expressions.xml 11.3 KB
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<?xml version="1.0" encoding="ISO-8859-1" standalone="yes"?>
<page name="manual_expressions">

<title>Expressions</title>

<box title="Value constructors expressions" link="val">

<p>
The page <local href="manual_types_patterns"/> presents
the different kind of values: scalar constant (integers, characters, atoms),
structured values (pairs, records, sequences, XML elements),
and functional values (abstractions). Value themselves are
expressions, and the value constructors for structured values
operate also on expressions.
</p>

<p>
This page presents the other kinds of expressions in the language.
</p>

</box>

<box title="Pattern matching" link="match">

<p>
A fundamental operation in CDuce is pattern matching:
</p>

<sample><![CDATA[
match %%e%% with
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>

<p>
The first vertical bar <code>|</code> can be omitted.
The semantics is to try to match the result of the evaluation
of <code>%%e%%</code> successively with each pattern
<code>%%pi%%</code>. The first matching pattern triggers
the corresponding expression in the right hand side,
which can use the variables bound by the pattern.
Note that a first match policy, as for the disjunction patterns.
</p>

<p>
The static type system ensures that the pattern matching is exhaustive:
the type computed for <code>%%e%%</code> must be
a subtype of the union of the types accepted by all the patterns.
</p>

<p>
Local definition is a lighter notation for a pattern matching with
a single branch:
</p>

<sample><![CDATA[
let %%p%% = %%e1%% in %%e2%%
]]></sample>

<p>
is equivalent to:
</p>

<sample><![CDATA[
match %%e1%% with %%p%% -> %%e2%%
]]></sample>

<p>
Note that the pattern <code>%%p%%</code> need not be a simple
capture variable.
</p>

</box>

<box title="Functions" link="fun">

<section title="Abstraction">

<p>
The general form for a function expression is:
</p>

<sample><![CDATA[
fun %%f%% (%%t1%% -> %%s1%%; %%...%%; %%tn%% -> %%sn%%)
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>

<p>
The first line is the <em>interface</em> of the function,
and the remaining is the <em>body</em>, which is
a form of pattern matching (the first vertical bar <code>|</code> can
thus be omitted).
</p>

<p>
The identifier <code>%%f%%</code> is optional; it is useful
to define a recursive function (the body of the function can
use this identifier to refer to the function itself).
</p>

<p>
The interface of the function specifies some constraints on the
behavior of the function. Namely, when the function
receive an argument of type, say <code>%%ti%%</code>, the result
(if any) must be of type <code>%%si%%</code>. The type system
ensures this property by type-checking the body once for each constraint.
</p>

<p>
The function operate by pattern-matching the argument (which is a
value) exactly as for standard pattern matching. Actually, it
is always possible to add a line <code> x -> match x with </code>
between the interface and the body without changing the semantics.
</p>

<p>
When there is a single constraint in the interface, there is
an alternative notation, which is lighter for several argument
(that is, when the argument is a tuple):

</p>
<sample><![CDATA[
fun %%f%% (%%x1%% : %%t1%%, %%...%%, %%xn:tn%%) : %%s%% = %%e%%
]]></sample>
<p>
which is strictly equivalent to:
</p>
<sample><![CDATA[
fun %%f%% ((%%t1%%,%%...%%,%%tn%%) -> %%s%%) (%%x1%%,%%...%%,%%xn%%) -> %%e%%
]]></sample>

<p>
The standard notation for local binding a function is:
</p>
<sample><![CDATA[
let %%f%% = fun %%g%% (...) ... in ...
]]></sample>
<p>
Here, <code>%%f%%</code> is the "external" name for the function,
and <code>%%g%%</code> is the "internal" name (used when the function
need to call itself recursively, for instance). When the two names coincide
(or when you don't need an internal name), there is a lighter
notation:
</p>
<sample><![CDATA[
let fun %%f%% (...) ... in ...
]]></sample>

</section>

<section title="Application">

<p>
The only way
to use a function is ultimately to apply it to an argument. The notation
is simply a juxtaposition of the function and its argument.
E.g.:

</p>
<sample><![CDATA[
(fun f (x : Int) : Int = x + 1) 10
]]></sample>

<p>evaluates to 11. The static type system ensures that
applications cannot fail.</p>

<p>
Note that even if there is no functional "patterns" in CDuce,
it is possible to use in a pattern a type constraint
with a functional type, as in:
</p>

<sample><![CDATA[
fun (Any -> Int)
 | f & (Int -> Int) -> f 5 
 | x & Int -> x
 | _ -> 0;;
]]></sample>


</section>

</box>

<box title="Sequences" link="seq">

<p>
The concatenation operator is written <code>@</code>. There
is also a <code>flatten</code> operator which takes a sequence of 
sequences and returns their concatenation.
</p>

<p>
There are two built-in constructions to iterate over a sequence.
Both have a very precise typing which takes into account
the position of elements in the input sequence as given by
its static type. The <code>map</code> construction is:
</p>
<sample><![CDATA[
map %%e%% with
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>
<p>
Note the syntactic similarity with pattern matching. Actually,
<code>map</code> is a pattern matching form,
where the branches are applied in turn to each element of the
input sequence (the result of the evaluation of <code>%%e%%</code>).
The semantics is to return a sequence of the same length, where
each element in the input sequence is replaced by the result of
the matching branch.
</p>

<p>
Contrary to <code>map</code>, the <code>transform</code> construction
can return a sequence of a different length. This is achieved
by letting each branch return a sequence instead of a single
element. The syntax is:
</p>
<sample><![CDATA[
transform %%e%% with
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>
<p>
There is always an implicit default branch <code>_ -> []</code>
at then end of <code>transform</code>, which means that
unmatched elements of the input sequence are simply discarded.
</p>

<p>
Note that <code>map</code> can be simulated by <code>transform</code>
by replacing each expression <code>%%ei%%</code> with
<code>[ %%ei%% ]</code>.
</p>

<p>
Conversely, <code>transform</code> can be simulated by
<code>map</code> by using the <code>flatten</code> operator.
Indeed, we can rewrite <code>transform %%e%% with %%...%%</code>
as <code>flatten (map %%e%% with %%...%% | _ -> [])</code>.
</p>
</box>

<box title="Exceptions" link="exn">

<p>
The following construction raises an exception:
</p>
<sample><![CDATA[
raise %%e%%
]]></sample>
<p>
The result of the evaluation of <code>%%e%%</code> is the
<em>argument</em> of the exception. 
</p>

<p>
It is possible to catch an exception with an exception handler:
</p>
<sample><![CDATA[
try %%e%% with
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>
<p>
Whenever the evaluation of <code>%%e%%</code> raises an exception,
the handler tries to match the argument of the exception with
the patterns (following a first-match policy). If no pattern matches,
the exception is propagated.
</p>

<p> Note that contrary to ML, there is no exception name: the only
information carried by the exception is its argument. Consequently,
it is the responsibility of the programmer to put enough information
in the argument to recognize the correct exceptions. Note also
that a branch <code>(`A,x) -> %%e%%</code> in an exception
handler gives no static information about the capture variable
<code>x</code> (its type is <code>Any</code>). 
<b>Note:</b> 
it is possible that the support for exceptions will change in the future
to match ML-like named exceptions.
</p>

</box>

<box title="Record operators" link="record">

<p>
There are three kinds of operators on records:
</p>
<ul>
 <li>
   Field projection: 
   <sample>%%e%%.%%l%%</sample> 
   where
   <code>%%l%%</code> is the name of a label which must be
   present in the result of the evaluation of <code>%%e%%</code>.
   This construction is equivalent to: <code>match %%e%% with
   { %%l%% = x } -> x</code>.
 </li>
 <li>
   Record concatenation:  
   <sample>%%e1%% + %%e2%%</sample>
   The two expressions must evaluate to records, which
   are merged together. If both have a field with the same
   name, the one on the right have precedence. Note
   that the operator <code>+</code> is overloaded: it also operates
   on integers.
 </li>
 <li>
   Field suppression:  
   <sample>%%e%% \ %%l%%</sample>
   deletes the field <code>%%l%%</code> in the record resulting from 
   the evaluation of <code>%%e%%</code> whenever it is present.
 </li>
</ul>

</box>

<box title="Arithmetic operators" link="arith">

<p>
Binary arithmetic operators on integers:
<code>+,-,*,div,mod</code>. Note that <code>/</code> is used
for projection and <em>not</em> for division.
</p>

</box>

<box title="Generic comparison, if-then-else" link="comp">

<p>
Binary comparison operators (returns booleans):
<code><![CDATA[=,<<,<=,>>,>=]]></code>. Note that <code>&lt;</code>
is used for XML elements and is this not available for comparison.
</p>

<p>
The semantics of the comparison is not specified when
the values contain functions. Otherwise, the comparison
gives a total ordering on CDuce values. The result type
for all the comparison operators is <code>Bool</code>, except
for equality when the arguments are known statically to be different
(their types are disjoint); in this case, the result type
is the singleton <code>`false</code>.
</p>

<p>
The if-then-else construction is standard:
</p>
<sample><![CDATA[
if %%e1%% then %%e2%% else %%e3%%
]]></sample>
<p>
and is equivalent to:
</p>
<sample><![CDATA[
match %%e1%% with `true -> %%e2%% | `false -> %%e3%%
]]></sample>
<p>
Note that the else-clause is mandatory.
</p>
</box>

<box title="Upward coercion" link="upward">

<p>
It is possible to "forget" that an expression has a precise type,
and give it a super-type:
</p>
<sample><![CDATA[
(%%e%% : %%t%%)
]]></sample>
<p>
The type of this expression if <code>%%t%%</code>, and
<code>%%e%%</code> must provably have this type (it can have a
subtype). This "upward coercion" can be combined with the local let
binding:
</p>
<sample><![CDATA[
let %%p%% : %%t%% = %%e%% in %%...%%
]]></sample>
<p>which is equivalent to:</p>
<sample><![CDATA[
let %%p%% = (%%e%% : %%t%%) in %%...%%
]]></sample>
<p>
Note that the upward coercion allows earlier detection of type errors,
better localization in the program, and more informative messages.
</p>

</box>

<box title="XML-specific constructions" link="xml">

<p>
The projection takes a sequence of XML elements and returns
the concatenation of all their children with a given type.
The syntax is:
</p>
<sample><![CDATA[
%%e%%/%%t%%
]]></sample>
<p>
which is equivalent to:
</p>
<sample><![CDATA[
transform %%e%% with <_>[ (x::%%t%% | _)* ] -> x
]]></sample>
<p>
For instance, the expression
<code><![CDATA[
[ <a>[ <x>"A" <y>"B" ] <b>[ <y>"C" <x>"D"] ] / <x>_
]]></code>
evaluates to
<code><![CDATA[
 [ <x>"A" <x>"D" ]
]]></code>.
</p>

<p>
Another XML-specific construction is <code>xtransform</code>
which is a generalization of <code>transform</code> to XML trees:
</p>
<sample><![CDATA[
xtransform %%e%% with
 | %%p1%% -> %%e1%%
%%...%%
 | %%pn%% -> %%en%%
]]></sample>
<p>
Here, when an XML elements in the input sequence is not matched
by a pattern, the element is copied except that the transformation
is applied recursively to its content. Elements in the input sequence
which are not matched and are not XML elements are copied verbatim.
</p>

</box>

</page>