'something as (quote something). (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 λ-expressions (sometimes called "anonymous functions") with a prefix of either λ 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 λ-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:
| Scheme | OCaml | Haskell | |
| Rosetta Code | Rosetta Code | Rosetta Code | |
| PLEAC | PLEAC | PLEAC | |
| n/a | langref.org | ||
| code codex | code codex | code codex | |
| 99 problems | 99 problems | 99 problems | |