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Sat.hs

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+{- |
+Module      :  Sat
+Description :  Simple SAT solver
+Copyright   :  (c) Dimitri Lozeve
+License     :  BSD3
+
+Maintainer  :  Dimitri Lozeve <dimitri.lozeve@gmail.com>
+Stability   :  unstable
+Portability :  portable
+
+A simple SAT solver.
+-}
+
+module Sat where
+
+import Data.List
+
+-- Variables are represented by positive integers
+type Var = Int
+
+-- A literal is either a variable, or the negation of a variable
+data Lit = Pos Var | Neg Var deriving (Eq, Show)
+
+-- A clause is a disjunction of literals, represented by a list of
+-- literals
+type Clause = [Lit]
+
+-- A formula, represented in its Conjunctive Normal Form (CNF), is a
+-- conjunction of clauses, represented as a list
+type CNF = [Clause]
+
+-- An assignment is a list of literals. For instance, if an assignment
+-- contains (Pos 5), it means that in this assignment, the variable 5
+-- is assigned to True.
+type Assignment = [Lit]
+
+----------------------------------------------------------------------
+
+-- Literal Evaluation
+
+-- Negates a literal
+notLit :: Lit -> Lit
+notLit (Pos x) = Neg x
+notLit (Neg x) = Pos x
+
+-- Evaluates a CNF by fixing the value of a given literal
+evalLit :: Lit -> CNF -> CNF
+evalLit _ [] = []
+evalLit lit f = foldr g [] f
+  where g c acc
+          | lit `elem` c = acc
+          | notLit lit `elem` c = (c \\ [notLit lit]):acc
+          | otherwise = c:acc
+
+-- Pure Literal rule
+
+-- Tests whether a literal is pure, i.e. only appears as positive or
+-- negative
+testPureLit :: Lit -> CNF -> Bool
+testPureLit _ [] = True
+testPureLit (Pos x) (c:cs) = Neg x `notElem` c && testPureLit (Pos x) cs
+testPureLit (Neg x) (c:cs) = Pos x `notElem` c && testPureLit (Neg x) cs
+
+-- Tests whether a variable appears only as a pure literal
+testPureVar :: Var -> CNF -> Bool
+testPureVar x f = testPureLit (Pos x) f || testPureLit (Neg x) f
+
+
+
+----------------------------------------------------------------------
+
+-- Examples for testing purposes
+
+test1 :: CNF
+test1 = [[Neg 1, Pos 2], [Pos 3, Neg 2], [Pos 4, Neg 5], [Pos 5, Neg 4]]