Test.ChasingBottoms.SemanticOrd

Generic semantic equality and order. The semantic order referred to is that of a typical CPO for Haskell types, where e.g. (True, bottom) <=! (True, False), but where (True, True) and (True, False) are incomparable.

The implementation is based on isBottom, and has the same limitations. Note that non-bottom functions are not handled by any of the functions described below.

One could imagine using QuickCheck for testing equality of functions, but I have not managed to tweak the type system so that it can be done transparently.

Documentation

data Tweak

The behaviour of some of the functions below can be tweaked.

Constructors

Tweak

Fields

approxDepth :: Maybe Nat

If equal to Just n, an approxAll n is performed on all arguments before doing whatever the function is supposed to be doing.

timeOutLimit :: Maybe Int

If equal to Just n, then all computations that take more than n seconds to complete are considered to be equal to bottom. This functionality is implemented using isBottomTimeOut.

Instances

Eq Tweak

Ord Tweak

Show Tweak

noTweak :: Tweak

No tweak (both fields are Nothing).

class SemanticEq a where

SemanticEq contains methods for testing whether two terms are semantically equal.

Minimal complete definition

semanticEq

Methods

(==!), (/=!) :: a -> a -> Bool infix 4 ==!, /=!

semanticEq :: Tweak -> a -> a -> Bool

Instances

Data a => SemanticEq a

class SemanticEq a => SemanticOrd a where

SemanticOrd contains methods for testing whether two terms are related according to the semantic domain ordering.

Minimal complete definition

semanticCompare, semanticJoin, semanticMeet

Methods

(<!), (<=!), (>=!), (>!) :: a -> a -> Bool infix 4 <!, <=!, >=!, >!

semanticCompare :: Tweak -> a -> a -> Maybe Ordering

semanticCompare tweak x y returns Nothing if x and y are incomparable, and Just o otherwise, where o :: Ordering represents the relation between x and y.

(\/!) :: a -> a -> Maybe a infix 5

(/\!) :: a -> a -> a infixl 5

semanticJoin :: Tweak -> a -> a -> Maybe a

semanticMeet :: Tweak -> a -> a -> a

x \/! y and x /\! y compute the least upper and greatest lower bounds, respectively, of x and y in the semantical domain ordering. Note that the least upper bound may not always exist. This functionality was implemented just because it was possible (and to provide analogues of max and min in the Ord class). If anyone finds any use for it, please let me know.

Instances

Data a => SemanticOrd a