ba

Declared In:	Powerset Boolean Algebra
See Also:	https://en.wikipedia.org/wiki/Boolean_algebra_(structure)

Introduction

The Powerset Boolean Algebra

Discussion

Class implementing a Powerset Boolean Algebra. It uses an SCSE object as its underlying distributive lattice.

Member Functions

ba(const ba &): Copy Constructor.
ba(std :: vector, unsigned int, bool): Constructor.
map_e: Mapping of the extrusion function.
map_s: Mapping of the space function.
~ba: Destructor.

ba(const ba &)

Copy Constructor.

public

ba(
    const ba<ELEM_TYPE>& BA );

Parameters

BA: already instantiated BA.

Complexity

Constant.

ba(std :: vector, unsigned int, bool)

Constructor.

public

ba(
    std::vector<ELEM_TYPE> atoms,
    unsigned int n = 1,
    bool inverted = false );

Parameters

atoms: set of elements to build the powerset lattice.
n: number of space/extrusion functions.
inverted: true ⊥ = atoms, ⊤ = ∅, ⨆ = ∩, ⨅ = ∪ and false ⊥ = ∅, ⊤ = atoms, ⨆ = ∪, ⨅ = ∩

Discussion

This constructor will build a Powerset BA (inverted depending on the last parameter) from the set atoms with n space/extrusion functions.

Complexity

2ⁿ where n is the number of atoms.

map_e

Mapping of the extrusion function.

public

void map_e(
    const std::function<std::set<ELEM_TYPE>(
            int,
            std::set<ELEM_TYPE>,
            std::set<ELEM_TYPE>)>& e_func );

Discussion

Maps the elements of the powerset according to a user-defined extrusion function.

Complexity

2ⁿ where n is the number of atoms.

e_func

a function with three parameters; an integer representing the index of the extrusion function, a set representing the element to map and a set representing the atoms. The result is a set (the image of the element being mapped).

map_s

Mapping of the space function.

public

void map_s(
    const std::function<std::set<ELEM_TYPE>(
            int,
            std::set<ELEM_TYPE>,
            std::set<ELEM_TYPE>)>& s_func,
    typename scse< std::set<ELEM_TYPE> >::E_CHOICE_FUNCTION e_func = 
    scse< std::set<ELEM_TYPE> >::E_CHOICE_FUNCTION::EC_MANUAL );

Parameters

e_func: one of E_CHOICE_FUNCTION. The elements will be mapped according to the extrusion function option given here.

Discussion

Maps the elements of the powerset according to a user-defined space function.

Complexity

2ⁿ where n is the number of atoms.

s_func

a function with three parameters; an integer representing the index of the space function, a set representing the element to map and a set representing the atoms. The result is a set (the image of the element being mapped).

~ba

Destructor.

public

~ba(
    void );

Complexity

Constant.

Member Data

m_atoms
m_elems
m_n
m_scse

m_atoms

public

std::set<ELEM_TYPE> m_atoms;

Discussion

Set of elements constructing the powerset lattice

m_elems

public

std::set< std::set<ELEM_TYPE> > m_elems;

Discussion

Elements of the powerset lattice (Cons)

m_n

public

unsigned int m_n;

Discussion

Number of space/extrusion functions

m_scse

public

scse< std::set<ELEM_TYPE> > m_scse;

Discussion

SCSE representing the distributive lattice of the Powerset BA

Last Updated: Wednesday, March 16, 2016