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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<TITLE>Transfer language reference</TITLE>
</HEAD><BODY BGCOLOR="white" TEXT="black">
<P ALIGN="center"><CENTER><H1>Transfer language reference</H1>
<FONT SIZE="4">
<I>Author: Björn Bringert <bringert@cs.chalmers.se></I><BR>
Last update: Wed Mar 1 13:52:22 2006
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">Current implementation status</A>
<LI><A HREF="#toc2">Layout syntax</A>
<LI><A HREF="#toc3">Imports</A>
<LI><A HREF="#toc4">Function declarations</A>
<LI><A HREF="#toc5">Data type declarations</A>
<LI><A HREF="#toc6">Lambda expressions</A>
<LI><A HREF="#toc7">Local definitions</A>
<LI><A HREF="#toc8">Types</A>
<UL>
<LI><A HREF="#function_types">Function types</A>
<LI><A HREF="#toc10">Basic types</A>
<LI><A HREF="#toc11">Records</A>
<LI><A HREF="#tuples">Tuples</A>
<LI><A HREF="#toc13">Lists</A>
</UL>
<LI><A HREF="#toc14">Case expressions</A>
<LI><A HREF="#patterns">Patterns</A>
<UL>
<LI><A HREF="#toc16">Constructor patterns</A>
<LI><A HREF="#toc17">Variable patterns</A>
<LI><A HREF="#toc18">Wildcard patterns</A>
<LI><A HREF="#toc19">Record patterns</A>
<LI><A HREF="#toc20">Disjunctive patterns</A>
<LI><A HREF="#toc21">List patterns</A>
<LI><A HREF="#toc22">Tuple patterns</A>
<LI><A HREF="#toc23">String literal patterns</A>
<LI><A HREF="#toc24">Integer literal patterns</A>
</UL>
<LI><A HREF="#metavariables">Metavariables</A>
<LI><A HREF="#toc26">Overloaded functions</A>
<UL>
<LI><A HREF="#toc27">Type class extension</A>
<LI><A HREF="#toc28">Extending multiple classes</A>
</UL>
<LI><A HREF="#prelude">Standard prelude</A>
<LI><A HREF="#toc30">Operators</A>
<UL>
<LI><A HREF="#toc31">Unary operators</A>
<LI><A HREF="#toc32">Binary operators</A>
</UL>
<LI><A HREF="#toc33">Compositional functions</A>
<LI><A HREF="#toc34">do notation</A>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<P>
<B>WARNING: The Transfer language is still experimental. Its syntax, type system and semantics may change without notice. I will try to help you with any problems this might cause, but I will not refrain from changing the language solely for reasons of backwards compatibility.</B>
</P>
<P>
This document describes the features of the Transfer language.
See the <A HREF="transfer-tutorial.html">Transfer tutorial</A>
for an example of a Transfer program, and how to compile and use
Transfer programs.
</P>
<P>
Transfer is a dependently typed functional programming language
with eager evaluation. The language supports generalized algebraic
datatypes, pattern matching and function overloading.
</P>
<A NAME="toc1"></A>
<H2>Current implementation status</H2>
<P>
<B>Not all features of the Transfer language have been implemented yet</B>. The most
important missing piece is the type checker. This means that there are almost
no checks done on Transfer programs before they are run. It also means that
the values of metavariables are not inferred. Thus metavariables cannot
be used where their values matter. For example, dictionaries for overloaded
functions must be given explicitly, not as metavariables.
</P>
<A NAME="toc2"></A>
<H2>Layout syntax</H2>
<P>
Transfer uses layout syntax, where the indentation of a piece of code
determines which syntactic block it belongs to.
</P>
<P>
To give the block structure without using layout
syntax, you can enclose the block in curly braces and
separate the parts of the blocks with semicolons.
</P>
<P>
For example, this case expression:
</P>
<PRE>
case x of
p1 -> e1
p2 -> e2
</PRE>
<P></P>
<P>
is equivalent to this one:
</P>
<PRE>
case x of {
p1 -> e1 ;
p2 -> e2
}
</PRE>
<P></P>
<P>
Here the layout is insignificant, as the structure is given with
braces and semicolons. Thus it is equivalent to:
</P>
<PRE>
case x of { p1 -> e1 ; p2 -> e2 }
</PRE>
<P></P>
<A NAME="toc3"></A>
<H2>Imports</H2>
<P>
A Transfer module starts with some imports. Most modules will have to
import the prelude, which contains definitons used by most programs:
</P>
<PRE>
import prelude
</PRE>
<P></P>
<P>
For more information about the standard prelude, see <A HREF="#prelude">Standard prelude</A>.
</P>
<A NAME="toc4"></A>
<H2>Function declarations</H2>
<P>
Functions need to be given a type and a definition. The type is given
by a typing judgement on the form:
</P>
<PRE>
f : T
</PRE>
<P></P>
<P>
where <CODE>f</CODE> is the function's name, and <CODE>T</CODE> its type. See
<A HREF="#function_types">Function types</A> for a how the types of functions
are written.
</P>
<P>
The definition of the function is then given as a sequence of pattern
equations. The first equation whose patterns match the function arguments
is used when the function is called. Pattern equations are on the form:
</P>
<PRE>
f p11 ... p1m = exp1
...
f pn1 ... pnm = expn
</PRE>
<P></P>
<P>
where <CODE>p11</CODE> to <CODE>pnm</CODE> are patterns, see <A HREF="#patterns">Patterns</A>.
</P>
<P>
Pattern equations can also have guards, boolean expressions which determine
whether to use the equation when the pattern has been matched. Pattern equations
with guards are written:
</P>
<PRE>
f p11 ... p1m | guard1 = exp1
...
f pn1 ... pnm | guardn = expn
</PRE>
<P></P>
<P>
Pattern equations with and without guards can be mixed in the definiton of
a function.
</P>
<P>
Any variables bound in the patterns are in scope in the guards and
right hand sides of each pattern equation.
</P>
<A NAME="toc5"></A>
<H2>Data type declarations</H2>
<P>
Transfer supports Generalized Algebraic Datatypes.
They are declared thusly:
</P>
<PRE>
data D : T where
c1 : Tc1
...
cn : Tcn
</PRE>
<P></P>
<P>
Here <CODE>D</CODE> is the name of the data type, <CODE>T</CODE> is the type of the type
constructor, <CODE>c1</CODE> to <CODE>cn</CODE> are the data constructor names, and
<CODE>Tc1</CODE> to <CODE>Tcn</CODE> are their types.
</P>
<P>
FIXME: explain the constraints on the types of type and data constructors.
</P>
<A NAME="toc6"></A>
<H2>Lambda expressions</H2>
<P>
<I>Lambda expressions</I> are terms which express functions, without
giving names to them. For example:
</P>
<PRE>
\x -> x + 1
</PRE>
<P></P>
<P>
is the function which takes an argument, and returns the value of the
argument + 1.
</P>
<A NAME="toc7"></A>
<H2>Local definitions</H2>
<P>
To give local definition to some names, use:
</P>
<PRE>
let x1 = exp1
...
xn = expn
in exp
</PRE>
<P></P>
<P>
Here, the variables <CODE>x1</CODE> to <CODE>xn</CODE> are in scope in all the expressions
<CODE>exp1</CODE> to <CODE>expn</CODE>, and in <CODE>exp</CODE>. Thus let-defined functions can be
mutually recursive.
</P>
<A NAME="toc8"></A>
<H2>Types</H2>
<A NAME="function_types"></A>
<H3>Function types</H3>
<P>
Functions types are of the form:
</P>
<PRE>
A -> B
</PRE>
<P></P>
<P>
This is the type of functions which take an argument of type
<CODE>A</CODE> and returns a result of type <CODE>B</CODE>.
</P>
<P>
To write functions which take more than one argument, we use <I>currying</I>.
A function which takes n arguments is a function which takes one
argument and returns a function which takes n-1 arguments. Thus,
</P>
<PRE>
A -> (B -> C)
</PRE>
<P></P>
<P>
or, equivalently, since <CODE>-></CODE> associates to the right:
</P>
<PRE>
A -> B -> C
</PRE>
<P></P>
<P>
is the type of functions which take teo arguments, the first of type
<CODE>A</CODE> and the second of type <CODE>B</CODE>. This arrangement lets us do
<I>partial application</I> of function to fewer arguments than the function
is declared to take, returning a new function which takes the rest
of the arguments.
</P>
<H4>Dependent function types</H4>
<P>
In a function type, the value of an argument can be used later
in the type. Such dependent function types are written:
</P>
<PRE>
(x : A) -> B
</PRE>
<P></P>
<P>
Here, <CODE>x</CODE> is in scope in <CODE>B</CODE>.
</P>
<A NAME="toc10"></A>
<H3>Basic types</H3>
<H4>Integers</H4>
<P>
The type of integers is called <CODE>Integer</CODE>.
Standard decmial integer literals, such as <CODE>0</CODE> and <CODE>1234</CODE> are used to
represent values of this type.
</P>
<H4>Floating-point numbers</H4>
<P>
The only currently supported floating-point type is <CODE>Double</CODE>, which supports
IEEE-754 double-precision floating-point numbers. Double literals are written
in decimal notation, e.g. <CODE>123.456</CODE>.
</P>
<H4>Strings</H4>
<P>
There is a primitive <CODE>String</CODE> type. String literals are written
with double quotes, e.g. <CODE>"this is a string"</CODE>.
FIXME: This might be replaced by a list of
characters representation in the future.
</P>
<H4>Booleans</H4>
<P>
Booleans are not a built-in type, though some features of the Transfer language
depend on them. The <CODE>Bool</CODE> type is defined in the
<A HREF="#prelude">Standard prelude</A>.
</P>
<PRE>
data Bool : Type where
True : Bool
False : Bool
</PRE>
<P></P>
<P>
In addition to normal pattern matching on booleans, you can use the built-in
if-expression:
</P>
<PRE>
if exp1 then exp2 else exp3
</PRE>
<P></P>
<P>
where <CODE>exp1</CODE> must be an expression of type <CODE>Bool</CODE>.
</P>
<A NAME="toc11"></A>
<H3>Records</H3>
<H4>Record types</H4>
<P>
Record types are created by using a <CODE>sig</CODE> expression:
</P>
<PRE>
sig { l1 : T1; ... ; ln : Tn }
</PRE>
<P></P>
<P>
Here, <CODE>l1</CODE> to <CODE>ln</CODE> are the field labels and <CODE>T1</CODE> to <CODE>Tn</CODE> are field types.
</P>
<H4>Record values</H4>
<P>
Record values are constructed using <CODE>rec</CODE> expressions:
</P>
<PRE>
rec { l1 = exp1; ... ; ln = expn }
</PRE>
<P></P>
<H4>Record projection</H4>
<P>
Fields are selected from records using the <CODE>.</CODE> operator. This expression selects
the field <CODE>l</CODE> from the record value <CODE>r</CODE>:
</P>
<PRE>
r.l
</PRE>
<P></P>
<H4>Records and layout syntax</H4>
<P>
The curly braces and semicolons are simply explicit layout syntax, so
the record type and record expression above can also be written as:
</P>
<PRE>
sig l1 : T1
...
ln : Tn
</PRE>
<P></P>
<PRE>
rec l1 = exp1
...
ln = expn
</PRE>
<P></P>
<A NAME="record_subtyping"></A>
<H4>Record subtyping</H4>
<P>
A record of some type R1 can be used as a record of any type R2
such that for every field <CODE>p1 : T1</CODE> in R2, <CODE>p1 : T1</CODE> is also a
field of T1.
</P>
<A NAME="tuples"></A>
<H3>Tuples</H3>
<P>
Tuples on the form:
</P>
<PRE>
(exp1, ..., expn)
</PRE>
<P></P>
<P>
are syntactic sugar for records with fields <CODE>p1</CODE> to <CODE>pn</CODE>. The expression
above is equivalent to:
</P>
<PRE>
rec { p1 = exp1; ... ; pn = expn }
</PRE>
<P></P>
<A NAME="toc13"></A>
<H3>Lists</H3>
<P>
The <CODE>List</CODE> type is not built-in, though there is some special syntax for it.
The list type is declared as:
</P>
<PRE>
data List : Type -> Type where
Nil : (A:Type) -> List A
Cons : (A:Type) -> A -> List A -> List A
</PRE>
<P></P>
<P>
The empty list can be written as <CODE>[]</CODE>. There is an operator <CODE>::</CODE> which can
be used instead of <CODE>Cons</CODE>. These are just syntactic sugar for expressions
using <CODE>Nil</CODE> and <CODE>Cons</CODE>, with the type arguments hidden.
</P>
<A NAME="toc14"></A>
<H2>Case expressions</H2>
<P>
Pattern matching is done in pattern equations and with the
<CODE>case</CODE> construct:
</P>
<PRE>
case exp of
p1 | guard1 -> rhs1
...
pn | guardn -> rhsn
</PRE>
<P></P>
<P>
where <CODE>p1</CODE> to <CODE>pn</CODE> are patterns, see <A HREF="#patterns">Patterns</A>.
<CODE>guard1</CODE> to <CODE>guardn</CODE> are boolean expressions. Case arms can also be written
without guards, such as:
</P>
<PRE>
pk -> rhsk
</PRE>
<P></P>
<P>
This is the same as writing:
</P>
<PRE>
pk | True -> rhsk
</PRE>
<P></P>
<A NAME="patterns"></A>
<H2>Patterns</H2>
<A NAME="toc16"></A>
<H3>Constructor patterns</H3>
<P>
Constructor patterns are written as:
</P>
<PRE>
C p1 ... pn
</PRE>
<P></P>
<P>
where <CODE>C</CODE> is a data constructor which takes <CODE>n</CODE> arguments.
If the value to be matched is <CODE>C v1 ... vn</CODE>,
then <CODE>v1</CODE> to <CODE>vn</CODE> will be matched against <CODE>p1</CODE> to <CODE>pn</CODE>.
</P>
<A NAME="toc17"></A>
<H3>Variable patterns</H3>
<P>
A variable pattern is a single identifier:
</P>
<PRE>
x
</PRE>
<P></P>
<P>
A variable pattern matches any value, and binds the variable name to the
value. A variable may not occur more than once in a pattern.
Note that variable patterns may not use the same identifier as data constructors
which are in scope, since they will then be interpreted as constructor
patterns.
</P>
<A NAME="toc18"></A>
<H3>Wildcard patterns</H3>
<P>
Wildcard patterns are written with a single underscore:
</P>
<PRE>
_
</PRE>
<P></P>
<P>
Wildcard patterns match all values and bind no variables.
</P>
<A NAME="toc19"></A>
<H3>Record patterns</H3>
<P>
Record patterns match record values:
</P>
<PRE>
rec { l1 = p1; ... ; ln = pn }
</PRE>
<P></P>
<P>
A record value matches a record pattern if the record value has all the
fields <CODE>l1</CODE> to <CODE>ln</CODE>, and their values match <CODE>p1</CODE> to <CODE>pn</CODE>.
</P>
<P>
Note that a record value may have more fields than the record pattern.
The values of these fields do not influence the pattern matching.
</P>
<A NAME="toc20"></A>
<H3>Disjunctive patterns</H3>
<P>
It is possible to write a pattern on the form:
</P>
<PRE>
p1 || ... || pn
</PRE>
<P></P>
<P>
A value will match this pattern if it matches any of the patterns <CODE>p1</CODE> to <CODE>pn</CODE>.
FIXME: talk about how this is expanded
</P>
<A NAME="toc21"></A>
<H3>List patterns</H3>
<P>
When pattern matching on lists, there are two special constructs.
A whole list can by matched be a list of patterns:
</P>
<PRE>
[p1, ... , pn]
</PRE>
<P></P>
<P>
This pattern will match lists of length n, such that each element
in the list matches the corresponding pattern. The empty list pattern:
</P>
<PRE>
[]
</PRE>
<P></P>
<P>
is a special case of this. It matches the empty list, oddly enough.
</P>
<P>
Non-empty lists can also be matched with <CODE>::</CODE>-patterns:
</P>
<PRE>
p1::p2
</PRE>
<P></P>
<P>
This pattern matches non-empty lists such that the first element of
the list matches <CODE>p1</CODE> and the rest of the list matches <CODE>p2</CODE>.
</P>
<A NAME="toc22"></A>
<H3>Tuple patterns</H3>
<P>
Tuples patterns on the form:
</P>
<PRE>
(p1, ... , pn)
</PRE>
<P></P>
<P>
are syntactic sugar for record patterns, in the same way as
tuple expressions, see <A HREF="#tuples">Tuples</A>.
</P>
<A NAME="toc23"></A>
<H3>String literal patterns</H3>
<P>
String literals can be used as patterns.
</P>
<A NAME="toc24"></A>
<H3>Integer literal patterns</H3>
<P>
Integer literals can be used as patterns.
</P>
<A NAME="metavariables"></A>
<H2>Metavariables</H2>
<P>
Metavariables are written as questions marks:
</P>
<PRE>
?
</PRE>
<P></P>
<P>
A metavariable is a way to tell the type checker that:
"you should be able to figure out what this should be,
I can't be bothered to tell you".
</P>
<P>
Metavariables can be used to avoid having to give type
and dictionary arguments explicitly.
</P>
<A NAME="toc26"></A>
<H2>Overloaded functions</H2>
<P>
In Transfer, functions can be overloaded by having them take a record
of functions as an argument. For example, the functions for equality
and inequality in the Transfer <A HREF="#prelude">Prelude</A> are defined as:
</P>
<PRE>
Eq : Type -> Type
Eq A = sig eq : A -> A -> Bool
eq : (A : Type) -> Eq A -> A -> A -> Bool
eq _ d = d.eq
neq : (A : Type) -> Eq A -> A -> A -> Bool
neq A d x y = not (eq A d x y)
</PRE>
<P></P>
<P>
We call <CODE>Eq</CODE> a <I>type class</I>, though it's actually just a record type
used to pass function implementations to overloaded functions. We
call a value of type <CODE>Eq A</CODE> an Eq <I>dictionary</I> for the type A.
The dictionary is used to look up the version of some function for the
particular type we want to use the function on. Thus, in order to use
the <CODE>eq</CODE> function on two integers, we need a dictionary of type
<CODE>Eq Integer</CODE>:
</P>
<PRE>
eq_Integer : Eq Integer
eq_Integer = rec eq = prim_eq_Integer
</PRE>
<P></P>
<P>
where <CODE>prim_eq_Integer</CODE> is the built-in equality function for
integers. To check whether two numbers <CODE>x</CODE> and <CODE>y</CODE> are equal, we
can then call the overloaded <CODE>eq</CODE> function with the dictionary:
</P>
<PRE>
eq Integer eq_Integer x y
</PRE>
<P></P>
<P>
Giving the type at which to use the overloaded function, and the appropriate
dictionary can be cumbersome. <A HREF="#metavariables">Metavariables</A> come to the rescue:
</P>
<PRE>
eq ? ? x y
</PRE>
<P></P>
<P>
The type checker can in most cases figure out the values of the type and
dictionary arguments. <B>NOTE: this is not implemented yet.</B>
</P>
<A NAME="toc27"></A>
<H3>Type class extension</H3>
<P>
By using record subtyping, see <A HREF="#record_subtyping">Record subtyping</A>, we can
create type classes which extend other type classes. A dictionary for the
new type class can also be used as a dictionary for old type class.
</P>
<P>
For example, we can extend the <CODE>Eq</CODE> type class above to <CODE>Ord</CODE>, a type
class for orderings:
</P>
<PRE>
Ord : Type -> Type
Ord A = sig eq : A -> A -> Bool
compare : A -> A -> Ordering
</PRE>
<P></P>
<P>
To extend an existing class, we keep the fields of the class we want to
extend, and add any new fields that we want. Because of record subtyping,
for any type <CODE>A</CODE>, a value of type <CODE>Ord A</CODE> is also a value of type <CODE>Eq A</CODE>.
</P>
<A NAME="toc28"></A>
<H3>Extending multiple classes</H3>
<P>
A type class can also extend several classes, by simply having all the fields
from all the classes we want to extend. The <CODE>Num</CODE> class in the
<A HREF="#prelude">Standard prelude</A> is an example of this.
</P>
<A NAME="prelude"></A>
<H2>Standard prelude</H2>
<P>
The standard prelude, see <A HREF="../transfer/lib/prelude.tra">prelude.tra</A>,
contains definitions of a number of standard types, functions and
type classes.
</P>
<A NAME="toc30"></A>
<H2>Operators</H2>
<P>
Most built-in operators in the Transfer language are translated
to calls to overloaded functions. This means that they can be
used at any type for which there is a dictionary for the type class
in question.
</P>
<A NAME="toc31"></A>
<H3>Unary operators</H3>
<TABLE CELLPADDING="4" BORDER="1">
<TR>
<TH>Operator</TH>
<TH>Precedence</TH>
<TH>Translation</TH>
</TR>
<TR>
<TD><CODE>-</CODE></TD>
<TD ALIGN="center">10</TD>
<TD ALIGN="center"><CODE>-x => negate ? ? x</CODE></TD>
</TR>
</TABLE>
<P></P>
<A NAME="toc32"></A>
<H3>Binary operators</H3>
<TABLE CELLPADDING="4" BORDER="1">
<TR>
<TH>Operator</TH>
<TH>Precedence</TH>
<TH>Associativity</TH>
<TH>Translation of <CODE>x op y</CODE></TH>
</TR>
<TR>
<TD ALIGN="center"><CODE>>>=</CODE></TD>
<TD ALIGN="center">3</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>bind ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>>></CODE></TD>
<TD ALIGN="center">3</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>bind ? ? x (\_ -> y)</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>||</CODE></TD>
<TD ALIGN="center">4</TD>
<TD ALIGN="center">right</TD>
<TD ALIGN="center"><CODE>if x then True else y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>&&</CODE></TD>
<TD ALIGN="center">5</TD>
<TD ALIGN="center">right</TD>
<TD ALIGN="center"><CODE>if x then y else False</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>==</CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>eq ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>/=</CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>neq ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE><</CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>lt ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE><=</CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>le ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>></CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>gt ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>>=</CODE></TD>
<TD ALIGN="center">6</TD>
<TD ALIGN="center">none</TD>
<TD ALIGN="center"><CODE>ge ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>::</CODE></TD>
<TD ALIGN="center">7</TD>
<TD ALIGN="center">right</TD>
<TD ALIGN="center"><CODE>Cons ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>+</CODE></TD>
<TD ALIGN="center">8</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>plus ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>-</CODE></TD>
<TD ALIGN="center">8</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>minus ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>*</CODE></TD>
<TD ALIGN="center">9</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>times ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>/</CODE></TD>
<TD ALIGN="center">9</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>div ? ? x y</CODE></TD>
</TR>
<TR>
<TD ALIGN="center"><CODE>%</CODE></TD>
<TD ALIGN="center">9</TD>
<TD ALIGN="center">left</TD>
<TD ALIGN="center"><CODE>mod ? ? x y</CODE></TD>
</TR>
</TABLE>
<P></P>
<A NAME="toc33"></A>
<H2>Compositional functions</H2>
<A NAME="toc34"></A>
<H2>do notation</H2>
<P>
Sequences of operations in the Monad type class can be written
using do-notation, like in Haskell:
</P>
<PRE>
do x <- f
y <- g x
h y
</PRE>
<P></P>
<P>
is equivalent to:
</P>
<PRE>
f >>= \x -> g x >>= \y -> h y
</PRE>
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