Reachable variables exercise

Carlos Camarao carlos.camarao at
Thu Sep 16 09:31:23 EDT 2010

Hi. Consider for example an expression e0 like:

  fst (True,e)

where e is any expression.

e0 should have type Bool IMHO irrespectively of the type of e. In Haskell
this is the case if e's type is monomorphic, or polymorphic, or
constrained and there is a default in the current module that removes
the constraints. However, e0 is not type-correct if e has a
constrained type and the constraints are not subject to
defaulting. For example:

  class O a where o::a
  main = print $ fst(True,o)

generates a type error; in GHC:

  Ambiguous type variable `a' in the constraint:
     `O a' arising from a use of `o' at ...
    Probable fix: add a type signature that fixes these type variable(s)

A solution (that avoids type signatures) can be given as follows.

The type of f e, for f of type, say, K=>t'->t and e of type K'=> t'
should be:

      K  +_t   K' => t      (not K U K' => t)

where K  +_t  K'  denotes the constraint-set obtained by adding from K'
only constraints with type variables reachable from t.

(A type variable is reachable if it appears in the same constraint as
either a type variable free in the type, or another reachable type

Comments? Does that need and deserve a proposal?


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