- What do you mean by "The type Cont Int a describes an impure computation, which may abort with an Int value, for example". Aborting with an Int value is akin to exceptions?
I see that using Cont monad wasn't a good idea. The point can be made simply, with an Error monad or applicative. Here is a simple function to multiply a list of integers:
muls :: [Integer] -> Either e Integer muls [] = pure 1 muls (h:t) = (h*) <$> muls t
We give the signature (which the compiler accepts) with the polymorphic return type Either e Integer, fully polymorphic over e. Therefore, muls throws no exceptions. Here is a bit more optimized function, which stops all multiplications once zero is encountered.
mulse :: [Integer] -> Either Integer Integer mulse [] = pure 1 mulse (0:t) = Left 0 mulse (h:t) = (h*) <$> mulse t
We cannot make the return type (Either e Integer), it must be (Either Integer Integer). The function can indeed throw an exception. If we handle the exception
muls' :: [Integer] -> Either e Integer muls' l = either pure pure $ mulse l
the effect is encapsulated and the type is polymorphic again.
- for me it's not clear when to choose an "applicative" or a "monadic" DSL? Betsides, what's the rational behind the name "let_" (never seen it before)?
Other pointers where this idiom is realised?? Lots of places; ST monad comes to mind, and the Region monad. This
The first rule of thumb is to use the simplest structure that does the job. Another good rule is to distinguish the DSL from its implementation. For example, the DSL below http://okmij.org/ftp/tagless-final/index.html#call-by-any has no monads. It is a simple lambda-calculus with constants. Its implementation in Haskell, the embedding, does use monads, sometimes quite specific monads (e.g., IO, to print the trace of evaluation). But these monads are not exposed to the DSL programmer. That article also shows off let_. > data Eff = Effect | NoEffect > -- first type parameter is used to track effects > data Exp :: Eff -> * -> * where > ReadAccount :: Exp r Int --ReadAccount can be used in whatever > monad (with or without effect) > WriteAccount :: Exp NoEffect Int -> Exp Effect () --WriteAccount > takes an effect-less expression, and returns an effectfull expression This is exactly what I had in mind (and probably Jacques as well). trick is often used to track, for example, information flow security (the label then reflects the sensitivity level of data processed by the computation, Low or High). See, for example, http://www.cse.chalmers.se/~russo/seclib.htm http://www.scs.stanford.edu/~deian/pubs/stefan:2011:flexible-slides.pdf or just search for information flow control or information flow security in Haskell. Edward Yang has a lot to say on this topic.