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 val | box -> varid val, varid val -> box where

A class abstracting a type of many-dimensional points, intervals or anything indexed by a subset of dimensions.

More generally, this class abstracts most of Data.Map.Map.

Methods

noinfo :: box

isNoinfo :: box -> Bool

unary :: val -> box

constructor using defaultVar

singleton :: varid -> val -> box

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

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

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

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

insert :: varid -> val -> box -> box

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

delete :: varid -> box -> box

member :: varid -> box -> Bool

notMember :: varid -> box -> Bool

union :: box -> box -> box

unionWith :: (val -> val -> val) -> box -> box -> box

keys :: box -> [varid]

elems :: box -> [val]

filter :: (val -> Bool) -> box -> box

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

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

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

for all variables that appear in both boxes, apply the function and add the result to the list

zipWithDefault :: val -> (val -> val -> a) -> box -> box -> [(varid, a)]

For all variables that appear in either of the two boxes, apply the function and add the result to the list.

Supply the default value when the variable is missing from either box.

zipWithDefaultSecond :: val -> (val -> val -> a) -> box -> box -> [(varid, a)]

For all variables that appear in the first box, apply the function and add the result to the list.

Supply the default value when the variable is missing from the second box.

findWithDefault :: val -> varid -> box -> val

lookup

Arguments

:: String

identification of caller location to use in error messages

-> varid

-> box

-> val

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 val => DomainBox (Box val) VarID val

class (DomainBox box1 varid val1, DomainBox box2 varid val2) => DomainBoxMappable box1 box2 varid val1 val2 where

A class linking two domain box types that share the index type so that boxes of the two types can be converted etc.

Methods

map :: (val1 -> val2) -> box1 -> box2

mapWithKey :: (varid -> val1 -> val2) -> box1 -> box2

intersectionWith :: (val1 -> val2 -> val1) -> box1 -> box2 -> box1

difference :: box1 -> box2 -> box1

Instances

(Show val1, Show val2) => DomainBoxMappable (Box val1) (Box val2) VarID val1 val2

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.

split :: box -> varid -> ira -> (box, box)

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