Module

Data.Operator.PartialOrd

Package: purescript-higher-order
Repository: matthew-hilty/purescript-higher-order

#PartialOrd1 Source

class PartialOrd1 f  where

The PartialOrd1 typeclass represents type constructors f that have an asociated partial ordering of values of type f a independent of any choice of a.

PartialOrd1 instances should satisfy the laws of partial orderings:

Reflexivity: a .<=? a == Just true
Antisymmetry: if a .<=? b == Just true and b .<=? a == Just true then a .== b
Transitivity: if a .<=? b == Just true and b .<=? c == Just true then a .<=? c == Just true

That is, partial orderings should satisfy all the laws of total orderings

Reflexivity: a .<= a
Antisymmetry: if a .<= b and b .<= a then a .== b
Transitivity: if a .<= b and b .<= c then a .<= c

... EXCEPT the law of connexity, which follows:

Connexity: a .<= b or b .<= a

Members

pCompare1 :: forall a. f a -> f a -> Maybe Ordering

Instances

(Ord1 f) => PartialOrd1 f

#pBetween1 Source

pBetween1 :: forall f a. PartialOrd1 f => f a -> f a -> f a -> Maybe Boolean

#pClamp1 Source

pClamp1 :: forall f a. PartialOrd1 f => f a -> f a -> f a -> Maybe (f a)

#pComparing1 Source

pComparing1 :: forall f b a. PartialOrd1 f => (a -> f b) -> a -> a -> Maybe Ordering

#pGreaterThan1 Source

pGreaterThan1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe Boolean

#(.>?) Source

Operator alias for Data.Operator.PartialOrd.pGreaterThan1 (left-associative / precedence 4)

#pGreaterThanOrEq1 Source

pGreaterThanOrEq1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe Boolean

#(.>=?) Source

Operator alias for Data.Operator.PartialOrd.pGreaterThanOrEq1 (left-associative / precedence 4)

#pLessThan1 Source

pLessThan1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe Boolean

#(.<?) Source

Operator alias for Data.Operator.PartialOrd.pLessThan1 (left-associative / precedence 4)

#pLessThanOrEq1 Source

pLessThanOrEq1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe Boolean

#(.<=?) Source

Operator alias for Data.Operator.PartialOrd.pLessThanOrEq1 (left-associative / precedence 4)

#pMax1 Source

pMax1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe (f a)

#pMin1 Source

pMin1 :: forall f a. PartialOrd1 f => f a -> f a -> Maybe (f a)

Modules: Data.Bottom; Data.Operator.Bottom; Data.Operator.Eq; Data.Operator.Generic.Rep; Data.Operator.Ord; Data.Operator.PartialOrd; Data.Operator.Top; Data.PartialOrd; Data.Top