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** *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.

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.

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.)

### Comments

    ...  # this is a comment in Kapulet, that goes until the end of the line

    ...  ; this is a comment in Scheme, that goes until the end of the line

    ...  -- this is a comment in Haskell, that goes until the end of the line

Note that for Haskell's comments, the `--` must be immediately followed by something like a space or a letter. `-->` does not begin a comment; it's a legal operator symbol.

OCaml doesn't have comments of that sort. It only has "block" comments like this:

    (* ... *)

which may last for several lines. These comments *nest*, so that:

    (* ... (* inner *) ... *)

is a single comment.

Haskell also has block comments, though it `{- writes them differently -}`.
Haskell's block comments also nest.

Racket and Scheme also have block comments, though they `#| write them differently |#`.
These block comments also nest. Another form of block comments is `#;( ... )`. Those may contain nested parentheses, and extend until the next *matching* `)`. So prefixing `#;` to a complex parenthesized expression is a way to turn the whole thing into a comment. (These two comment styles aren't part of the official Scheme standard, but they are widely implemented.)



### Variables

Our [[syntax for variables|topics/week1#variables]] in Kapulet is close to that in the other languages. Haskell and OCaml differ only in that they do not permit trailing `?` or `!`; however, they do permit trailing `'`s (and even permit `'`s *in the middle* of a variable too, which Kapulet does not). Scheme permits all of these characters, plus many more punctuation symbols as well, to occur anywhere in a variable. Scheme also permits variables to begin with capital letters, or to consist solely of the single character `_`; but the other languages reserve these terms for special purposes.

In addition to the variables made of letters (more properly, of alphanumerics), Haskell and OCaml and Kapulet also permit some variables made exclusively of punctuation symbols, like `<` or Haskell's `>=>` and `<$>`. In Haskell, these always have infix syntax, and the variables made of letters never do. (But the former can have their infix syntax suppressed with parentheses, and the latter can be "flagged" to temporarily take on infix syntax, as we'll discuss below.)

In OCaml and Kapulet, some variables made of letters also have infix syntax, such as `comp` in Kapulet or `mod` in OCaml. I haven't presented to you the complex mechanisms needed to declare this.



### Infix operators and parentheses


Kapulet, OCaml, and Haskell all understand some expressions like `+` to be infix operators. So you would write:

    1 + 2

not:

    + 1 2

Although all three of these languages permits you to enclose an infix operator in parentheses to make a *section*, which no longer has infix syntax. In Kapulet, `( + )` is the same as &lambda; `(x, y). x + y`, whereas in OCaml and Haskell it's a *curried* function, which we can write (in Kapulet syntax) as &lambda; `x y. x + y`. We'll discuss sections and curried functions below.

Kapulet and OCaml have some operators spelled with letters also taking infix syntax, such as `comp` in Kapulet or `mod` in OCaml. In Haskell, this is never the case: variables that are made of letters are only treated as function terms being applied to arguments *when they're at the start* of a list of expressions; and variables that are made of punctuation symbols, and not enclosed in parentheses, will only be treated as infix operators. However, Haskell permits you to temporarily "flag" a  function term made of letters to behave like an infix operator, by enclosing it in `` ` `` marks. Thus in Haskell you can write:

    3 `mod` 2

But without the `` ` ``, you'd have to write: `mod 3 2`.

Scheme has no infix operators. It ruthlessly demands that all functions to be applied to arguments come at the start of a list of expressions, regardless of whether those functions are spelled using letters, punctuation symbols, or a mix of the two. Thus in Scheme one always writes:

    (+ 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:

    ((+) 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 ()`. 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.

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 `'`.) FIXME

In Scheme, you can also write `(+ 3 2 10)`, and so on. You only have to write `(+ (+ 3 2) 10)` if you really want to.

Parentheses have many other roles in Scheme, as well; they're a ubiquitous part of the syntax, and don't always express function application. You might sometimes feel they are overused.

You may sometimes see `[ ... ]` being used instead of `( ... )`. This is just a stylistic variant, they work exactly the same. The official Scheme standard doesn't permit that, but most Scheme implementations do. It can help keep track of which closing `]` or `)` goes with which opening `[` or `)`. The opening and closing symbols always have to correspond.


In Scheme, the default style for defining functions is as taking several arguments simultaneously, that is the *uncurried* style. In OCaml and Haskell, the default style is to define them *curried*. Curried functions can easily be partially applied:

    (* OCaml *)
    let add  = fun x y -> x + y in
    let add2 = add 2 in
        add2 3
    ;;

will result in `5`.

In Scheme, the default would be to define `add` like this:

    (define add (lambda (x y) (+ x y)))

Then 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))
    (add2 3)

will result in `5`. This is the best one can do in official Scheme, but there are various syntax extensions and macros out there to make it possible to write this sort of thing more succinctly.

OCaml and Haskell also permit defining functions in uncurried form:

    (* OCaml *)
    let add  = fun (x, y) -> x + y in
    let add2 = fun add 2 in ...

Here the last displayed line will fail, because `add` expects as its argument a tuple of two numbers.

Kapulet essentially works like OCaml and Haskell; though for pedagogical reasons I started out by introducing uncurried definitions, rather than the *curried* definitions those other languages predominantly use.

[[As we mentioned|topics/week1_advanced_notes#sections]], in Kapulet, OCaml, and Haskell, there is a shorthand that enables you to write things like:

    # Kapulet
    let
      ten_minus match lambda x. 10 - x;
      and_ys    match lambda x. x & ys;
      plus      match lambda (x, y). x + y
    in (ten_minus, and_ys)

like this:

    # Kapulet
    let
      ten_minus match (10 - );
      and_ys    match ( & ys);
      plus      match ( + )
    in (ten_minus, and_ys)

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-consing operator `::`. You have to write `fun x xs -> x :: xs`, not `( :: )`. Whereas in Kapulet `( & )`, `(x & )`, and `( & xs)` are all sections using its sequence-consing operator `&`; and in Haskell, `( : )`, `(x : )`, and `( : xs)` are the same.

Thirdly, in Kapulet, `( - 10)` also expresses &lambda; `x. x - 10` (consistently with `(10 - )`), but Haskell (and OCaml) treat this form differently, and interpret it as meaning the integer `- 10`. Here's how to express some things in Kapulet:

    # Kapulet
    (0 - 2)
    ( - 2)         # ( - 2) 10 == 8
    (0 - )
    ( - ) (5, 3)
    

and here are their translations into Haskell:

    -- Haskell
    ( -2 )
    (subtract 2)  -- subtract 2 10 == 8
    negate        -- (0 - ) also works
    ( - ) 5 3

OCaml expresses `(0 - )` or `negate` as `~-`. You can write `3 * (0 - 2)` in OCaml as either `3 * ( -2 )` or as `3 * ~-2`.

I know all these languages fairly well, and I still find this last issue difficult to keep track of. You may be starting to understand why I spoke of "warts."


### Equality and Booleans

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 notion is written `!=` in Kapulet, `/=` in Haskell, and `<>` in OCaml. (Again, `!=` means something else in OCaml.)

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:

    ; Scheme
    (and)
    (and bool1)
    (and bool1 bool2)
    (and bool1 bool2 bool3)

As you'd expect `(and bool1)` evaluates the same as plain `bool1`; similarly with `(or bool1)`. What do you think `(and)` with no arguments should evaluate to? How about `(or)`?

These relations are written in Haskell and OCaml as `&&`, `||`, and `not`. (Haskell uses `and` and `or` to express functions that form the 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`. They're 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-ish", like `0` and the empty list. Thus `(if 0 'yes 'no)` will evaluate to `'yes`.

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 "true-ish" 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.



### Sequences, Lists, and Tuples

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

    1 & 2 & 3 & []

can also be written:

    [1, 2, 3]

Haskell is very similar, except that it calls these Lists, and its cons-ing operator is written `:`. OCaml also calls them `list`s, and its cons-operator is written `::`. (OCaml *also* uses `:`, but it uses it to deal with types, and Haskell in turn also uses `::`, but that's what *it* uses to deal with types. Grr.)

Kapulet writes the operator that concatenates or appends sequences as `&&`. Thus:

    # Kapulet
    [1, 2] && [3, 4, 5]

evaluates to `[1, 2, 3, 4, 5]`. Haskell writes this operator as `++`. In Haskell, a `String` is just a List of `Char`, so `++` is also the operator we use to append strings:

    -- Haskell
    "over" ++ "due"

evaluates to `"overdue"`. In OCaml, `string`s aren't implemented as `list`s, so their append operators are different: `^` for `string`s and `@` for `list`s:

    (* OCaml *)
    [1; 2] @ [3; 4; 5] ;;
    "over" ^ "due" ;;

evaluate to `[1; 2; 3; 4; 5]` and `"overdue"`. Note that OCaml separates its `list` items with semicolons not commas. If you write `[1, 2, 3]` in OCaml, it will think that's a one-element list whose first element is a triple, that is, what you'd write in Haskell as `[(1, 2, 3)]`.

Here are some list functions in Kapulet:

    length
    (&&)
    # the following were defined in homework
    empty?
    tail
    drop
    take
    split
    filter
    partition
    map
    map2
    # the following were defined in extra credit
    unmap2
    takewhile
    dropwhile
    reverse
    # new functions
    join         # converts [[10, 20], [30], [], [40, 50]]
                 # to [10, 20, 30, 40, 50] (but only "joining" a single layer of []s)
    (mem)        # infix syntax, 2 mem [1, 2, 3] == 'true
    nth          # nth [10, 20, 30] 1 == 20, because the first element
                 # is at position 0; fails if index is out of bounds
    all? p xs    # all? odd? [1, 3, 5] == 'true
    any? p xs    # any? even? [1, 3, 5] == 'false



Here are the corresponding functions in Haskell:

    length
    (++)
    null
    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 -}
    take
    splitAt
    filter
    Data.List.partition
    map
    zipWith  {- zip handles the special case where f is the function that forms ordered pairs
                both zipWith and zip stop with the shortest list -}
    unzip    {- unlike unmap2, doesn't take an explicit f argument
                just assumes it's (\(x, y) -> (x, y)) -}
    takeWhile
    dropWhile
    reverse
    concat   -- corresponding to join
    elem     -- not infix syntax, but often written as: 2 `elem` [1, 2, 3]
    (!!)     -- infix syntax: [10, 20, 30] !! 1 == 20; fails if index is out of bounds
    all p xs
    any p xs



Here they are in OCaml:

    length
    (@)          (* or List.append *)
    (* no function corresponding to empty? *)
    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 *)
    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 *)
    List.rev
    List.concat  (* also List.flatten, which still only "joins" a single layer of []s *)
    List.mem     (* not infix syntax *)
    List.nth     (* List.nth [10; 20; 30] 1 = 20; fails if index is out of bounds *)
    List.for_all p xs
    List.exists p xs


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 has a claim to correspond to Kapulet's sequences, Haskell's Lists, and OCaml's `list`s. Each is also somewhat different. The dominant differences are:

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).

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:

    (list)

and lists with more elements like this:

    (list 10)
    (list 10 x)
    (list 10 x 'alpha)
    (list 10 x 'alpha (list 'beta 'gamma) 'delta 20)

In the preceding, the `x` is a variable and is evaluated to be whatever value it's bound to in the context where the displayed expressions are being evaluated. If one has a list specification that contains no variables, no matter how deeply embedded, then a certain shorthand becomes available, using a `'` prefix, like this:

    '()                          ; same as (list)
    '(10)                        ; same as (list 10)
    '(10 alpha)                  ; same as (list 10 'alpha)
    '(10 alpha (beta gamma) 20)  ; same as (list 10 'alpha (list 'beta 'gamma) 20)

Scheme can also write <code>'<em>something</em></code> as <code>(quote <em>something</em>)</code>. (The `quote` is not a function being applied to some argument; this is a special syntax that only superficially *looks* like a function application.)


Here are the `list` functions in Scheme corresponding to the functions listed in the other languages:

    cons              ; corresponds to Kapulet's ( & ), Haskell's ( : ), OCaml's `::`
    length
    append            ; corresponds to Kapulet's ( && ), Haskell's ( ++ ), OCaml's ( @ )
                      ; can be applied to one or more arguments
    null?             ; corresponds to Kapulet's empty?, Haskell's null
    car               ; corresponds to Haskell's head
    cdr               ; corresponds to Kapulet's and Haskell's tail
    (list-tail xs k)  ; corresponds to Kapulet's drop (k, xs); fails if out-of-bounds
    ; no official function corresponding to take or split or filter or partition
    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
    reverse
    ; no official function corresponding to join/concat
    member            ; corresponds to Kapulet's (mem) and Haskell's elem
    (list-ref xs k)   ; corresponds to Kapulet's `nth xs k`
    ; no official function corresponding to all or any

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.



### Pattern-matching

The complex expression that's written like this in Kapulet:

    # Kapulet
    case some_expression of
      0 then result0;
      1 then result1;
      x then resultx
    end

is written very similarly in Haskell:

    -- Haskell
    case some_expression {
      0 -> result0;
      1 -> result1;
      x -> resultx
    }

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.

This is written only a little bit differently in OCaml:

    (* OCaml *)
    match some_expression with
      0 -> result0 |
      1 -> result1 |
      x -> resultx

Note there is no closing `end` or `}`. You can enclose the whole expression in parentheses if you want to, and when embedding it in some larger expressions (like another `match` expression), you may need to. Sometimes the `|` dividers are written at the start of a line, and you are allowed to include an extra one before the first line, so you could also see this written as:

    (* OCaml *)
    match some_expression with
      | 0 -> result0
      | 1 -> result1
      | x -> resultx

The syntax for [[guards|topics/week1_advanced_notes#guards]] and [[as-patterns|topics/week1_advanced_notes#as-patterns]] also only varies slightly between these languages:

    # Kapulet
    case some_expression of
      pat1   when guard             then result1;
      pat1   when different_guard   then result2;
      ((complex_pat) as var, pat4)  then result3
    end

    -- Haskell
    case some_expression {
      pat1 | guard              -> result1;
           | different_guard    -> result2;
      (var@(complex_pat), pat4) -> result3
    }

    (* OCaml *)
    match some_expression with
      pat1   when guard             -> result0 |
      pat1   when different_guard   -> result1 |
      ((complex_pat) as var, pat4   -> result3


The official Scheme standard only provides for a limited version of this. There is a `case` construction, available since at least "version 5" of the Scheme standard (r5rs), but it only accepts literal values as patterns, not any complex patterns containing them or any patterns containing variables. Here is how it looks:

    ; Scheme
    (case some_expression
      ((0) 'result0)
      ((1) 'result1)
      ((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.

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`-expression, 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, after we've introduced you to the notion of *datatypes*.

What programmers using standard Scheme tend to do instead is to use *predicates* that query the type and/or structure of an unknown value, and then take separate evaluation paths depending on the result. This can be done with an `if...then...else...` construction, or with Scheme's more general `cond` construction. In Scheme, these two are equivalent:

    ; Scheme
    (if test1 'result1
              (if test2 'result2
                        (if test3 'result3 'somethingelse)))

    (cond
      (test1 'result1)
      (test2 'result2)
      (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). But you can also use more complex tests you write on the spot, or use antecedently-defined functions:

    ; Scheme...in case the parens left any doubt
    (define smallprime? (lambda (x) (if (= x 2) #t (if (= x 3) #t (if (= x 5) #t #f)))))

    (cond
      ((= x 0) 'infant)
      ((smallprime? x) 'myfavorite)
      ((and (> x 10) (< x 20)) 'teenaged)
      (else 'unknown))

Remember that in Scheme, an expression doesn't have to evaluate to `#t` to be treated as "truth-like". *Every* value other than `#f` is treated as truth-like. So `(if 0 'zero 'nope)` evaluates to `'zero`.

You may sometimes see Scheme `cond` constructions written with this kind of clause:

    (cond
      ...
      (test-expression => function-value)
      ...)

That's the same as the following:

    (cond
      ...
      (test-expression (function-value test-expression))
      ...)

Except that it only evaluates the test-expression once.

The clauses in Scheme's `cond` expressions can contain *multiple* expressions after the test. This only becomes useful when you're working with mutable values and side-effects, which we've not gotten to yet. The `if` expressions only take a single expression for the "then" branch and a single expression for the "else" branch. You can turn a complex series of expressions, which may involve side-effects, into a single expression by wrapping it in a `(begin ...)` construction. The `(begin ...)` construction as a whole evaluates to whatever the last expression it contains does.

Scheme standards after r5rs also provide two further conditional constructions, which are for the situations where you want to perform a meaningful action only on the "then" branch, or only on the "else" branch:

    (when test-expression
       result-expression1...)

    (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.

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` or *anything else*. They are stricter about types here than Scheme is.

In the special case where both a then-branch and an else-branch evaluate to `()`, and the else-branch involves no complex expression but merely the literal `()`, then OCaml permits you to omit the else-branch. So in OCaml you can write this:

     if test-expression then then-result

instead of

     if test-expression then then-result else ()

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



### 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:

    lambda (x, y) z. result

means the same as:

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

The parentheses could have been omitted around `lambda z. result`; they're just there to focus your attention.

Haskell and OCaml are very similar to this, they just use some slightly different notation. In Haskell you'd write:

    -- Haskell
    \(x, y) z -> result

and in OCaml you'd write:

    (* 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 define curried functions. On the other hand, `function` can take multiple *variant* patterns for that single position. Thus with `function` you can say:

    (* OCaml *)
    function []    -> result1 |
             x::xs -> result2

whereas with `fun` you'd have to write:

    (* OCaml *)
    fun ys -> match ys with
                []    -> result1 |
                x::xs -> result2

In Scheme, lambda expressions are written like this:

    ; Scheme
    (lambda (vars...) body-expressions...)

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

    ; Scheme
    (lambda () ...)
    (lambda (x) ...)
    (lambda (x y) ...)
    (lambda (x y z) ...)

There is special syntax for defining functions that may take varying numbers of arguments (recall `and` and `+`), to have them bind a single variable to a list containing all of their arguments (or all of the arguments after the third...). I won't explain that syntax here.



### Let, Letrec, and Define

Kapulet has the syntax:

    # Kapulet
    let
      pat1  match expr1;
      pat2  match expr2;
      pat3  match expr3
    in result

which is equivalent to:

    # Kapulet
    let
      pat1  match expr1
    in let
      pat2  match expr2
    in let
      pat3  match expr3
    in result

There is also a `letrec` form. In `let`, the bindings in `pat1` are in effect for the evaluation of all of `expr2`, `expr3`, and `result` (but not any further, if this is part of a more complex expression); similarly for the bindings in `pat2` and `pat3`. In `letrec`, all of the bindings on the left-hand side are in effect for all of the right-hand side expressions, as well as for the result.

OCaml only has the second, more verbose form of this, and writes it a bit differently:

    (* OCaml *)
    let
      pat1  = expr1
    in let
      pat2  = expr2
    in let
      pat3  = expr3
    in result

If you want to define some mutually recursive functions with `letrec`, there's a special syntax for that, using `letrec ... and ... in ...`:

    (* OCaml *)
    letrec
      even  = fun x -> if x = 0 then true else odd x
    and
      odd   = fun x -> if x = 0 then false else even x
    in ...

Haskell has both of the syntactic forms that Kapulet does, though like OCaml, it uses `=` rather than `match`. And it wraps all multiple patterns with `{ ... }` (see earlier remarks about Haskell and whitespace/indentation FIXME):

    -- Haskell
    let {
      pat1  = expr1;
      pat2  = expr2;
      pat3  = expr3
    } in result

Also, in Haskell `let` always means `letrec`. There is no term in Haskell that means what simple `let` does in Kapulet and OCaml.

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:

1.  When there's only a single pattern-binding clause, as in `(let ((var expression)) result)`, `let` and `let*` work the same.
2.  When there are multiple pattern-binding clauses, as in `(let ((var1 expression1) (var2 expression2)) result)`, then they work somewhat differently and `let*` is probably the one that works like you're expecting.

The `let*` form is the one that corresponds to `let` in Kapulet. I recommend you get in the habit of just always using `let*` (or `letrec`) in Scheme.

When you're at the "toplevel" of your program, or of a library/module/compilation-unit (the terminology differs), there is also another syntactic form possible. In Kapulet, you'd write:

    # Kapulet
    let
      pat1  match expr1;
      ...
    end
    ... # rest of program or library

Notice that this form ends with `end`, not with `in result`. The above is roughly equivalent to:

    # Kapulet
    let
      pat1  match expr1;
      ...
    in ... # rest of program or library
    
That is, the bindings initiated by the clauses of the `let`-expression 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
      x  match 0
    end
    let
      x  match 1
    end
    x

evaluates to `1`, just like:

    # Kapulet
    let
      x  match 0
    in let
      x  match 1
    in x

does. There's a similar form for `letrec`.

OCaml can do the same:

    let
      x = 0;;
    let
      x = 1;;
    x

The double-semicolons are hints to OCaml's "toplevel interpreter" that a syntactic unit has finished. In some contexts they're not needed, but it does no harm to include them if you're not sure.

Haskell's "toplevel interpreter" (ghci) permits a syntactic form that looks superficially quite like these:

    let x = 2
    x

but under the covers something quite different is happening (you're working "inside the IO Monad", except that simple expressions like `x` that don't evaluate to monadic values are also evaluated, as a special case). If you're writing in a *file* that you want Haskell to interpret or compile, on the other hand, you have to do something a bit different (which you can't easily also do inside ghci). [[Recall|topics/week1_advanced_notes#funct-declarations]] the shortcut by which we permitted:

    # Kapulet
    let
      f  match lambda pat1. body1;
      g  match lambda pat2 pat3. body2;
      ...

to be written more concisely as:

    # Kapulet
    let
      f pat1      = body1;
      g pat2 pat3 = body2;
      ...

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:

    -- Haskell file.hs
    f pat1      = body1

    g pat2 pat3 = body2
    ...

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

    -- 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 this *within* Haskell's `let`-constructions, too.) This is what corresponds *in Haskell files* to `let ... end` in Kapulet.

Scheme has a version of `letrec ... end`, which it writes as `define`. Thus in Scheme this:

    ; Scheme
    (define var1 expr1)
    ... ; rest of program

evaluates the same as this:

    ; Scheme
    (letrec ((var1 expr1))
            ... ; rest of program
                )

Some versions of Scheme permit you also to include `define` inside some (but not all) complex expressions. Thus you can write:

    (lambda (x)
      (define var1 expr1)
      ...)

instead of:

    (lambda (x)
      (letrec ((var1 expr1))
      ...))

There is no analogue to this in the other languages.





FIXME

symbol=?

characters: #\c  #\xff  #\space  #\newline



### Other functions

Same in all: `succ`, `pred`, `fst`, `snd`.

Same in Kapulet and Haskell (modulo the differences between multivalues and tuples), aren't predefined in OCaml: `id`, `const`, `flip`, `curry`, `uncurry`.

Kapulet's `(comp)` is Haskell's `( . )`; isn't predefined in OCaml.

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.)

Kapulet's `odd?` and `even?` are Haskell's `odd`, `even`; aren't predefined in OCaml.

Kapulet's `swap` (defined in homework) is Haskell's `Data.Tuple.swap`.

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




### More to come ...

(This page is being worked on...)



### 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.






FIXME


## 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)




## Why did you name these pages "Rosetta"? ##

The [Rosetta Stone](https://en.wikipedia.org/wiki/Rosetta_Stone) is a famous slab discovered during Napoleon's invasion of Egypt, that had the same decree written in ancient Greek (which modern scholars understood) and two ancient Egyptian scripts (which they didn't). The slab enabled us to recover understanding of those Egyptian scripts; and has since come to be a symbol for the simultaneous expression of a single idea in multiple languages. A number of websites do this for various programming languages:

<table><th>
<td>Scheme
<td>OCaml
<td>Haskell
<tr>
<td rowspan=10>&nbsp;
<td><a href="http://rosettacode.org/wiki/Category:Scheme">Rosetta Code</a>
<td><a href="http://rosettacode.org/wiki/Category:OCaml">Rosetta Code</a>
<td><a href="http://rosettacode.org/wiki/Category:Haskell">Rosetta Code</a>
<tr>
<td><a href="http://pleac.sourceforge.net/pleac_guile/index.html">PLEAC</a>
<td><a href="http://pleac.sourceforge.net/pleac_ocaml/index.html">PLEAC</a>
<td><a href="http://pleac.sourceforge.net/pleac_haskell/index.html">PLEAC</a>
<tr>
<td>n/a
<td colspan=2 align=center><hr><a href="http://langref.org/ocaml+haskell/solved">langref.org</a>
<tr>
<td><a href="http://www.codecodex.com/wiki/Category:Scheme">code codex</a>
<td><a href="http://www.codecodex.com/wiki/Category:Objective_Caml">code codex</a>
<td><a href="http://www.codecodex.com/wiki/Category:Haskell">code codex</a>
<tr>
<td><a href="http://community.schemewiki.org/?ninety-nine-scheme-problems">99 problems</a>
<td><a href="http://ocaml.org/learn/tutorials/99problems.html">99 problems</a>
<td><a href="https://wiki.haskell.org/H-99:_Ninety-Nine_Haskell_Problems">99 problems</a>
</table>

See also the [Project Euler](https://projecteuler.net/) programming challenges.