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ef6eb55 | 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 | -- PAX ConstraintDAG — HyperKitty 7-node pipeline as a verified Lean 4 structure
-- Ahmad Ali Parr · PAX Architecture · sm_86
import Mathlib.Data.Finset.Basic
namespace PAX.ConstraintDAG
/-- The 7 nodes of the HyperKitty Constraint DAG -/
inductive ConstraintNode : Type
| Input -- 🧠 Raw kernel request
| Memory -- 📚 Abjad/weight store
| Retrieval -- 🔍 Proof obligation lookup
| Transform -- ⚙ PTX/Futhark generation
| Constraint -- ⚖ Invariant checking
| Proof -- 🔐 Lean 4 verification
| Output -- 🌐 Sealed kernel + receipt
deriving DecidableEq, Repr
/-- DAG as adjacency relation -/
def isEdge : ConstraintNode → ConstraintNode → Prop
| .Input, .Memory => True
| .Memory, .Retrieval => True
| .Retrieval, .Transform => True
| .Transform, .Constraint => True
| .Constraint, .Proof => True
| .Proof, .Output => True
| _, _ => False
instance : DecidablePred (isEdge n) := by
intro n m
cases n <;> cases m <;> simp [isEdge] <;> exact inferInstance
/-- Topological order for the 7-node chain -/
def topoOrder : ConstraintNode → ℕ
| .Input => 0
| .Memory => 1
| .Retrieval => 2
| .Transform => 3
| .Constraint => 4
| .Proof => 5
| .Output => 6
/-- Acyclicity: edges only go forward in topo order -/
theorem dag_acyclic (n m : ConstraintNode) (h : isEdge n m) :
topoOrder n < topoOrder m := by
cases n <;> cases m <;> simp [isEdge, topoOrder] at *
/-- Single source -/
theorem single_source (n : ConstraintNode) :
(∃ m, isEdge m n) → n ≠ .Input := by
cases n <;> simp [isEdge]
/-- Single sink -/
theorem single_sink (n : ConstraintNode) :
(∃ m, isEdge n m) → n ≠ .Output := by
cases n <;> simp [isEdge]
end PAX.ConstraintDAG
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