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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<HEAD>
<META NAME="generator" CONTENT="http://txt2tags.sf.net">
<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: Tue Dec 6 14:26:07 2005
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">Layout syntax</A>
<LI><A HREF="#toc2">Imports</A>
<LI><A HREF="#toc3">Function declarations</A>
<LI><A HREF="#toc4">Data type declarations</A>
<LI><A HREF="#toc5">Lambda expressions</A>
<LI><A HREF="#toc6">Local definitions</A>
<LI><A HREF="#toc7">Types</A>
<UL>
<LI><A HREF="#function_types">Function types</A>
<LI><A HREF="#toc9">Basic types</A>
<LI><A HREF="#toc10">Records</A>
<LI><A HREF="#toc11">Tuples</A>
<LI><A HREF="#toc12">Lists</A>
</UL>
<LI><A HREF="#toc13">Pattern matching</A>
<UL>
<LI><A HREF="#toc14">Constructor patterns</A>
<LI><A HREF="#toc15">Variable patterns</A>
<LI><A HREF="#toc16">Wildcard patterns</A>
<LI><A HREF="#toc17">Record patterns</A>
<LI><A HREF="#toc18">Disjunctive patterns</A>
<LI><A HREF="#toc19">List patterns</A>
<LI><A HREF="#toc20">Tuple patterns</A>
<LI><A HREF="#toc21">String literal patterns</A>
<LI><A HREF="#toc22">Integer literal patterns</A>
</UL>
<LI><A HREF="#toc23">Meta variables</A>
<LI><A HREF="#toc24">Type classes</A>
<LI><A HREF="#toc25">Operators</A>
<LI><A HREF="#toc26">Compositional functions</A>
<LI><A HREF="#toc27">do notation</A>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></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.
</P>
<A NAME="toc1"></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 of a piece of code without using layout
syntax, you can enclose the block in curly braces (<CODE>{ }</CODE>) and
separate the parts of the blocks with semicolons (<CODE>;</CODE>).
</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 the above is equivalent to:
</P>
<PRE>
case x of { p1 -> e1 ; p2 -> e2 }
</PRE>
<P></P>
<A NAME="toc2"></A>
<H2>Imports</H2>
<P>
A Transfer module start 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>
<A NAME="toc3"></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 the 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 p1 ... p1n = exp
...
f qn1 ... qnm = exp
</PRE>
<P></P>
<A NAME="toc4"></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>
<A NAME="toc5"></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="toc6"></A>
<H2>Local definitions</H2>
<P>
To give local definition to some names, use:
</P>
<PRE>
let x1 : T1 = exp1
...
xn : Tn = expn
in exp
</PRE>
<P></P>
<A NAME="toc7"></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 1
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 2 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>
(x1 : T1) -> ... -> (xn : Tn) -> T
</PRE>
<P></P>
<P>
Here, <CODE>x1</CODE> can be used in <CODE>T2</CODE> to <CODE>Tn</CODE>, <CODE>x1</CODE> can be used
in <CODE>T2</CODE> to <CODE>Tn</CODE>
</P>
<A NAME="toc9"></A>
<H3>Basic types</H3>
<H4>Integers</H4>
<P>
The type of integers is called <CODE>Integer</CODE>.
standard decmial integer literals 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. This might be replaced by a list of
characters representation in the future. String literals are written
with double quotes, e.g. <CODE>"this is a string"</CODE>.
</P>
<H4>Booleans</H4>
<P>
Booleans are not a built-in type, though some features of the Transfer language
depend on them.
</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="toc10"></A>
<H3>Records</H3>
<P>
Record types are created by using a <CODE>sig</CODE> expression:
</P>
<PRE>
sig { p1 : T1; ... ; pn : Tn }
</PRE>
<P></P>
<P>
Here, <CODE>p1</CODE> to <CODE>pn</CODE> are the field labels and <CODE>T1</CODE> to <CODE>Tn</CODE> are their types.
</P>
<P>
Record values are constructed using <CODE>rec</CODE> expressions:
</P>
<PRE>
rec { p1 = exp1; ... ; pn = expn }
</PRE>
<P></P>
<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 p1 : T1
pn : Tn
</PRE>
<P></P>
<PRE>
rec p1 = exp1
pn = expn
</PRE>
<P></P>
<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="toc11"></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="toc12"></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 lists can be written as <CODE>[]</CODE>. There is a 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="toc13"></A>
<H2>Pattern matching</H2>
<P>
Pattern matching is done in pattern equations and by using the
<CODE>case</CODE> construct:
</P>
<PRE>
case exp of
p1 | guard1 -> rhs1
...
pn | guardn -> rhsn
</PRE>
<P></P>
<P>
<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>
<P>
The syntax of patterns are decribed below.
</P>
<A NAME="toc14"></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 the constructor <CODE>C</CODE> applied to
arguments <CODE>v1</CODE> to <CODE>vn</CODE>, then <CODE>v1</CODE> to <CODE>vn</CODE> will be matched
against <CODE>p1</CODE> to <CODE>pn</CODE>.
</P>
<A NAME="toc15"></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.
</P>
<A NAME="toc16"></A>
<H3>Wildcard patterns</H3>
<P>
Wildcard patterns are written as with a single underscore:
</P>
<PRE>
_
</PRE>
<P></P>
<P>
Wildcard patterns match all values and bind no variables.
</P>
<A NAME="toc17"></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 and
they will still match.
</P>
<A NAME="toc18"></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="toc19"></A>
<H3>List patterns</H3>
<A NAME="toc20"></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.
</P>
<A NAME="toc21"></A>
<H3>String literal patterns</H3>
<P>
String literals can be used as patterns.
</P>
<A NAME="toc22"></A>
<H3>Integer literal patterns</H3>
<P>
Integer literals can be used as patterns.
</P>
<A NAME="toc23"></A>
<H2>Meta variables</H2>
<A NAME="toc24"></A>
<H2>Type classes</H2>
<A NAME="toc25"></A>
<H2>Operators</H2>
<A NAME="toc26"></A>
<H2>Compositional functions</H2>
<A NAME="toc27"></A>
<H2>do notation</H2>
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