| Safe Haskell | Safe-Inferred |
|---|---|
| Language | GHC2021 |
Plutarch.Internal.Ord
Synopsis
- class PEq t => PPartialOrd t where
- class PPartialOrd t => POrd t where
Documentation
class PEq t => PPartialOrd t where Source #
Partial ordering relation.
Laws
#<= must form a partial order. More precisely:
x #<= x=True(#<=is reflexive)(x #<= y) #&& (y #<= x)=x #== y(#<=is anti-symmetric)(x #<= y) #&& (y #<= z)=x #<= z(@#<= is transitive)
Furthermore, #< must be an equivalent strict partial order to #<=:
x #<= y=(x #< y) #|| (x #== y)x #< x=False(#<is irreflexive)x #< y=pnot (y #< x)(#<is asymmetric)(x #< y) #&& (y #< z)=x #< z(#<is transitive)
Lastly, if you define #>= or #>, ensure that the following also hold:
x #> y=y #< xx #>= y=pnot (x #< y)
The default implementations of #>= and #> ensure these laws.
Minimal complete definition
Nothing
Methods
(#<=) :: Term s t -> Term s t -> Term s PBool infix 4 Source #
(#<) :: Term s t -> Term s t -> Term s PBool infix 4 Source #
(#>=) :: forall (s :: S). Term s t -> Term s t -> Term s PBool infix 4 Source #
@since WIP
(#>) :: forall (s :: S). Term s t -> Term s t -> Term s PBool infix 4 Source #
@since WIP
Instances
class PPartialOrd t => POrd t where Source #
Total ordering relation.
Laws
pmax and pmin must form a commutative semiring without identity
elements, where addition also distributes over multiplication. More
precisely:
pmax x y=pmax y x(pmaxis commutative)pmin x y=pmin y x(pminis commutative)pmax x (pmax y z)=pmax (pmax x y) z(pmaxis associative)pmin x (pmin y z)=pmin (pmin x y) z(pminis associative)pmax x (pmin y z)=pmin (pmax x y) (pmax x z)(pmaxdistributes overpmin)pmin x (pmax y z)=pmax (pmin x y) (pmin x z)(pmindistributes overpmax)
Furthermore, the following must hold relative #<:
pmin x y=if (x #< y) then x else ypmax x y=if (x #< y) then y else x
Laws 7 and 8 are also the defaults, as for most types, this is the best you can do.
Minimal complete definition
Nothing
Methods
pmax :: forall (s :: S). Term s t -> Term s t -> Term s t Source #
@since WIP
pmin :: forall (s :: S). Term s t -> Term s t -> Term s t Source #
@since WIP