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.
This document describes the features of the Transfer language. See the Transfer tutorial for an example of a Transfer program, and how to compile and use Transfer programs.
Transfer is a dependently typed functional programming language with eager evaluation. The language supports generalized algebraic datatypes, pattern matching and function overloading.
Not all features of the Transfer language have been implemented yet. 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.
Transfer uses layout syntax, where the indentation of a piece of code determines which syntactic block it belongs to.
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.
For example, this case expression:
case x of p1 -> e1 p2 -> e2
is equivalent to this one:
case x of { p1 -> e1 ; p2 -> e2 }
Here the layout is insignificant, as the structure is given with braces and semicolons. Thus it is equivalent to:
case x of { p1 -> e1 ; p2 -> e2 }
A Transfer module starts with some imports. Most modules will have to import the prelude, which contains definitons used by most programs:
import prelude
For more information about the standard prelude, see Standard prelude.
Functions need to be given a type and a definition. The type is given by a typing judgement on the form:
f : T
where f
is the function's name, and T
its type. See
Function types for a how the types of functions
are written.
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:
f p11 ... p1m = exp1 ... f pn1 ... pnm = expn
where p11
to pnm
are patterns, see Patterns.
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:
f p11 ... p1m | guard1 = exp1 ... f pn1 ... pnm | guardn = expn
Pattern equations with and without guards can be mixed in the definiton of a function.
Any variables bound in the patterns are in scope in the guards and right hand sides of each pattern equation.
Transfer supports Generalized Algebraic Datatypes. They are declared thusly:
data D : T where c1 : Tc1 ... cn : Tcn
Here D
is the name of the data type, T
is the type of the type
constructor, c1
to cn
are the data constructor names, and
Tc1
to Tcn
are their types.
FIXME: explain the constraints on the types of type and data constructors.
Lambda expressions are terms which express functions, without giving names to them. For example:
\x -> x + 1
is the function which takes an argument, and returns the value of the argument + 1.
To give local definition to some names, use:
let x1 = exp1 ... xn = expn in exp
Here, the variables x1
to xn
are in scope in all the expressions
exp1
to expn
, and in exp
. Thus let-defined functions can be
mutually recursive.
Functions types are of the form:
A -> B
This is the type of functions which take an argument of type
A
and returns a result of type B
.
To write functions which take more than one argument, we use currying. A function which takes n arguments is a function which takes one argument and returns a function which takes n-1 arguments. Thus,
A -> (B -> C)
or, equivalently, since ->
associates to the right:
A -> B -> C
is the type of functions which take teo arguments, the first of type
A
and the second of type B
. This arrangement lets us do
partial application of function to fewer arguments than the function
is declared to take, returning a new function which takes the rest
of the arguments.
In a function type, the value of an argument can be used later in the type. Such dependent function types are written:
(x : A) -> B
Here, x
is in scope in B
.
The type of integers is called Integer
.
Standard decmial integer literals, such as 0
and 1234
are used to
represent values of this type.
The only currently supported floating-point type is Double
, which supports
IEEE-754 double-precision floating-point numbers. Double literals are written
in decimal notation, e.g. 123.456
.
There is a primitive String
type. String literals are written
with double quotes, e.g. "this is a string"
.
FIXME: This might be replaced by a list of
characters representation in the future.
Booleans are not a built-in type, though some features of the Transfer language
depend on them. The Bool
type is defined in the
Standard prelude.
data Bool : Type where True : Bool False : Bool
In addition to normal pattern matching on booleans, you can use the built-in if-expression:
if exp1 then exp2 else exp3
where exp1
must be an expression of type Bool
.
Record types are created by using a sig
expression:
sig { l1 : T1; ... ; ln : Tn }
Here, l1
to ln
are the field labels and T1
to Tn
are field types.
Record values are constructed using rec
expressions:
rec { l1 = exp1; ... ; ln = expn }
Fields are selected from records using the .
operator. This expression selects
the field l
from the record value r
:
r.l
The curly braces and semicolons are simply explicit layout syntax, so the record type and record expression above can also be written as:
sig l1 : T1 ... ln : Tn
rec l1 = exp1 ... ln = expn
A record of some type R1 can be used as a record of any type R2
such that for every field p1 : T1
in R2, p1 : T1
is also a
field of T1.
Tuples on the form:
(exp1, ..., expn)
are syntactic sugar for records with fields p1
to pn
. The expression
above is equivalent to:
rec { p1 = exp1; ... ; pn = expn }
The List
type is not built-in, though there is some special syntax for it.
The list type is declared as:
data List : Type -> Type where Nil : (A:Type) -> List A Cons : (A:Type) -> A -> List A -> List A
The empty list can be written as []
. There is an operator ::
which can
be used instead of Cons
. These are just syntactic sugar for expressions
using Nil
and Cons
, with the type arguments hidden.
Pattern matching is done in pattern equations and with the
case
construct:
case exp of p1 | guard1 -> rhs1 ... pn | guardn -> rhsn
where p1
to pn
are patterns, see Patterns.
guard1
to guardn
are boolean expressions. Case arms can also be written
without guards, such as:
pk -> rhsk
This is the same as writing:
pk | True -> rhsk
Constructor patterns are written as:
C p1 ... pn
where C
is a data constructor which takes n
arguments.
If the value to be matched is C v1 ... vn
,
then v1
to vn
will be matched against p1
to pn
.
A variable pattern is a single identifier:
x
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.
Wildcard patterns are written with a single underscore:
_
Wildcard patterns match all values and bind no variables.
Record patterns match record values:
rec { l1 = p1; ... ; ln = pn }
A record value matches a record pattern if the record value has all the
fields l1
to ln
, and their values match p1
to pn
.
Note that a record value may have more fields than the record pattern. The values of these fields do not influence the pattern matching.
It is possible to write a pattern on the form:
p1 || ... || pn
A value will match this pattern if it matches any of the patterns p1
to pn
.
FIXME: talk about how this is expanded
When pattern matching on lists, there are two special constructs. A whole list can by matched be a list of patterns:
[p1, ... , pn]
This pattern will match lists of length n, such that each element in the list matches the corresponding pattern. The empty list pattern:
[]
is a special case of this. It matches the empty list, oddly enough.
Non-empty lists can also be matched with ::
-patterns:
p1::p2
This pattern matches non-empty lists such that the first element of
the list matches p1
and the rest of the list matches p2
.
Tuples patterns on the form:
(p1, ... , pn)
are syntactic sugar for record patterns, in the same way as tuple expressions, see Tuples.
String literals can be used as patterns.
Integer literals can be used as patterns.
Metavariables are written as questions marks:
?
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".
Metavariables can be used to avoid having to give type and dictionary arguments explicitly.
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 Prelude are defined as:
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)
We call Eq
a type class, though it's actually just a record type
used to pass function implementations to overloaded functions. We
call a value of type Eq A
an Eq dictionary 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 eq
function on two integers, we need a dictionary of type
Eq Integer
:
eq_Integer : Eq Integer eq_Integer = rec eq = prim_eq_Integer
where prim_eq_Integer
is the built-in equality function for
integers. To check whether two numbers x
and y
are equal, we
can then call the overloaded eq
function with the dictionary:
eq Integer eq_Integer x y
Giving the type at which to use the overloaded function, and the appropriate dictionary can be cumbersome. Metavariables come to the rescue:
eq ? ? x y
The type checker can in most cases figure out the values of the type and dictionary arguments. NOTE: this is not implemented yet.
By using record subtyping, see Record subtyping, 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.
For example, we can extend the Eq
type class above to Ord
, a type
class for orderings:
Ord : Type -> Type Ord A = sig eq : A -> A -> Bool compare : A -> A -> Ordering
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 A
, a value of type Ord A
is also a value of type Eq A
.
A type class can also extend several classes, by simply having all the fields
from all the classes we want to extend. The Num
class in the
Standard prelude is an example of this.
The standard prelude, see prelude.tra, contains definitions of a number of standard types, functions and type classes.
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.
Operator | Precedence | Translation |
---|---|---|
- |
10 | -x => negate ? ? x |
Operator | Precedence | Associativity | Translation of x op y |
---|---|---|---|
>>= |
3 | left | bind ? ? x y |
>> |
3 | left | bind ? ? x (\_ -> y) |
|| |
4 | right | if x then True else y |
&& |
5 | right | if x then y else False |
== |
6 | none | eq ? ? x y |
/= |
6 | none | neq ? ? x y |
< |
6 | none | lt ? ? x y |
<= |
6 | none | le ? ? x y |
> |
6 | none | gt ? ? x y |
>= |
6 | none | ge ? ? x y |
:: |
7 | right | Cons ? ? x y |
+ |
8 | left | plus ? ? x y |
- |
8 | left | minus ? ? x y |
* |
9 | left | times ? ? x y |
/ |
9 | left | div ? ? x y |
% |
9 | left | mod ? ? x y |
Sequences of operations in the Monad type class can be written using do-notation, like in Haskell:
do x <- f y <- g x h y
is equivalent to:
f >>= \x -> g x >>= \y -> h y