Syntax Extensions¶
Idris supports the implementation of Embedded Domain Specific
Languages (EDSLs) in several ways [1]. One way, as we have already
seen, is through extending do
notation. Another important way is
to allow extension of the core syntax. In this section we describe two
ways of extending the syntax: syntax
rules and dsl
notation.
syntax
rules¶
We have seen if...then...else
expressions, but these are not built
in. Instead, we can define a function in the prelude as follows (we
have already seen this function in Section Laziness):
ifThenElse : (x:Bool) -> Lazy a -> Lazy a -> a;
ifThenElse True t e = t;
ifThenElse False t e = e;
and then extend the core syntax with a syntax
declaration:
syntax if [test] then [t] else [e] = ifThenElse test t e;
The left hand side of a syntax
declaration describes the syntax
rule, and the right hand side describes its expansion. The syntax rule
itself consists of:
- Keywords — here,
if
,then
andelse
, which must be valid identifiers - Non-terminals — included in square brackets,
[test]
,[t]
and[e]
here, which stand for arbitrary expressions. To avoid parsing ambiguities, these expressions cannot use syntax extensions at the top level (though they can be used in parentheses). - Names — included in braces, which stand for names which may be bound on the right hand side.
- Symbols — included in quotations marks, e.g.
:=
. This can also be used to include reserved words in syntax rules, such aslet
orin
.
The limitations on the form of a syntax rule are that it must include at least one symbol or keyword, and there must be no repeated variables standing for non-terminals. Any expression can be used, but if there are two non-terminals in a row in a rule, only simple expressions may be used (that is, variables, constants, or bracketed expressions). Rules can use previously defined rules, but may not be recursive. The following syntax extensions would therefore be valid:
syntax [var] ":=" [val] = Assign var val;
syntax [test] "?" [t] ":" [e] = if test then t else e;
syntax select [x] from [t] "where" [w] = SelectWhere x t w;
syntax select [x] from [t] = Select x t;
Syntax macros can be further restricted to apply only in patterns (i.e.,
only on the left hand side of a pattern match clause) or only in terms
(i.e. everywhere but the left hand side of a pattern match clause) by
being marked as pattern
or term
syntax rules. For example, we
might define an interval as follows, with a static check that the lower
bound is below the upper bound using so
:
data Interval : Type where
MkInterval : (lower : Double) -> (upper : Double) ->
So (lower < upper) -> Interval
We can define a syntax which, in patterns, always matches Oh
for
the proof argument, and in terms requires a proof term to be provided:
pattern syntax "[" [x] "..." [y] "]" = MkInterval x y Oh
term syntax "[" [x] "..." [y] "]" = MkInterval x y ?bounds_lemma
In terms, the syntax [x...y]
will generate a proof obligation
bounds_lemma
(possibly renamed).
Finally, syntax rules may be used to introduce alternative binding
forms. For example, a for
loop binds a variable on each iteration:
syntax for {x} "in" [xs] ":" [body] = forLoop xs (\x => body)
main : IO ()
main = do for x in [1..10]:
putStrLn ("Number " ++ show x)
putStrLn "Done!"
Note that we have used the {x}
form to state that x
represents
a bound variable, substituted on the right hand side. We have also put
in
in quotation marks since it is already a reserved word.
dsl
notation¶
The well-typed interpreter in Section Example: The Well-Typed Interpreter is a simple example of a common programming pattern with dependent types. Namely: describe an object language and its type system with dependent types to guarantee that only well-typed programs can be represented, then program using that representation. Using this approach we can, for example, write programs for serialising binary data [2] or running concurrent processes safely [3].
Unfortunately, the form of object language programs makes it rather
hard to program this way in practice. Recall the factorial program in
Expr
for example:
fact : Expr G (TyFun TyInt TyInt)
fact = Lam (If (Op (==) (Var Stop) (Val 0))
(Val 1) (Op (*) (App fact (Op (-) (Var Stop) (Val 1)))
(Var Stop)))
Since this is a particularly useful pattern, Idris provides syntax overloading [1] to make it easier to program in such object languages:
mkLam : TTName -> Expr (t::g) t' -> Expr g (TyFun t t')
mkLam _ body = Lam body
dsl expr
variable = Var
index_first = Stop
index_next = Pop
lambda = mkLam
A dsl
block describes how each syntactic construct is represented
in an object language. Here, in the expr
language, any variable is
translated to the Var
constructor, using Pop
and Stop
to
construct the de Bruijn index (i.e., to count how many bindings since
the variable itself was bound); and any lambda is translated to a
Lam
constructor. The mkLam
function simply ignores its first
argument, which is the name that the user chose for the variable. It
is also possible to overload let
and dependent function syntax
(pi
) in this way. We can now write fact
as follows:
fact : Expr G (TyFun TyInt TyInt)
fact = expr (\x => If (Op (==) x (Val 0))
(Val 1) (Op (*) (app fact (Op (-) x (Val 1))) x))
In this new version, expr
declares that the next expression will
be overloaded. We can take this further, using idiom brackets, by
declaring:
(<*>) : (f : Lazy (Expr G (TyFun a t))) -> Expr G a -> Expr G t
(<*>) f a = App f a
pure : Expr G a -> Expr G a
pure = id
Note that there is no need for these to be part of an implementation of
Applicative
, since idiom bracket notation translates directly to
the names <*>
and pure
, and ad-hoc type-directed overloading
is allowed. We can now say:
fact : Expr G (TyFun TyInt TyInt)
fact = expr (\x => If (Op (==) x (Val 0))
(Val 1) (Op (*) [| fact (Op (-) x (Val 1)) |] x))
With some more ad-hoc overloading and use of interfaces, and a new syntax rule, we can even go as far as:
syntax "IF" [x] "THEN" [t] "ELSE" [e] = If x t e
fact : Expr G (TyFun TyInt TyInt)
fact = expr (\x => IF x == 0 THEN 1 ELSE [| fact (x - 1) |] * x)
[1] | (1, 2) Edwin Brady and Kevin Hammond. 2012. Resource-Safe systems programming with embedded domain specific languages. In Proceedings of the 14th international conference on Practical Aspects of Declarative Languages (PADL‘12), Claudio Russo and Neng-Fa Zhou (Eds.). Springer-Verlag, Berlin, Heidelberg, 242-257. DOI=10.1007/978-3-642-27694-1_18 http://dx.doi.org/10.1007/978-3-642-27694-1_18 |
[2] | Edwin C. Brady. 2011. IDRIS —: systems programming meets full dependent types. In Proceedings of the 5th ACM workshop on Programming languages meets program verification (PLPV ‘11). ACM, New York, NY, USA, 43-54. DOI=10.1145/1929529.1929536 http://doi.acm.org/10.1145/1929529.1929536 |
[3] | Edwin Brady and Kevin Hammond. 2010. Correct-by-Construction Concurrency: Using Dependent Types to Verify Implementations of Effectful Resource Usage Protocols. Fundam. Inf. 102, 2 (April 2010), 145-176. http://dl.acm.org/citation.cfm?id=1883636 |