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92416a2 | 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 | 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
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