
 

-

 *   [Haskell for OCaml Programmers](http://science.raphael.poss.name/haskell-for-ocaml-programmers.pdf)
 *   [Introduction to OCaml for Haskellers](http://foswiki.cs.uu.nl/foswiki/pub/Stc/BeyondFunctionalProgrammingInHaskell:AnIntroductionToOCaml/ocaml.pdf), [another](http://blog.ezyang.com/2010/10/ocaml-for-haskellers/)
 *   Haskell Wiki on [OCaml](https://wiki.haskell.org/OCaml)
 *   [ML Dialects and Haskell](http://hyperpolyglot.org/ml)
 *   [Differences between Haskell and SML?](http://www.quora.com/What-are-the-key-differences-between-Haskell-and-Standard-ML?browse)
 *   [Comparing SML to OCaml](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html)
 *   [Haskell for OCaml Programmers](http://science.raphael.poss.name/haskell-for-ocaml-programmers.pdf)
 *   [Introduction to OCaml for Haskellers](http://foswiki.cs.uu.nl/foswiki/pub/Stc/BeyondFunctionalProgrammingInHaskell:AnIntroductionToOCaml/ocaml.pdf), [another](http://blog.ezyang.com/2010/10/ocaml-for-haskellers/)
 *   Haskell Wiki on [OCaml](https://wiki.haskell.org/OCaml)
 *   [ML Dialects and Haskell](http://hyperpolyglot.org/ml)
 *   [Differences between Haskell and SML?](http://www.quora.com/What-are-the-key-differences-between-Haskell-and-Standard-ML?browse)
 *   [Comparing SML to OCaml](http://www.mpi-sws.org/~rossberg/sml-vs-ocaml.html)

+*   [Haskell vs Scheme](http://www.reddit.com/r/programming/comments/nq1k/haskell_and_scheme_which_one_and_why/)