SubHask.Algebra

Comparisons

type family Logic a :: *

type ValidLogic a

type ClassicalLogic a

class Eq_ a

type Eq a

type ValidEq a

law_Eq_reflexive

law_Eq_symmetric

law_Eq_transitive

class POrd_ b

type POrd a

law_POrd_commutative

law_POrd_associative

theorem_POrd_idempotent

class Lattice_ b

type Lattice a

isChain

isAntichain

data POrdering

law_Lattice_commutative

law_Lattice_associative

theorem_Lattice_idempotent

law_Lattice_infabsorption

law_Lattice_supabsorption

law_Lattice_reflexivity

law_Lattice_antisymmetry

law_Lattice_transitivity

defn_Lattice_greaterthan

class MinBound_ b

type MinBound a

law_MinBound_inf

class Bounded b

law_Bounded_sup

supremum

supremum_

infimum

infimum_

class Complemented b

law_Complemented_not

class Heyting b

modusPonens

law_Heyting_maxbound

law_Heyting_infleft

law_Heyting_infright

law_Heyting_distributive

class Boolean b

law_Boolean_infcomplement

law_Boolean_supcomplement

law_Boolean_infdistributivity

law_Boolean_supdistributivity

class Graded b

law_Graded_pred

law_Graded_fromEnum

class Ord_ a

law_Ord_totality

law_Ord_min

law_Ord_max

type Ord a

data Ordering

min

max

maximum

maximum_

minimum

minimum_

argmin

argmax

class Enum b

law_Enum_succ

law_Enum_toEnum

Boolean helpers

(||)

(&&)

true

false

and

or

Set-like

type family Elem s

type family SetElem s t

class Container s

law_Container_preservation

class Constructible s

law_Constructible_singleton

defn_Constructible_cons

defn_Constructible_snoc

defn_Constructible_fromList

defn_Constructible_fromListN

theorem_Constructible_cons

fromString

fromList

fromListN

insert

empty

isEmpty

class Foldable s

law_Foldable_sum

theorem_Foldable_tofrom

defn_Foldable_foldr

defn_Foldable_foldr'

defn_Foldable_foldl

defn_Foldable_foldl'

defn_Foldable_foldr1

defn_Foldable_foldr1'

defn_Foldable_foldl1

defn_Foldable_foldl1'

foldtree1

length

reduce

concat

headMaybe

tailMaybe

lastMaybe

initMaybe

indexed containers

type family Index s

type family SetIndex s a

class IxContainer s

law_IxContainer_preservation

defn_IxContainer_bang

defn_IxContainer_findWithDefault

defn_IxContainer_hasIndex

(!?)

class Sliceable s

class IxConstructible s

law_IxConstructible_lookup

defn_IxConstructible_consAt

defn_IxConstructible_snocAt

defn_IxConstructible_fromIxList

insertAt

Maybe

class CanError a

data Maybe' a

data Labeled' x y

Number-like

Classes with one operator

class Semigroup g

law_Semigroup_associativity

defn_Semigroup_plusequal

type family Actor s

class Action s

law_Action_compatibility

defn_Action_dotplusequal

(+.)

class Cancellative g

law_Cancellative_rightminus1

law_Cancellative_rightminus2

defn_Cancellative_plusequal

class Monoid g

isZero

notZero

law_Monoid_leftid

law_Monoid_rightid

defn_Monoid_isZero

class Abelian m

law_Abelian_commutative

class Group g

law_Group_leftinverse

law_Group_rightinverse

defn_Group_negateminus

Classes with two operators

class Rg r

law_Rg_multiplicativeAssociativity

law_Rg_multiplicativeCommutivity

law_Rg_annihilation

law_Rg_distributivityLeft

theorem_Rg_distributivityRight

defn_Rg_timesequal

class Rig r

isOne

notOne

law_Rig_multiplicativeId

type Rng r

defn_Ring_fromInteger

class Ring r

indicator

class Integral a

law_Integral_divMod

law_Integral_quotRem

law_Integral_toFromInverse

fromIntegral

class Field r

class OrdField r

class RationalField r

convertRationalField

toFloat

toDouble

class BoundedField r

infinity

negInfinity

class ExpRing r

(^)

class ExpField r

class Real r

class QuotientField r s

Sizes

class Normed g

abs

class Metric v

isFartherThan

lb2distanceUB

law_Metric_nonnegativity

law_Metric_indiscernables

law_Metric_symmetry

law_Metric_triangle

Linear algebra

type family Scalar m

type IsScalar r

type HasScalar a

type family a >< b :: *

class Cone m

class Module v

law_Module_multiplication

law_Module_addition

law_Module_action

law_Module_unital

defn_Module_dotstarequal

(*.)

class FreeModule v

law_FreeModule_commutative

law_FreeModule_associative

law_FreeModule_id

defn_FreeModule_dotstardotequal

class FiniteModule v

class VectorSpace v

class Banach v

class Hilbert v

innerProductDistance

innerProductNorm

class TensorAlgebra v

Helper functions

simpleMutableDefn