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Mon Jan 17 10:38:11 EST 2011

## Monadic let (a failed attempt at State continuation monad in Haskell)

For practical code generation we need at least the following
ingredients:
- Continuation monad for let insertion.
- State monad for variable names.
I'm lacking the ``muscle memory'' that comes with experience. How do
we start this? Essentially we want to make it easy to use, employing
standard `do' notation. Let's start with what that would look like:
f x y =
do
a <- x + y
return a * a
This gives an error message:
Occurs check: cannot construct the infinite type: t = m t
Expected type: m t
Inferred type: t
In the second argument of `(*)', namely `a'
In the expression: return a * a
Ok, that is silly. This one typechecks:
f4 x y =
do
a <- x + y
return (a * a)
So what does this mean? It has the following type:
f4 :: (Num (m b), Monad m, Num b) => m b -> m b -> m b
Both the underlying type b and the monadic type (m b) need to behave
as a Num. To summarize:
Num b from a * a
Num (m b) from x + y
So how to define the monad? What confuses me is the type:
m a -> (a -> m b) -> m b
I'd expect a == b. Probably because I want to express a writer monad?
I'm getting frustrated. It makes no sense...
Some questions.
* What is the thing that is bound by `bind'? Meaning the `a' type
above? It is a code expression.
* Does it make sense to actually add monadic values? Is it possible
to only have 'let' be made explicit by using a do notation, and
not any other form of combination?
This means merging of dictonaries. Do the examples in the paper
use this?
* How do the two types fit in this? Why am I so conceptually stuck
on "list append" ?

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