1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196
// boolean_expression: a Rust crate for Boolean expressions and BDDs. // // Copyright (c) 2016 Chris Fallin <cfallin@c1f.net>. Released under the MIT // License. // use std::collections::HashMap; use std::fmt::Debug; use std::cmp::Ord; use std::hash::Hash; use simplify; /// An `Expr` is a simple Boolean logic expression. It may contain terminals /// (i.e., free variables), constants, and the following fundamental operations: /// AND, OR, NOT. #[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)] pub enum Expr<T> where T: Clone + Debug + Eq + Ord + Hash, { /// A terminal (free variable). This expression node represents a value that /// is not known until evaluation time. Terminal(T), /// A boolean constant: true or false. Const(bool), /// The logical complement of the contained expression argument. Not(Box<Expr<T>>), /// The logical AND of the two expression arguments. And(Box<Expr<T>>, Box<Expr<T>>), /// The logical OR of the two expression arguments. Or(Box<Expr<T>>, Box<Expr<T>>), } impl<T> Expr<T> where T: Clone + Debug + Eq + Ord + Hash, { /// Returns `true` if this `Expr` is a terminal. pub fn is_terminal(&self) -> bool { match self { &Expr::Terminal(_) => true, _ => false, } } /// Returns `true` if this `Expr` is a constant. pub fn is_const(&self) -> bool { match self { &Expr::Const(_) => true, _ => false, } } /// Returns `true` if this `Expr` is a NOT node. pub fn is_not(&self) -> bool { match self { &Expr::Not(_) => true, _ => false, } } /// Returns `true` if this `Expr` is an AND node. pub fn is_and(&self) -> bool { match self { &Expr::And(_, _) => true, _ => false, } } /// Returns `true` if this `Expr` is an OR node. pub fn is_or(&self) -> bool { match self { &Expr::Or(_, _) => true, _ => false, } } /// Builds a NOT node around an argument, consuming the argument /// expression. pub fn not(e: Expr<T>) -> Expr<T> { Expr::Not(Box::new(e)) } /// Builds an AND node around two arguments, consuming the argument /// expressions. pub fn and(e1: Expr<T>, e2: Expr<T>) -> Expr<T> { Expr::And(Box::new(e1), Box::new(e2)) } /// Builds an OR node around two arguments, consuming the argument /// expressions. pub fn or(e1: Expr<T>, e2: Expr<T>) -> Expr<T> { Expr::Or(Box::new(e1), Box::new(e2)) } /// Evaluates the expression with a particular set of terminal assignments. /// If any terminals are not assigned, they default to `false`. pub fn evaluate(&self, vals: &HashMap<T, bool>) -> bool { match self { &Expr::Terminal(ref t) => *vals.get(t).unwrap_or(&false), &Expr::Const(val) => val, &Expr::And(ref a, ref b) => a.evaluate(vals) && b.evaluate(vals), &Expr::Or(ref a, ref b) => a.evaluate(vals) || b.evaluate(vals), &Expr::Not(ref x) => !x.evaluate(vals), } } /// Simplify an expression in a relatively cheap way using well-known logic /// identities. /// /// This function performs certain reductions using DeMorgan's Law, /// distribution of ANDs over ORs, and certain identities involving /// constants, to simplify an expression. The result will always be in /// sum-of-products form: nodes will always appear in order (from /// expression tree root to leaves) `OR -> AND -> NOT`. In other words, /// `AND` nodes may only have `NOT` nodes (or terminals or constants) as /// children, and `NOT` nodes may only have terminals or constants as /// children. /// /// This function explicitly does *not* perform any sort of minterm reduction. /// The terms may thus be redundant (i.e., `And(a, b)` may appear twice), and /// combinable terms may exist (i.e., `And(a, b)` and `And(a, Not(b))` may /// appear in the `OR`'d list of terms, where these could be combined to /// simply `a` but are not). For example: /// /// ``` /// use boolean_expression::Expr; /// /// // This simplifies using DeMorgan's Law: /// let expr = Expr::not(Expr::or(Expr::Terminal(0), Expr::Terminal(1))); /// let simplified = expr.simplify_via_laws(); /// assert_eq!(simplified, /// Expr::and(Expr::not(Expr::Terminal(0)), /// Expr::not(Expr::Terminal(1)))); /// /// // This doesn't simplify, though: /// let expr = Expr::or( /// Expr::and(Expr::Terminal(0), Expr::Terminal(1)), /// Expr::and(Expr::Terminal(0), Expr::not(Expr::Terminal(1)))); /// let simplified = expr.clone().simplify_via_laws(); /// assert_eq!(simplified, expr); /// ``` /// /// For better (but more expensive) simplification, see `simplify_via_bdd()`. pub fn simplify_via_laws(self) -> Expr<T> { simplify::simplify_via_laws(self) } /// Simplify an expression via a roundtrip through a `BDD`. This procedure /// is more effective than `Expr::simplify_via_laws()`, but more expensive. /// This roundtrip will implicitly simplify an arbitrarily complicated /// function (by construction, as the BDD is built), and then find a /// quasi-minimal set of terms using cubelist-based reduction. For example: /// /// ``` /// use boolean_expression::Expr; /// /// // `simplify_via_laws()` cannot combine these terms, but /// // `simplify_via_bdd()` will: /// let expr = Expr::or( /// Expr::and(Expr::Terminal(0), Expr::Terminal(1)), /// Expr::and(Expr::Terminal(0), Expr::not(Expr::Terminal(1)))); /// let simplified = expr.simplify_via_bdd(); /// assert_eq!(simplified, Expr::Terminal(0)); /// ``` pub fn simplify_via_bdd(self) -> Expr<T> { simplify::simplify_via_bdd(self) } /// Map terminal values using the specified mapping function. pub fn map<F, R>(&self, f: F) -> Expr<R> where F: Fn(&T) -> R, R: Clone + Debug + Eq + Ord + Hash, { self.map1(&f) } fn map1<F, R>(&self, f: &F) -> Expr<R> where F: Fn(&T) -> R, R: Clone + Debug + Eq + Ord + Hash, { match self { &Expr::Terminal(ref t) => Expr::Terminal(f(t)), &Expr::Const(val) => Expr::Const(val), &Expr::Not(ref n) => Expr::not(n.map1(f)), &Expr::And(ref a, ref b) => Expr::and(a.map1(f), b.map1(f)), &Expr::Or(ref a, ref b) => Expr::or(a.map1(f), b.map1(f)), } } }