/usr/share/spark/checker/rules/LOGIC.RUL is in spark 2012.0.deb-11.
This file is owned by root:root, with mode 0o644.
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% (C) Altran Praxis Limited
% -----------------------------------------------------------------------------
%
% The SPARK toolset is free software; you can redistribute it and/or modify it
% under terms of the GNU General Public License as published by the Free
% Software Foundation; either version 3, or (at your option) any later
% version. The SPARK toolset is distributed in the hope that it will be
% useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
% Public License for more details. You should have received a copy of the GNU
% General Public License distributed with the SPARK toolset; see file
% COPYING3. If not, go to http://www.gnu.org/licenses for a complete copy of
% the license.
%
% =============================================================================
%-------------------------------------------------------------------------------
% RULE FAMILIES CONTAINED HEREIN :-
%
% assoc : associativity of "and", "or" & "<->"
% commut : commutativity of "and", "or" & "<->"
% distrib : distributivity of "and" over "or" and vice versa
% equivalence : simplification of logical "<->" expressions
% implies : simplification of logical "->" expressions
% logical : general logical simplification rules
% logical_and : simplification of logical "and" expressions
% logical_not : simplification of logical "not" expressions
% logical_or : simplification of logical "or" expressions
%-------------------------------------------------------------------------------
% MODEL DECLARATIONS FOR THIS FILE :-
%
% rule_family assoc:
% X and Y requires [ X:any, Y:any ] &
% X or Y requires [ X:any, Y:any ] &
% X <-> Y requires [ X:any, Y:any ].
%
% rule_family commut:
% X and Y requires [ X:any, Y:any ] &
% X or Y requires [ X:any, Y:any ] &
% X <-> Y requires [ X:any, Y:any ].
%
% rule_family distrib:
% X and Y requires [ X:any, Y:any ] &
% X or Y requires [ X:any, Y:any ].
%
% rule_family equivalence:
% X <-> Y requires [ X:any, Y:any ].
%
% rule_family implies:
% X -> Y requires [ X:any, Y:any ].
%
% rule_family logical_and:
% X and Y requires [ X:any, Y:any ].
%
% rule_family logical_not:
% not X requires [ X:any ].
%
% rule_family logical_or:
% X or Y requires [ X:any, Y:any ].
%
% rule_family logical:
% not X requires [ X:any ] &
% X and Y requires [ X:any, Y:any ] &
% X or Y requires [ X:any, Y:any ] &
% X -> Y requires [ X:any, Y:any ] &
% X <-> Y requires [ X:any, Y:any ].
%-------------------------------------------------------------------------------
/*** SIMPLIFICATION OF LOGICAL EXPRESSIONS Rules ***/
/*** Simplification of logical "not" expressions ***/
logical_not(1): not true may_be_replaced_by false.
logical_not(2): not false may_be_replaced_by true.
logical_not(3): not not A may_be_replaced_by A.
/*** Simplification of logical "and" expressions ***/
logical_and(1): A and true may_be_replaced_by A.
logical_and(2): true and A may_be_replaced_by A.
logical_and(3): A and false may_be_replaced_by false.
logical_and(4): false and A may_be_replaced_by false.
logical_and(5): A and A may_be_replaced_by A.
logical_and(6): A and not A may_be_replaced_by false.
logical_and(7): (not A) and A may_be_replaced_by false.
/*** Simplification of logical "or" expressions ***/
logical_or(1): A or false may_be_replaced_by A.
logical_or(2): false or A may_be_replaced_by A.
logical_or(3): A or true may_be_replaced_by true.
logical_or(4): true or A may_be_replaced_by true.
logical_or(5): A or A may_be_replaced_by A.
logical_or(6): A or not A may_be_replaced_by true.
logical_or(7): (not A) or A may_be_replaced_by true.
/*** Simplification of logical "->" expressions ***/
implies(1): A -> true may_be_replaced_by true.
implies(2): A -> false may_be_replaced_by not A.
implies(3): true -> A may_be_replaced_by A.
implies(4): false -> A may_be_replaced_by true.
implies(5): A -> A may_be_replaced_by true.
implies(6): A -> not A may_be_replaced_by not A.
implies(7): (not A) -> A may_be_replaced_by A.
/*** Simplification of logical "<->" expressions ***/
equivalence(1): A <-> true may_be_replaced_by A.
equivalence(2): true <-> A may_be_replaced_by A.
equivalence(3): A <-> false may_be_replaced_by not A.
equivalence(4): false <-> A may_be_replaced_by not A.
equivalence(5): A <-> A may_be_replaced_by true.
equivalence(6): A <-> not A may_be_replaced_by false.
equivalence(7): (not A) <-> A may_be_replaced_by false.
/*** ASSOCIATIVITY of "and", "or" & "<->" Rules ***/
assoc(5): A and (B and C) & (A and B) and C are_interchangeable.
assoc(6): A or (B or C) & (A or B) or C are_interchangeable.
assoc(7): A <-> (B <-> C) & (A <-> B) <-> C are_interchangeable.
/*** COMMUTATIVITY of "and", "or" & "<->" Rules ***/
commut(3): A and B may_be_replaced_by B and A.
commut(4): A or B may_be_replaced_by B or A.
commut(5): A <-> B may_be_replaced_by B <-> A.
/*** DISTRIBUTIVITY of "and" and "or" over each other Rules ***/
distrib(5): (A and B) or C & (A or C) and (B or C) are_interchangeable.
distrib(6): (A and B) or C & (C or A) and (C or B) are_interchangeable.
distrib(7): C or (A and B) & (C or A) and (C or B) are_interchangeable.
distrib(8): C or (A and B) & (A or C) and (B or C) are_interchangeable.
distrib(9): (A or B) and C & (A and C) or (B and C) are_interchangeable.
distrib(10): (A or B) and C & (C and A) or (C and B) are_interchangeable.
distrib(11): C and (A or B) & (C and A) or (C and B) are_interchangeable.
distrib(12): C and (A or B) & (A and C) or (B and C) are_interchangeable.
/*** Other handy logical equivalences (DeMorgan, etc.) ***/
logical(1): not (A or B) & (not A) and (not B) are_interchangeable.
logical(2): not (A and B) & (not A) or (not B) are_interchangeable.
logical(3): A -> B & (not A) or B are_interchangeable.
logical(4): A <-> B & (A -> B) and (B -> A) are_interchangeable.
logical(5): A -> (B -> C) may_be_replaced_by (A and B) -> C.
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