Data.Number.ER.Real.DomainBox

Abstractions of the Box datatype, often used to represent sections of multi-dimensional function domains.

To be imported qualified, usually with prefix DBox.

VariableID(..) and DomainBox are usually imported separately and not qualified.

Documentation

class Ord varid => VariableID varid where

A class abstracting a type of variable identifiers for axes in function domains, polynomials etc.

Methods

newVarID :: Set varid -> varid

defaultVar :: varid

showVar :: varid -> String

Instances

VariableID VarID

class VariableID varid => DomainBox box varid ira | box -> varid ira, varid ira -> box where

A class abstracting a type of many-dimensional points or intervals.

Methods

noinfo :: box

isNoinfo :: box -> Bool

unary :: ira -> box

constructor using defaultVar

singleton :: varid -> ira -> box

toList :: box -> [(varid, ira)]

fromList :: [(varid, ira)] -> box

toAscList :: box -> [(varid, ira)]

fromAscList :: [(varid, ira)] -> box

toMap :: box -> Map varid ira

fromMap :: Map varid ira -> box

insert :: varid -> ira -> box -> box

insertWith :: (ira -> ira -> ira) -> varid -> ira -> box -> box

delete :: varid -> box -> box

member :: varid -> box -> Bool

notMember :: varid -> box -> Bool

union :: box -> box -> box

unionWith :: (ira -> ira -> ira) -> box -> box -> box

keys :: box -> [varid]

elems :: box -> [ira]

map :: (ira -> ira) -> box -> box

fold :: (ira -> a -> a) -> a -> box -> a

foldWithKey :: (varid -> ira -> a -> a) -> a -> box -> a

zipWith :: (ira -> ira -> a) -> box -> box -> [(varid, a)]

intersectionWith :: (ira -> ira -> ira) -> box -> box -> box

findWithDefault :: ira -> varid -> box -> ira

lookup

Arguments

:: String

identification of caller location to use in error messages

-> varid

-> box

-> ira

Pick the extents of a single variable in a domain box. If there is no information for this variable, assume the variable ranges over the whole real line.

Instances

Show ira => DomainBox (Box ira) VarID ira

class DomainBox box varid ira => DomainIntBox box varid ira | box -> varid ira, varid ira -> box where

A class abstracting a type of many-dimensional intervals.

Methods

compatible :: box -> box -> Bool

Check whether the two domains specify the same interval for each variable that they share.

unify

Arguments

:: String

identification of caller location to use in error messages

-> box

-> box

-> box

Assuming that two domains are compatible, take the most information from both of the domains about the ranges of variables.

bestSplit :: box -> (varid, ira)

Find the variable with the largest interval and return it together with the default splitting point in its domain.

classifyPosition

Arguments

:: box

domain d1

-> box

domain d2

-> (Bool, Bool, Bool, Bool)

Answers to these (mutually exclusive) questions:

• is d1 outside and not touching d2?
• is d1 outside and touching d2?
• is d1 intersecting and not inside d2?
• is d1 inside d2?

Instances

ERIntApprox ira => DomainIntBox (Box ira) VarID ira