Copyright  (c) Nils Anders Danielsson 20042015 

License  See the file LICENCE. 
Maintainer  http://www.cse.chalmers.se/~nad/ 
Stability  experimental 
Portability  nonportable (GHCspecific) 
Safe Haskell  None 
Language  Haskell98 
Generic semantic equality and order. The semantic order referred
to is that of a typical CPO for Haskell types, where e.g. (
, but where True
,
bottom
) <=!
(True
, False
)(
and True
, True
)(
are incomparable.True
, False
)
The implementation is based on isBottom
, and has the same
limitations. Note that nonbottom 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.
 data Tweak = Tweak {
 approxDepth :: Maybe Nat
 timeOutLimit :: Maybe Int
 noTweak :: Tweak
 class SemanticEq a where
 class SemanticEq a => SemanticOrd a where
Documentation
The behaviour of some of the functions below can be tweaked.
Tweak  

class SemanticEq a where Source
SemanticEq
contains methods for testing whether two terms are
semantically equal.
Data a => SemanticEq a 
class SemanticEq a => SemanticOrd a where Source
SemanticOrd
contains methods for testing whether two terms are
related according to the semantic domain ordering.
(<!), (>!), (>=!), (<=!) :: a > a > Bool infix 4 <!, >!, >=!, <=! Source
semanticCompare :: Tweak > a > a > Maybe Ordering Source
returns semanticCompare
tweak x yNothing
if x
and y
are
incomparable, and
otherwise, where Just
oo ::
represents the relation between Ordering
x
and y
.
(\/!) :: a > a > Maybe a infix 5 Source
(/\!) :: a > a > a infixl 5 Source
semanticJoin :: Tweak > a > a > Maybe a Source
semanticMeet :: Tweak > a > a > a Source
x
and \/!
yx
compute the least upper and greatest
lower bounds, respectively, of /\!
yx
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.
Data a => SemanticOrd a 