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module demo::lang::logic::ast::Booleans

rascal-0.34.0

Usage​

import demo::lang::logic::ast::Booleans;

data Formula​

data Formula  
     = \true()
     | \false()
     | \not(Formula arg)
     | \and(Formula lhs, Formula rhs)
     | \and(set[Formula] args)
     | \or(Formula lhs, Formula rhs)
     | \or(set[Formula] args)
     | \if(Formula lhs, Formula rhs)
     | \fi(Formula lhs, Formula rhs)
     | \iff(Formula lhs, Formula rhs)
     ;

function or​

Formula or({Formula x}) = x;

function and​

Formula and({Formula x}) = x;

Formula and(Formula a, Formula b) = and({a,b});

function or​

Formula or(Formula a, Formula b) = or({a,b});

function and​

Formula and({*Formula a, and(set[Formula] b)}) = and(a + b);

function or​

Formula or({*Formula a, or(set[Formula] b)}) = or(a + b);

function simplify​

Formula simplify(or({\true(), *Formula _}))   = \true();

Formula simplify(and({\false(), *Formula _})) = \false();

Formula simplify(not(not(Formula g))) = g;

Formula simplify(not(\true()))        = \false();

Formula simplify(not(\false()))       = \true();

Formula simplify(\if(Formula l, Formula r))           = or(not(l),r);

Formula simplify(\fi(Formula l, Formula r))           = \if(r, l);

Formula simplify(\iff(Formula l, Formula r))          = and(\if(l,r),\fi(l,r));

Formula simplify(and({Formula g,\not(g),*Formula r})) = \false();

default Formula simplify(Formula f) = f;