uvmhs-0.0.1.0
Safe HaskellNone
LanguageHaskell2010

UVMHS.Core.Data.Set

Documentation

class (CSized s, Ord s, ToIter e s, Single e s, Monoid s, POrd s, JoinLattice s, Meet s, Difference s) => Set e s | s -> e where Source #

Minimal complete definition

pminView, pmaxView

Methods

pø :: s Source #

psingle :: e -> s Source #

padd :: e -> s -> s Source #

prem :: e -> s -> s Source #

(∈) :: e -> s -> 𝔹 infix 4 Source #

(⊆) :: s -> s -> 𝔹 infix 4 Source #

(∪) :: s -> s -> s infixl 5 Source #

(∩) :: s -> s -> s infixl 6 Source #

(∖) :: s -> s -> s infixl 5 Source #

pminView :: s -> 𝑂 (e ∧ s) Source #

pmaxView :: s -> 𝑂 (e ∧ s) Source #

pminElem :: s -> 𝑂 e Source #

pmaxElem :: s -> 𝑂 e Source #

pow𝐼 :: 𝐼 e -> s Source #

pvals :: s -> 𝐼 e Source #

Instances

Instances details
Ord e => Set e (𝑃 e) Source # 
Instance details

Defined in UVMHS.Core.Data.Set

Methods

pø :: 𝑃 e Source #

psingle :: e -> 𝑃 e Source #

padd :: e -> 𝑃 e -> 𝑃 e Source #

prem :: e -> 𝑃 e -> 𝑃 e Source #

(∈) :: e -> 𝑃 e -> 𝔹 Source #

(⊆) :: 𝑃 e -> 𝑃 e -> 𝔹 Source #

(∪) :: 𝑃 e -> 𝑃 e -> 𝑃 e Source #

(∩) :: 𝑃 e -> 𝑃 e -> 𝑃 e Source #

(∖) :: 𝑃 e -> 𝑃 e -> 𝑃 e Source #

pminView :: 𝑃 e -> 𝑂 (e ∧ 𝑃 e) Source #

pmaxView :: 𝑃 e -> 𝑂 (e ∧ 𝑃 e) Source #

pminElem :: 𝑃 e -> 𝑂 e Source #

pmaxElem :: 𝑃 e -> 𝑂 e Source #

pow𝐼 :: 𝐼 e -> 𝑃 e Source #

pvals :: 𝑃 e -> 𝐼 e Source #

Ord e => Set (Elem (StdESD e)) (ESet (StdESD e)) Source # 
Instance details

Defined in UVMHS.Core.Data.Dict

Methods

pø :: ESet (StdESD e) Source #

psingle :: Elem (StdESD e) -> ESet (StdESD e) Source #

padd :: Elem (StdESD e) -> ESet (StdESD e) -> ESet (StdESD e) Source #

prem :: Elem (StdESD e) -> ESet (StdESD e) -> ESet (StdESD e) Source #

(∈) :: Elem (StdESD e) -> ESet (StdESD e) -> 𝔹 Source #

(⊆) :: ESet (StdESD e) -> ESet (StdESD e) -> 𝔹 Source #

(∪) :: ESet (StdESD e) -> ESet (StdESD e) -> ESet (StdESD e) Source #

(∩) :: ESet (StdESD e) -> ESet (StdESD e) -> ESet (StdESD e) Source #

(∖) :: ESet (StdESD e) -> ESet (StdESD e) -> ESet (StdESD e) Source #

pminView :: ESet (StdESD e) -> 𝑂 (Elem (StdESD e) ∧ ESet (StdESD e)) Source #

pmaxView :: ESet (StdESD e) -> 𝑂 (Elem (StdESD e) ∧ ESet (StdESD e)) Source #

pminElem :: ESet (StdESD e) -> 𝑂 (Elem (StdESD e)) Source #

pmaxElem :: ESet (StdESD e) -> 𝑂 (Elem (StdESD e)) Source #

pow𝐼 :: 𝐼 (Elem (StdESD e)) -> ESet (StdESD e) Source #

pvals :: ESet (StdESD e) -> 𝐼 (Elem (StdESD e)) Source #

(⊇) :: Set e s => s -> s -> 𝔹 infix 4 Source #

(∉) :: Set e s => e -> s -> 𝔹 infix 4 Source #

pow :: forall s t e. (ToIter e t, Set e s) => t -> s Source #

unions :: (Set e s, ToIter s t) => t -> s Source #

intersFrom :: (Set e s, ToIter s t) => s -> t -> s Source #

sdiffsFrom :: (Set e s, ToIter s t) => s -> t -> s Source #

pø𝑃 :: 𝑃 a Source #

psingle𝑃 :: a -> 𝑃 a Source #

padd𝑃 :: Ord a => a -> 𝑃 a -> 𝑃 a Source #

prem𝑃 :: Ord a => a -> 𝑃 a -> 𝑃 a Source #

(∈♭) :: Ord a => a -> 𝑃 a -> 𝔹 Source #

(⊆♭) :: Ord a => 𝑃 a -> 𝑃 a -> 𝔹 Source #

(∪♭) :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

(∩♭) :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

(∖♭) :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

pminView𝑃 :: 𝑃 a -> 𝑂 (a ∧ 𝑃 a) Source #

pmaxView𝑃 :: 𝑃 a -> 𝑂 (a ∧ 𝑃 a) Source #

pminElem𝑃 :: 𝑃 a -> 𝑂 a Source #

pmaxElem𝑃 :: 𝑃 a -> 𝑂 a Source #

pow𝐼𝑃 :: Ord a => 𝐼 a -> 𝑃 a Source #

pvals𝑃 :: 𝑃 a -> 𝐼 a Source #

csize𝑃 :: 𝑃 a -> ℕ64 Source #

show𝑃 :: Show a => 𝑃 a -> 𝕊 Source #

iter𝑃 :: 𝑃 a -> 𝐼 a Source #

single𝑃 :: a -> 𝑃 a Source #

null𝑃 :: 𝑃 a Source #

append𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

unit𝑃 :: (Ord a, Null a) => 𝑃 a Source #

cross𝑃 :: (Ord a, Append a) => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

zero𝑃 :: 𝑃 a Source #

plus𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

one𝑃 :: (Ord a, Zero a) => 𝑃 a Source #

times𝑃 :: (Ord a, Plus a) => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

plte𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝔹 Source #

bot𝑃 :: 𝑃 a Source #

join𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

meet𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

diff𝑃 :: Ord a => 𝑃 a -> 𝑃 a -> 𝑃 a Source #

all𝑃 :: (Ord a, All a) => 𝐼 (𝑃 a) Source #

pow𝑃 :: (Ord a, ToIter a t) => t -> 𝑃 a Source #

map𝑃 :: Ord b => (a -> b) -> 𝑃 a -> 𝑃 b Source #

uniques𝑃 :: (Ord a, ToIter a t) => t -> 𝐼 a Source #

Orphan instances

Ord a => Single a (𝑃 a) Source # 
Instance details

Methods

single :: a -> 𝑃 a Source #

ToIter a (𝑃 a) Source # 
Instance details

Methods

iter :: 𝑃 a -> 𝐼 a Source #

Show a => Show (𝑃 a) Source # 
Instance details

Methods

showsPrec :: Int -> 𝑃 a -> ShowS #

show :: 𝑃 a -> String #

showList :: [𝑃 a] -> ShowS #

Ord a => Additive (𝑃 a) Source # 
Instance details

(Ord a, Zero a) => One (𝑃 a) Source # 
Instance details

Methods

one :: 𝑃 a Source #

Ord a => Plus (𝑃 a) Source # 
Instance details

Methods

(+) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

(Ord a, Plus a) => Times (𝑃 a) Source # 
Instance details

Methods

(×) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

Zero (𝑃 a) Source # 
Instance details

Methods

zero :: 𝑃 a Source #

(Ord a, All a) => All (𝑃 a) Source # 
Instance details

Methods

all :: 𝐼 (𝑃 a) Source #

CSized (𝑃 a) Source # 
Instance details

Methods

csize :: 𝑃 a -> ℕ64 Source #

Bot (𝑃 a) Source # 
Instance details

Methods

bot :: 𝑃 a Source #

Ord a => Difference (𝑃 a) Source # 
Instance details

Methods

(⊟) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

Ord a => Join (𝑃 a) Source # 
Instance details

Methods

(⊔) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

Ord a => JoinLattice (𝑃 a) Source # 
Instance details

Ord a => Meet (𝑃 a) Source # 
Instance details

Methods

(⊓) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

Ord a => POrd (𝑃 a) Source # 
Instance details

Methods

(⊑) :: 𝑃 a -> 𝑃 a -> 𝔹 Source #

Ord a => Append (𝑃 a) Source # 
Instance details

Methods

(⧺) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

(Ord a, Append a) => Cross (𝑃 a) Source # 
Instance details

Methods

(⨳) :: 𝑃 a -> 𝑃 a -> 𝑃 a Source #

Ord a => Monoid (𝑃 a) Source # 
Instance details

Null (𝑃 a) Source # 
Instance details

Methods

null :: 𝑃 a Source #

(Ord a, Monoid a) => Prodoid (𝑃 a) Source # 
Instance details

(Ord a, Null a) => Unit (𝑃 a) Source # 
Instance details

Methods

unit :: 𝑃 a Source #