Syntax Extensions — Idris 1.0 documentation

# 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` and `else`, 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 as `let` or `in`.

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