Test.ChasingBottoms.Approx

Documentation

class Approx a where

Approx is a class for approximation functions as described in The generic approximation lemma, Graham Hutton and Jeremy Gibbons, Information Processing Letters, 79(4):197-201, Elsevier Science, August 2001, http://www.cs.nott.ac.uk/~gmh/bib.html.

Instances are provided for all members of the Data type class. Due to the limitations of the Data.Generics approach to generic programming, which is not really aimed at this kind of application, the implementation is only guaranteed to perform correctly, with respect to the paper (and modulo any bugs), on non-mutually-recursive sum-of-products datatypes. In particular, nested and mutually recursive types are not handled correctly with respect to the paper. The specification below is correct, though (if we assume that the Data instances are well-behaved).

In practice the approxAll function can probably be more useful than approx. It traverses down all subterms, and it should be possible to prove a variant of the approximation lemma which approxAll satisfies.

Methods

approxAll :: Nat -> a -> a

approxAll n x traverses n levels down in x and replaces all values at that level with bottoms.

approx :: Nat -> a -> a

approx works like approxAll, but the traversal and replacement is only performed at subterms of the same monomorphic type as the original term. For polynomial datatypes this is exactly what the version of approx described in the paper above does.

Instances

Data a => Approx a

Defined in Test.ChasingBottoms.Approx

Methods

approxAll :: Nat -> a -> a

approx :: Nat -> a -> a