| import Mathlib | |
| namespace OAI | |
| namespace UniqueGames.BinaryFormula | |
| structure Literal where | |
| name : Nat | |
| positive : Bool | |
| deriving DecidableEq | |
| def Literal.eval (literal : Literal) (assignment : Nat → Bool) : Bool := | |
| if literal.positive then assignment literal.name else !(assignment literal.name) | |
| abbrev Clause := Vector Literal 3 | |
| def Clause.eval (clause : Clause) (assignment : Nat → Bool) : Bool := | |
| (clause[0].eval assignment || clause[1].eval assignment) || clause[2].eval assignment | |
| structure Formula where | |
| clauses : List Clause | |
| def Formula.Satisfiable (F : Formula) : Prop := | |
| ∃ assignment : Nat → Bool, ∀ clause ∈ F.clauses, clause.eval assignment = true | |
| def clauseNames (clause : Clause) : List Nat := | |
| [clause[0].name, clause[1].name, clause[2].name] | |
| def sourceNames (F : Formula) : List Nat := | |
| F.clauses.flatMap clauseNames | |
| end UniqueGames.BinaryFormula | |
| end OAI | |