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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
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an alternative notation, which is lighter for several arguments
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(that is, when the argument is a tuple):

</p>
<sample><![CDATA[
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fun %%f%% (%%p1%% : %%t1%%, %%...%%, %%pn : tn%%) : %%s%% = %%e%%
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]]></sample>
<p>
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(note the blank spaces around the colons which are mandatory when the
pattern is a variable 
<footnote>
The reason why the blank spaces are mandatory with variables is that the XML
recommendation allows colons to occur in variables ("names" in XML terminology:
see section on <a href="namespaces.html">namespaces</a>), so the blanks disambiguate
the variables. Actually only the blank on the right handside is necessary:
CDuce accepts <code>fun %%f%% (%%x1%% :%%t1%%, %%...%%, %%xn :tn%%):%%s%% =
%%e%%</code>, as well (see also <a
href="tutorial_getting_started.html#bnote1">this paragraph</a> on
<code>let</code> declarations in the tutorial).</footnote>) which is strictly
equivalent to:
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</p>
<sample><![CDATA[
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fun %%f%% ((%%t1%%,%%...%%,%%tn%%) -> %%s%%) (%%p1%%,%%...%%,%%pn%%) -> %%e%%
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]]></sample>
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<p>
It is also possible to define currified functions with this syntax:
</p>
<sample><![CDATA[
fun %%f%% (%%p1%% : %%t1%%, %%...%%, %%pn : tn%%) (%%q1%% : %%s1%%, %%...%%, %%qm : sm%%) %%...%% : %%s%% = %%e%%
]]></sample>
<p>
which is strictly
equivalent to:
</p>
<sample><![CDATA[
fun %%f%% ((%%t1%%,%%...%%,%%tn%%) -> (%%s1%%,%%...%%,%%sm%%) -> %%...%% -> %%s%%) 
 (%%p1%%,%%...%%,%%pn%%) -> 
  fun ((%%s1%%,%%...%%,%%sm%%) -> %%...%% -> %%s%%)
   (%%q1%%,%%...%%,%%qm%%) -> 
     %%...%%
     %%e%%
]]></sample>

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<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
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needs to call itself recursively, for instance). When the two names coincide
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(or when you don't need an internal name), there are lighter
notations:
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</p>
<sample><![CDATA[
let fun %%f%% (...) ... in ...
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let %%f%% (...) ... in ...
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]]></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>
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Note that even if there is no functional "pattern" in CDuce,
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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
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 | _ -> 0
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]]></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>

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<box title="Generic comparisons, if-then-else" link="comp">
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<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>
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<p>
The infix operators <code>||</code> and <code>&amp;&amp;</code>
denote respectively the logical or and the logical and. The prefix
operator <code>not</code> denotes the logical negation.
</p>


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</box>

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

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<section title="Loading XML documents">
<p>
The <code>load_xml</code> operator parse an XML document on the local
file system; the argument gives the filename:</p>
<sample><![CDATA[
load_xml %%e%%
]]></sample>
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<p>
The argument to <code>load_xml</code> is a Latin1 string (the type
system will issue a warning if the argument is of type
<code>String</code> but not <code>Latin1</code>, and an
exception might be raised at runtime).
</p>

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<p>
If the support for netclient or curl is available, it is also
possible to fetch an XML file from an URL, e.g.:
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<code>load_xml "http://..."</code>. A special <code>string://</code>
is always supported: the string following the scheme is parsed as it.
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</p>

<p>
There is also a <code>load_html</code> operator to parse in a
permissive way HTML documents. The result has type <code>[Any*]</code>.
</p>

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</section>

<section title="Pretty-printing XML documents">
<p>
Two operators can be used to produce a string from an XML document:
</p>
<sample><![CDATA[
print_xml %%e%%
print_xml_utf8 %%e%%
]]></sample>
<p>
They fail if the argument is not an XML document (this isn't checked
statically). The first operator
 <code>print_xml</code> prepares the document to be dumped to
a ISO-8859-1 encoded XML file: Unicode characters outside Latin1
are escaped accordingly, and the operator fails if the document
contains tag or attribute names which cannot be represented 
in ISO-8859-1.   The second operator <code>print_xml_utf8</code>
always succeed but produces a string suitable for being dumped
in an UTF-8 encoded file. See the variants of the
<code>dump_to_file</code> operator
in the section on <a href="#io">Input/output</a>.
</p>
<p>
In both cases, the resulting string does <em>not</em> contain
the XML prefix "&lt;?xml ...>".
</p>
</section>

<section title="Projection">

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<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>

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</section>

<section title="Iteration over XML trees">

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<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>

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</section>

</box>

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<box title="Converting to and from string" link="str">

<section title="Pretty-printing a value">

<p>
The operator <code>string_of</code> converts any value to a string,
using the same pretty-printing function as the CDuce interpreter itself.
The result has type <code>Latin1</code>.
</p>

</section>

<section title="Creating atoms from strings">

<p>
The operator <code>atom_of</code> converts a string to an atom.
E.g.: <code>atom_of "x"</code> evaluates to <code>`x</code>
</p>

</section>

<section title="Creating integers from strings">

<p>
The operator <code>int_of</code> converts a string to an integer.
It fails if the string is not a decimal representation of
an integer. There is a type-checking warning when the argument
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</p>

</section>

</box>

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<box title="Input-output" link="io">

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<section title="Displaying a string">

<p>
To print a string to standard output, you can use the construction:
</p>
<sample><![CDATA[
print %%e%%
]]></sample>
<p>
The string will be printed assuming the terminal accepts
ISO-8859-1 encoded characters (or standard output is
an ISO-8859-1 stream). The operator fails if the string
cannot be encoded in ISO-8859-1. Otherwise, it returns <code>`nil</code>.
A warning is issued if the argument is not provably of type <code>Latin1</code>.
</p>

</section>

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<section title="Loading files">

<p>
There are two operators available to load a file into a CDuce string:
</p>
<sample><![CDATA[
load_file %%e%%
load_file_utf8 %%e%%
]]></sample>
<p>
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The first one loads an ISO-8859-1 encoded file (resulting type: 
<code>Latin1</code>),
whereas the second
one loads a UTF-8 encoded file (resulting type: <code>String</code>).
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</p>
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<p>
If the support for netclient or curl is available, it is also
possible to fetch a file from an URL, e.g.:
<code>load_file "http://..."</code>.
</p>
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</section>

<section title="Dumping to files">

<p>
There are two operators available to dump a CDuce string to a file:
</p>
<sample><![CDATA[
dump_to_file %%e1%% %%e2%%
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dump_to_file_utf8 %%e1%% %%e2%%
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]]></sample>
<p>
The first one creates an ISO-8859-1 encoded file (it fails
when the CDuce string contains non Latin1 characters), whereas the second
one creates a UTF-8 encoded file.  In both cases, the first
argument is the filename and the second one is the string to dump.
</p>

</section>

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</box>

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<box title="Namespaces" link="ns">

<p>
It is possible in expression position to define a local
prefix-namespace binding or to set a local default namespace.
</p>

<sample><![CDATA[
namespace %%p%% = "%%...%%" in %%e%%
namespace "%%...%%" in %%e%%
]]></sample>

<p>
See <local href="namespaces"/> for more details.
</p>

</box>

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<box title="References" link="ref">

<p>
The construction <code>ref %%T%% %%e%%</code> is used to build a
<em>reference</em> initialized with the result of the expression
<code>%%e%%</code>; later, the reference can receive any value
of type <code>%%T%%</code>.  The reference is actually a value of type
<code>{| get = [] -> T ; set = T -> [] |}</code>. 
</p>

<p>
Three syntactic sugar constructions are provided to facilitate
the use of references:
</p>

<sample>
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!%%e%%        ===  %%e%%.get []           {{ Dereferencing }}
%%e1%% := %%e2%%  ===  %%e1%%.set %%e2%%          {{ Assignment }}
%%e1%% ; %%e2%%   ===  let [] = %%e1%% in %%e2%%   {{Sequencing}}
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</sample>

</box>

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<box title="Queries" link="sel">

<p>
CDuce is endowed with a <code>select_from_where</code> syntax to perform some SQL-like queries. The general form of select expressions is
</p>
<sample><![CDATA[
select %%e%% from
   %%p1%% in %%e1%%
   %%p2%% in %%e2%%
       :
   %%pn%% in %%en%%
where %%b%%
]]></sample>
<p>
where <code>%%e%%</code> is an expression <code>%%b%%</code> a boolean
expression, the <code>%%pi%%</code>'s are patterns, and the
<code>%%ei%%</code>'s are sequence expressions.
</p>
<p>
A <code>select</code> expression works like a set of nested
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<code>transform</code> expressions. The advantage of using select rather than
transform is that queries are automatically optimized by applying classical
logic SQL optimization techniques (this automatic optimization can be
disabled).
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</p>
</box>
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</page>