Class that handles equivalence laws. More...

#include <equivLaws.h>

Public Types
typedef bool(*	EquivLaw) (std::shared_ptr< Expression > &)
	Function pointer type for an equivalence law.

Static Public Member Functions
static void	replace (std::shared_ptr< Expression > &expression, std::shared_ptr< Expression > newExpression)
	Replace the current expression with the new expression.

static bool	identity (std::shared_ptr< Expression > &expression)
	Applies the identity law (p & T) = p, (p \| F) = p.

static bool	domination (std::shared_ptr< Expression > &expression)
	Applies the domination law (p \| T) = T, (p & F) = F.

static bool	idempotent (std::shared_ptr< Expression > &expression)
	Applies the idempotent law (p \| p) = p, (p & p) = p.

static bool	doubleNegation (std::shared_ptr< Expression > &expression)
	Applies the double negation law !!p = p.

static bool	commutative (std::shared_ptr< Expression > &expression)
	Applies the commutative law (p \| q) = (q \| p), (p & q) = (q & p)

static bool	associative (std::shared_ptr< Expression > &expression)
	Applies the associative law (p \| q) \| r = p \| (q \| r), (p & q) & r = p & (q & r)

static bool	associativeReversed (std::shared_ptr< Expression > &expression)
	Applies associative() but reversed p \| (q \| r) = (p \| q) \| r, p & (q & r) = (p & q) & r.

static bool	distributive (std::shared_ptr< Expression > &expression)
	Applies distributive law p \| (q & r) = (p \| q) & (p \| r), p & (q \| r) = (p & q) \| (p & r)

static bool	distributiveReversed (std::shared_ptr< Expression > &expression)
	Applies distributive() but reversed (p \| q) & (p \| r) = p \| (q & r), (p & q) \| (p & r) = p & (q \| r)

static bool	deMorgan (std::shared_ptr< Expression > &expression)
	Applies De Morgan's law !(p \| q) = !p & !q, !(p & q) = !p \| !q.

static bool	deMorganReversed (std::shared_ptr< Expression > &expression)
	Applies deMorgan() but reversed !p & !q = !(p \| q), !p \| !q = !(p & q)

static bool	absorption (std::shared_ptr< Expression > &expression)
	Applies the absorption law p \| (p & q) = p, p & (p \| q) = p.

static bool	negation (std::shared_ptr< Expression > &expression)
	Applies the negation law p \| !p = T, p & !p = F.

static bool	implication0 (std::shared_ptr< Expression > &expression)
	Applies implication: p -> q = !p \| q.

static bool	implication0Reversed (std::shared_ptr< Expression > &expression)
	Applies implication0() but reversed !p \| q = p -> q.

static bool	implication1 (std::shared_ptr< Expression > &expression)
	Applies implication: p -> q = !q -> !p.

static bool	implication1Reversed (std::shared_ptr< Expression > &expression)
	Applies implication1() but reversed !q -> !p = p -> q.

static bool	implication2 (std::shared_ptr< Expression > &expression)
	Applies implication: p \| q = !p -> q.

static bool	implication2Reversed (std::shared_ptr< Expression > &expression)
	Applies implication2() but reversed !p -> q = p \| q.

static bool	implication3 (std::shared_ptr< Expression > &expression)
	Applies implication: p & q = !(p -> !q)

static bool	implication3Reversed (std::shared_ptr< Expression > &expression)
	Applies implication3() but reversed !(p -> !q) = p & q.

static bool	implication4 (std::shared_ptr< Expression > &expression)
	Applies implication: !(p -> q) = p & !q.

static bool	implication4Reversed (std::shared_ptr< Expression > &expression)
	Applies implication4() but reversed p & !q = !(p -> q)

static bool	implication5 (std::shared_ptr< Expression > &expression)
	Applies implication: (p -> q) & (p -> r) = p -> (q & r)

static bool	implication5Reversed (std::shared_ptr< Expression > &expression)
	Applies implication5() but reversed p -> (q & r) = (p -> q) & (p -> r)

static bool	implication6 (std::shared_ptr< Expression > &expression)
	Applies implication: (p -> q) & (q -> r) = (p \| q) -> r.

static bool	implication6Reversed (std::shared_ptr< Expression > &expression)
	Applies implication6() but reversed (p \| q) -> r = (p -> q) & (q -> r)

static bool	implication7 (std::shared_ptr< Expression > &expression)
	Applies implication: (p -> q) \| (p -> r) = p -> (q \| r)

static bool	implication7Reversed (std::shared_ptr< Expression > &expression)
	Applies implication7() but reversed p -> (q \| r) = (p -> q) \| (p -> r)

static bool	implication8 (std::shared_ptr< Expression > &expression)
	Applies implication: (p -> q) \| (q -> r) = (p & q) -> r.

static bool	implication8Reversed (std::shared_ptr< Expression > &expression)
	Applies implication8() but reversed (p & q) -> r = (p -> q) \| (q -> r)

static bool	bidirectionalImplication0 (std::shared_ptr< Expression > &expression)
	Applies bidirectional implication: p <-> q = (p -> q) & (q -> p)

static bool	bidirectionalImplication0Reversed (std::shared_ptr< Expression > &expression)
	Applies bidirectionalImplication0() but reversed (p -> q) & (q -> p) = p <-> q.

static bool	bidirectionalImplication1 (std::shared_ptr< Expression > &expression)
	Applies bidirectional implication: p <-> q = q <-> p.

static bool	bidirectionalImplication2 (std::shared_ptr< Expression > &expression)
	Applies bidirectional implication: p <-> q = !p <-> !q.

static bool	bidirectionalImplication2Reversed (std::shared_ptr< Expression > &expression)
	Applies bidirectionalImplication2() but reversed !p <-> !q = p <-> q.

static bool	bidirectionalImplication3 (std::shared_ptr< Expression > &expression)
	Applies bidirectional implication: p <-> q = (p & q) \| (!p & !q)

static bool	bidirectionalImplication3Reversed (std::shared_ptr< Expression > &expression)
	Applies bidirectionalImplication3() but reversed (p & q) \| (!p & !q) = p <-> q.

static bool	bidirectionalImplication4 (std::shared_ptr< Expression > &expression)
	Applies bidirectional implication: !(p <-> q) = p <-> !q.

static bool	bidirectionalImplication4Reversed (std::shared_ptr< Expression > &expression)
	Applies bidirectionalImplication4() but reversed p <-> !q = !(p <-> q)

Static Public Attributes
static std::unordered_map< EquivLaw, std::string >	laws
	Map of equivalence laws to their string representations.

static std::unordered_map< EquivLaw, std::string >	implications
	Map of implication equivalences to their string representations.

static std::unordered_map< EquivLaw, std::string >	bidirectionalImplications
	Map of biimplication equivalences to their string representations.

Detailed Description

Class that handles equivalence laws.

Definition at line 15 of file equivLaws.h.

Member Typedef Documentation

◆ EquivLaw

typedef bool(* EquivLaws::EquivLaw) (std::shared_ptr< Expression > &)

Function pointer type for an equivalence law.

Parameters

expr	the expression to apply the law to

Returns: bool of whether the law was applied

Definition at line 24 of file equivLaws.h.

Member Function Documentation

◆ absorption()

bool EquivLaws::absorption ( std::shared_ptr< Expression > & expression )

static

Applies the absorption law
p | (p & q) = p, p & (p | q) = p.

Parameters

expression pointer to the current expression

Returns: bool of whether the absorption law was applied

Definition at line 408 of file equivLaws.cpp.

◆ associative()

bool EquivLaws::associative ( std::shared_ptr< Expression > & expression )

static

Applies the associative law
(p | q) | r = p | (q | r), (p & q) & r = p & (q & r)

Parameters

expression pointer to the current expression

Returns: bool of whether the associative law was applied

Definition at line 190 of file equivLaws.cpp.

◆ associativeReversed()

bool EquivLaws::associativeReversed ( std::shared_ptr< Expression > & expression )

static

Applies associative() but reversed
p | (q | r) = (p | q) | r, p & (q & r) = (p & q) & r.

Parameters

expression pointer to the current expression

Returns: bool of whether the associative law was applied

See also: associative()

Definition at line 214 of file equivLaws.cpp.

◆ bidirectionalImplication0()

bool EquivLaws::bidirectionalImplication0 ( std::shared_ptr< Expression > & expression )

static

Applies bidirectional implication: p <-> q = (p -> q) & (q -> p)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 879 of file equivLaws.cpp.

◆ bidirectionalImplication0Reversed()

bool EquivLaws::bidirectionalImplication0Reversed ( std::shared_ptr< Expression > & expression )

static

Applies bidirectionalImplication0() but reversed
(p -> q) & (q -> p) = p <-> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: bidirectionalImplication0()

Definition at line 903 of file equivLaws.cpp.

◆ bidirectionalImplication1()

bool EquivLaws::bidirectionalImplication1 ( std::shared_ptr< Expression > & expression )

static

Applies bidirectional implication: p <-> q = q <-> p.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 929 of file equivLaws.cpp.

◆ bidirectionalImplication2()

bool EquivLaws::bidirectionalImplication2 ( std::shared_ptr< Expression > & expression )

static

Applies bidirectional implication: p <-> q = !p <-> !q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 949 of file equivLaws.cpp.

◆ bidirectionalImplication2Reversed()

bool EquivLaws::bidirectionalImplication2Reversed ( std::shared_ptr< Expression > & expression )

static

Applies bidirectionalImplication2() but reversed
!p <-> !q = p <-> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: bidirectionalImplication2()

Definition at line 971 of file equivLaws.cpp.

◆ bidirectionalImplication3()

bool EquivLaws::bidirectionalImplication3 ( std::shared_ptr< Expression > & expression )

static

Applies bidirectional implication: p <-> q = (p & q) | (!p & !q)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 991 of file equivLaws.cpp.

◆ bidirectionalImplication3Reversed()

bool EquivLaws::bidirectionalImplication3Reversed ( std::shared_ptr< Expression > & expression )

static

Applies bidirectionalImplication3() but reversed
(p & q) | (!p & !q) = p <-> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: bidirectionalImplication3()

Definition at line 1017 of file equivLaws.cpp.

◆ bidirectionalImplication4()

bool EquivLaws::bidirectionalImplication4 ( std::shared_ptr< Expression > & expression )

static

Applies bidirectional implication: !(p <-> q) = p <-> !q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 1039 of file equivLaws.cpp.

◆ bidirectionalImplication4Reversed()

bool EquivLaws::bidirectionalImplication4Reversed ( std::shared_ptr< Expression > & expression )

static

Applies bidirectionalImplication4() but reversed
p <-> !q = !(p <-> q)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: bidirectionalImplication4()

Definition at line 1060 of file equivLaws.cpp.

◆ commutative()

bool EquivLaws::commutative ( std::shared_ptr< Expression > & expression )

static

Applies the commutative law
(p | q) = (q | p), (p & q) = (q & p)

Parameters

expression pointer to the current expression

Returns: bool of whether the commutative law was applied

Definition at line 169 of file equivLaws.cpp.

◆ deMorgan()

bool EquivLaws::deMorgan ( std::shared_ptr< Expression > & expression )

static

Applies De Morgan's law
!(p | q) = !p & !q, !(p & q) = !p | !q.

Parameters

expression pointer to the current expression

Returns: bool of whether De Morgan's law was applied

Definition at line 331 of file equivLaws.cpp.

◆ deMorganReversed()

bool EquivLaws::deMorganReversed ( std::shared_ptr< Expression > & expression )

static

Applies deMorgan() but reversed
!p & !q = !(p | q), !p | !q = !(p & q)

Parameters

expression pointer to the current expression

Returns: bool of whether De Morgan's law was applied

See also: deMorgan()

Definition at line 372 of file equivLaws.cpp.

◆ distributive()

bool EquivLaws::distributive ( std::shared_ptr< Expression > & expression )

static

Applies distributive law
p | (q & r) = (p | q) & (p | r), p & (q | r) = (p & q) | (p & r)

Parameters

expression pointer to the current expression

Returns: bool of whether the distributive law was applied

Definition at line 237 of file equivLaws.cpp.

◆ distributiveReversed()

bool EquivLaws::distributiveReversed ( std::shared_ptr< Expression > & expression )

static

Applies distributive() but reversed
(p | q) & (p | r) = p | (q & r), (p & q) | (p & r) = p & (q | r)

Parameters

expression pointer to the current expression

Returns: bool of whether the distributive law was applied

See also: distributive()

Definition at line 281 of file equivLaws.cpp.

◆ domination()

bool EquivLaws::domination ( std::shared_ptr< Expression > & expression )

static

Applies the domination law
(p | T) = T, (p & F) = F.

Parameters

expression pointer to the current expression

Returns: bool of whether the domination law was applied

Definition at line 103 of file equivLaws.cpp.

◆ doubleNegation()

bool EquivLaws::doubleNegation ( std::shared_ptr< Expression > & expression )

static

Applies the double negation law
!!p = p.

Parameters

expression pointer to the current expression

Returns: bool of whether the double negation law was applied

Definition at line 151 of file equivLaws.cpp.

◆ idempotent()

bool EquivLaws::idempotent ( std::shared_ptr< Expression > & expression )

static

Applies the idempotent law
(p | p) = p, (p & p) = p.

Parameters

expression pointer to the current expression

Returns: bool of whether the idempotence law was applied

Definition at line 129 of file equivLaws.cpp.

◆ identity()

bool EquivLaws::identity ( std::shared_ptr< Expression > & expression )

static

Applies the identity law
(p & T) = p, (p | F) = p.

Parameters

expression pointer to the current expression

Returns: bool of whether the identity law was applied

Definition at line 80 of file equivLaws.cpp.

◆ implication0()

bool EquivLaws::implication0 ( std::shared_ptr< Expression > & expression )

static

Applies implication: p -> q = !p | q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 459 of file equivLaws.cpp.

◆ implication0Reversed()

bool EquivLaws::implication0Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication0() but reversed
!p | q = p -> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication0()

Definition at line 480 of file equivLaws.cpp.

◆ implication1()

bool EquivLaws::implication1 ( std::shared_ptr< Expression > & expression )

static

Applies implication: p -> q = !q -> !p.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 500 of file equivLaws.cpp.

◆ implication1Reversed()

bool EquivLaws::implication1Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication1() but reversed
!q -> !p = p -> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 522 of file equivLaws.cpp.

◆ implication2()

bool EquivLaws::implication2 ( std::shared_ptr< Expression > & expression )

static

Applies implication: p | q = !p -> q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 542 of file equivLaws.cpp.

◆ implication2Reversed()

bool EquivLaws::implication2Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication2() but reversed
!p -> q = p | q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication2()

Definition at line 563 of file equivLaws.cpp.

◆ implication3()

bool EquivLaws::implication3 ( std::shared_ptr< Expression > & expression )

static

Applies implication: p & q = !(p -> !q)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 583 of file equivLaws.cpp.

◆ implication3Reversed()

bool EquivLaws::implication3Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication3() but reversed
!(p -> !q) = p & q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication3()

Definition at line 605 of file equivLaws.cpp.

◆ implication4()

bool EquivLaws::implication4 ( std::shared_ptr< Expression > & expression )

static

Applies implication: !(p -> q) = p & !q.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 625 of file equivLaws.cpp.

◆ implication4Reversed()

bool EquivLaws::implication4Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication4() but reversed
p & !q = !(p -> q)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication4()

Definition at line 646 of file equivLaws.cpp.

◆ implication5()

bool EquivLaws::implication5 ( std::shared_ptr< Expression > & expression )

static

Applies implication: (p -> q) & (p -> r) = p -> (q & r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 667 of file equivLaws.cpp.

◆ implication5Reversed()

bool EquivLaws::implication5Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication5() but reversed
p -> (q & r) = (p -> q) & (p -> r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication5()

Definition at line 695 of file equivLaws.cpp.

◆ implication6()

bool EquivLaws::implication6 ( std::shared_ptr< Expression > & expression )

static

Applies implication: (p -> q) & (q -> r) = (p | q) -> r.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 720 of file equivLaws.cpp.

◆ implication6Reversed()

bool EquivLaws::implication6Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication6() but reversed
(p | q) -> r = (p -> q) & (q -> r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication6()

Definition at line 748 of file equivLaws.cpp.

◆ implication7()

bool EquivLaws::implication7 ( std::shared_ptr< Expression > & expression )

static

Applies implication: (p -> q) | (p -> r) = p -> (q | r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 773 of file equivLaws.cpp.

◆ implication7Reversed()

bool EquivLaws::implication7Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication7() but reversed
p -> (q | r) = (p -> q) | (p -> r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication7()

Definition at line 801 of file equivLaws.cpp.

◆ implication8()

bool EquivLaws::implication8 ( std::shared_ptr< Expression > & expression )

static

Applies implication: (p -> q) | (q -> r) = (p & q) -> r.

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

Definition at line 826 of file equivLaws.cpp.

◆ implication8Reversed()

bool EquivLaws::implication8Reversed ( std::shared_ptr< Expression > & expression )

static

Applies implication8() but reversed
(p & q) -> r = (p -> q) | (q -> r)

Parameters

expression pointer to the current expression

Returns: bool of whether implication was applied

See also: implication8()

Definition at line 854 of file equivLaws.cpp.

◆ negation()

bool EquivLaws::negation ( std::shared_ptr< Expression > & expression )

static

Applies the negation law
p | !p = T, p & !p = F.

Parameters

expression pointer to the current expression

Returns: bool of whether the negation law was applied

Definition at line 429 of file equivLaws.cpp.

◆ replace()

void EquivLaws::replace	(	std::shared_ptr< Expression > &	expression,
		std::shared_ptr< Expression >	newExpression
	)

static

Replace the current expression with the new expression.

Parameters

expression	pointer to original expression
newExpression	pointer to expression to replace with

Definition at line 58 of file equivLaws.cpp.

Member Data Documentation

◆ bidirectionalImplications

std::unordered_map< EquivLaws::EquivLaw, std::string > EquivLaws::bidirectionalImplications

static

Initial value:

= {
        {bidirectionalImplication0, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication0Reversed, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication1, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication2, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication2Reversed, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication3, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication3Reversed, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication4, "Bidirectional Implication Equivalence"},
        {bidirectionalImplication4Reversed, "Bidirectional Implication Equivalence"},
}

Map of biimplication equivalences to their string representations.

Definition at line 46 of file equivLaws.h.

◆ implications

std::unordered_map< EquivLaws::EquivLaw, std::string > EquivLaws::implications

static

Initial value:

= {
    {implication0, "Implication Equivalence"},
    {implication0Reversed, "Implication Equivalence"},
    {implication1, "Implication Equivalence"},
    {implication1Reversed, "Implication Equivalence"},
    {implication2, "Implication Equivalence"},
    {implication2Reversed, "Implication Equivalence"},
    {implication3, "Implication Equivalence"},
    {implication3Reversed, "Implication Equivalence"},
    {implication4, "Implication Equivalence"},
    {implication4Reversed, "Implication Equivalence"},
    {implication5, "Implication Equivalence"},
    {implication5Reversed, "Implication Equivalence"},
    {implication6, "Implication Equivalence"},
    {implication6Reversed, "Implication Equivalence"},
    {implication7, "Implication Equivalence"},
    {implication7Reversed, "Implication Equivalence"},
    {implication8, "Implication Equivalence"},
    {implication8Reversed, "Implication Equivalence"},
}

Map of implication equivalences to their string representations.

Definition at line 24 of file equivLaws.h.

◆ laws

std::unordered_map< EquivLaws::EquivLaw, std::string > EquivLaws::laws

static

Initial value:

= {
    {identity, "Identity Law"},
    {domination, "Domination Law"},
    {idempotent, "Idempotent Law"},
    {doubleNegation, "Double Negation Law"},
    {commutative, "Commutative Law"},
    {associative, "Associative Law"},
    {associativeReversed, "Associative Law"},
    {distributive, "Distributive Law"},
    {distributiveReversed, "Distributive Law"},
    {deMorgan, "De Morgan's Law"},
    {deMorganReversed, "De Morgan's Law"},
    {absorption, "Absorption Law"},
    {negation, "Negation Law"},
}

Map of equivalence laws to their string representations.

Definition at line 8 of file equivLaws.h.

The documentation for this class was generated from the following files:

include/equivLaws.h
src/equivLaws.cpp

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ EquivLaw

Member Function Documentation

◆ absorption()

◆ associative()

◆ associativeReversed()

◆ bidirectionalImplication0()

◆ bidirectionalImplication0Reversed()

◆ bidirectionalImplication1()

◆ bidirectionalImplication2()

◆ bidirectionalImplication2Reversed()

◆ bidirectionalImplication3()

◆ bidirectionalImplication3Reversed()

◆ bidirectionalImplication4()

◆ bidirectionalImplication4Reversed()

◆ commutative()

◆ deMorgan()

◆ deMorganReversed()

◆ distributive()

◆ distributiveReversed()

◆ domination()

◆ doubleNegation()

◆ idempotent()

◆ identity()

◆ implication0()

◆ implication0Reversed()

◆ implication1()

◆ implication1Reversed()

◆ implication2()

◆ implication2Reversed()

◆ implication3()

◆ implication3Reversed()

◆ implication4()

◆ implication4Reversed()

◆ implication5()

◆ implication5Reversed()

◆ implication6()

◆ implication6Reversed()

◆ implication7()

◆ implication7Reversed()

◆ implication8()

◆ implication8Reversed()

◆ negation()

◆ replace()

Member Data Documentation

◆ bidirectionalImplications

◆ implications

◆ laws