Is there a way to chain Result mapping and unwrapping?

If you actually want to ignore the results as you are doing with if let you can use a macro like this:

macro_rules! iflet {
    ([$p:pat = $e:expr] $($rest:tt)*) => {
        if let $p = $e {
            iflet!($($rest)*);
        }
    };
    ($b:block) => {
        $b
    };
}


fn main() {
    iflet!([Ok(file) = env::var("CONF")]
           [Ok(mut reader) = File::open(&file)]
           [Ok(conf) = Json::from_reader(&mut reader)] {
        // do something with conf
    });
}

Playground (without Json part)

The macro is originally from an answer I made to a similar question on Options, but it works with any if let. Though, with Result you often want to use the Err in some way, so I would usually lean towards the approach explained by Shepmaster or ?/try!.

Is there such a mechanism in Rust?

Yes — although not all in one shot like you've presented. Let's review your theoretical signature:

impl<T, E> Result<T, E> {
    fn map_unwrap<F, U, D>(&self, op: F) -> Result<U, D>
    where
        F: FnOnce(T) -> Result<U, D>,
    {}
}

This cannot work - assume that we start with an Err variant - how would this code know how to convert from E to D? Additionally, &self isn't appropriate for functions that want to convert types; those usually take self.

There are two components that you will need to combine:

1. Result::and_then

   impl<T, E> Result<T, E> {
       fn and_then<U, F>(self, op: F) -> Result<U, E>
       where
           F: FnOnce(T) -> Result<U, E>,
       {}
   }
   

2. Result::map_err

   impl<T, E> Result<T, E> {
       fn map_err<F, O>(self, op: O) -> Result<T, F>
       where
           O: FnOnce(E) -> F,
       {}
   }
   

Then you will need a type that can represent both error types. I'll be lazy and use Box<Error>

Combined together, you need something like:

use std::env;
use std::fs::File;
use std::error::Error;

fn main() {
    let conf = env::var("CONF")
        .map_err(|e| Box::new(e) as Box<Error>)
        .and_then(|f| File::open(f).map_err(|e| Box::new(e) as Box<Error>));
}

Now each call converts the error value to a shared type, and the result is chainable with and_then. Presumably, your real code would create an error type that is suited to your problem, and then you would use that in the map_err call. I'd implement From, then you can have just:

let conf: Result<_, Box<Error>> = env::var("CONF")
    .map_err(Into::into)
    .and_then(|f| File::open(f).map_err(Into::into));