Hi Sandra,

Thank you for the references!

if you’re explicitly interested in sharing computations (rather than only modelling non-strictness) then the following approach by Fisher, Kiselyov and Shan might be of interest.

http://homes.sice.indiana.edu/ccshan/rational/S0956796811000189a.pdf (Purely functional lazy nondeterministic programming)

The are modelling the functional logic language Curry, but have also some remarks about modelling a lazy probabilistic language with their approach.
If you’re not interested in the sharing part of laziness, the paper might be a good first starting point nonetheless. They use a deep monadic embedding that you can use to model non-strictness. Other papers that use such an encoding are the following.

Their function 'share :: m a -> m (m a)' is interesting: I think the double wrapping m (m a) suggests how one could handle lazy effects in a monad.

A function (a->b) would get lifted to (m a -> m (m b)).

(i) the input changes from a to (m a) so that the function itself can decide whether to include the effect of the input into the output

(ii) the output changes from b to m (m b) so that it still has type (m b) after being unwrapped by the monad.

For example, if g takes type (m b) as input, then:

do 
  x <- f args   -- if f has return type (m b) then x has type b
  y <- g x      -- but x needs to have type (m b) here
  return y

-BenRI

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.192.7153&rep=rep1&type=pdf#page=8 (Transforming Functional Logic Programs into Monadic Functional Programs)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.134.9706&rep=rep1&type=pdf (Verifying Haskell Programs Using Constructive Type Theory)

Best regards
Sandra