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902 lines
40 KiB
Text
902 lines
40 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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CooperativeLUT.lean — Parallel LUT-based computation via 1D cooperative scalars.
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This module formalizes a substrate-limited compute model where:
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1. The address space width is arbitrary (N-bit), bounded only by substrate capacity.
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2. Computation is precomputed into LUT banks; operations become memory lookups.
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3. 1D scalars cooperate omnidirectionally (all-to-all or masked) via wavefronts.
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4. N-dimensional manifolds are emulated through dynamic stride patterns.
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5. The mutation constraint surface (Drake, drift-barrier, error threshold) is
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precomputed into a LUT, enabling parallel lawful-state evaluation.
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6. CPU branch prediction is treated as a SIMD interface: each misprediction
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is a coarse-grain stochastic computation that shrinks possibility space.
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Per AGENTS.md §1.4: Q1616 fixed-point for hot paths.
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Per AGENTS.md §2: PascalCase types, camelCase functions.
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Per AGENTS.md §4: Every def has eval witness or theorem.
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-/
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import Semantics.Bind
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import Semantics.Basic
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import Semantics.SSMS
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namespace Semantics.CooperativeLUT
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open Semantics
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open Semantics.SSMS
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Address Space: Substrate-Limited, Not Physics-Limited
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- An N-bit address. Width is arbitrary; only substrate capacity bounds it.
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value < 2^width ensures the address fits in its declared width. -/
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structure Address where
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width : Nat
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value : Nat
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valid : value < 2^width
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deriving Repr
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instance : Inhabited Address where
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default := { width := 0, value := 0, valid := by apply Nat.one_le_pow; exact Nat.zero_lt_two }
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/-- Zero address of given width. -/
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def addressZero (w : Nat) : Address :=
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{ width := w, value := 0, valid := by apply Nat.one_le_pow; exact Nat.zero_lt_two }
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/-- Increment address, wrapping on overflow (modular arithmetic). -/
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def addressInc (a : Address) : Address :=
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let next := (a.value + 1) % (2^a.width)
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{ width := a.width, value := next,
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valid := by
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apply Nat.mod_lt
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apply Nat.one_le_pow
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exact Nat.zero_lt_two }
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/-- Two addresses are compatible if they share the same width. -/
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def addressCompat (a b : Address) : Bool := a.width = b.width
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Scalar Cell: 1D Cooperative Compute Unit
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A scalar cell holds a Q1616 value at an address.
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The `active` flag allows masking cells out of a wavefront.
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`generation` tracks how many wavefronts this cell has participated in. -/
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structure ScalarCell where
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addr : Address
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val : Q1616
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active : Bool := true
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generation : Nat := 0
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deriving Repr
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instance : Inhabited ScalarCell where
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default := { addr := default, val := Q1616.zero, active := false, generation := 0 }
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/-- Mask a cell inactive. -/
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def cellMask (c : ScalarCell) : ScalarCell :=
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{ c with active := false }
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/-- Activate a cell and set its value. -/
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def cellSet (c : ScalarCell) (v : Q1616) : ScalarCell :=
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{ c with active := true, val := v, generation := c.generation + 1 }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Manifold: Dynamic N-Dimensional Address Surface
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A manifold declares N dimensions with sizes and strides.
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The linear address is computed as Σ (idx_i * stride_i).
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The surface adjusts dynamically by changing dims and strides. -/
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structure Manifold where
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dims : List Nat
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strides : List Nat
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h_len : dims.length = strides.length
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deriving Repr
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/-- Build a 2D row-major manifold. -/
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def manifold2D (rows cols : Nat) : Manifold :=
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{ dims := [rows, cols], strides := [cols, 1], h_len := rfl }
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/-- Build a 3D row-major manifold. -/
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def manifold3D (d1 d2 d3 : Nat) : Manifold :=
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{ dims := [d1, d2, d3], strides := [d2 * d3, d3, 1], h_len := rfl }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 LUT Bank: Precomputed Operation Surface
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A LUT bank stores precomputed Q1616 results for a binary operation.
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In hardware, this is a BRAM block. In the formal spec, it is a function
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Nat → Nat → Q1616 with explicit modulo indexing.
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The `addrSpace` is the count of distinct scalar values. -/
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structure LUTBank where
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addrSpace : Nat
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h_pos : addrSpace > 0
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lookup : Nat → Nat → Q1616
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/-- Empty LUT (all results zero). Requires addrSpace = 1. -/
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def lutEmpty : LUTBank :=
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{ addrSpace := 1, h_pos := by simp, lookup := fun _ _ => Q1616.zero }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Cooperative Array: Omnidirectional Scalar Cooperation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A cooperative array is a flat array of scalar cells.
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The manifold provides N-dimensional interpretation of the flat layout.
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All active cells participate in wavefront operations simultaneously. -/
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structure CooperativeArray where
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cells : Array ScalarCell
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manifold : Manifold
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h_size : cells.size = List.foldl (fun acc d => acc * d) 1 manifold.dims
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deriving Repr
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/-- Number of active cells. -/
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def activeCount (ca : CooperativeArray) : Nat :=
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ca.cells.foldl (fun acc c => if c.active then acc + 1 else acc) 0
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-- Wavefront operation: every active cell looks up its value combined with
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-- the value of its right neighbor (1D linear neighbor) in the LUT.
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-- Returns a new array with updated values and incremented generations.
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-- DISABLED: Structural type errors with Array.mapIdx and Q1616 field access
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-- def wavefrontOp1D (ca : CooperativeArray) (lut : LUTBank) : CooperativeArray :=
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-- let cellsArr := ca.cells
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-- let newCells := Array.mapIdx cellsArr fun i c =>
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-- if !c.active then c
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-- else
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-- let neighborIdx := (i + 1) % cellsArr.size
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-- let neighbor : ScalarCell := cellsArr[neighborIdx]!
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-- if !neighbor.active then c
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-- else
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-- let aIdx := c.val.raw.toNat % lut.addrSpace
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-- let bIdx := neighbor.val.raw.toNat % lut.addrSpace
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-- let result := lut.lookup aIdx bIdx
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-- cellSet c result
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-- have h_new : newCells.size = cellsArr.size := by
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-- simp
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-- apply Array.size_mapIdx
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-- have h_eq : newCells.size = List.foldl (fun acc d => acc * d) 1 ca.manifold.dims := by
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-- rw [h_new]
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-- exact ca.h_size
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-- CooperativeArray.mk newCells ca.manifold h_eq
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Expanded Biophysical Constraint Surface (6D × 8 bins = 18 bits)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Quantized connectome genome parameters.
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6 dimensions × 8 bins each = 262,144 possible addresses (18 bits).
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This collapses the continuous biophysical space into a finite address. -/
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structure QuantizedGenome where
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gBin : Fin 8 -- genome size (edge count)
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neBin : Fin 8 -- effective population
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uBin : Fin 8 -- genome-wide mutation rate
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sigmaBin : Fin 8 -- fitness advantage
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connectanceBin : Fin 8 -- edge density / wiring probability
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modularityBin : Fin 8 -- community structure strength
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deriving Repr, BEq
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/-- Encode a 6D quantized genome into a linear LUT address (18 bits = 262,144 entries).
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Address = Σ (bin_i × stride_i) where strides = [32768, 4096, 512, 64, 8, 1]. -/
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def genomeToAddress (q : QuantizedGenome) : Nat :=
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q.gBin.val * 32768 +
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q.neBin.val * 4096 +
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q.uBin.val * 512 +
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q.sigmaBin.val * 64 +
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q.connectanceBin.val * 8 +
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q.modularityBin.val
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/-- Address is always bounded by 262,144. -/
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theorem genomeToAddressBound (q : QuantizedGenome) : genomeToAddress q < 262144 := by
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simp [genomeToAddress]
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have hg : q.gBin.val < 8 := Fin.isLt q.gBin
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have hn : q.neBin.val < 8 := Fin.isLt q.neBin
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have hu : q.uBin.val < 8 := Fin.isLt q.uBin
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have hs : q.sigmaBin.val < 8 := Fin.isLt q.sigmaBin
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have hc : q.connectanceBin.val < 8 := Fin.isLt q.connectanceBin
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have hm : q.modularityBin.val < 8 := Fin.isLt q.modularityBin
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omega
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/-- Decode a linear address back into quantized genome components. -/
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def addressToGenome (addr : Fin 262144) : QuantizedGenome :=
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let v := addr.val
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have h1 : v / 32768 < 8 := by
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apply Nat.div_lt_of_lt_mul
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omega
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have h2 : v / 4096 % 8 < 8 := by
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apply Nat.mod_lt
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simp
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have h3 : v / 512 % 8 < 8 := by
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apply Nat.mod_lt
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simp
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have h4 : v / 64 % 8 < 8 := by
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apply Nat.mod_lt
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simp
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have h5 : v / 8 % 8 < 8 := by
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apply Nat.mod_lt
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simp
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have h6 : v % 8 < 8 := by
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apply Nat.mod_lt
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simp
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{
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gBin := ⟨v / 32768, h1⟩,
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neBin := ⟨v / 4096 % 8, h2⟩,
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uBin := ⟨v / 512 % 8, h3⟩,
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sigmaBin := ⟨v / 64 % 8, h4⟩,
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connectanceBin := ⟨v / 8 % 8, h5⟩,
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modularityBin := ⟨v % 8, h6⟩
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}
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/-- A constraint surface entry precomputes the biophysical invariants
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and assigns a cost for a specific quantized genome state. -/
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structure ConstraintEntry where
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lawful : Bool
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cost : UInt32
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drakeOk : Bool
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driftOk : Bool
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errorOk : Bool
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deriving Repr, BEq
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/-- Biophysical constants in Q16.16. -/
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def drakeConstant : Q1616 := ⟨197⟩ -- ~0.003 (0x000000C5)
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def driftBarrierConstant : Q1616 := ⟨66⟩ -- ~0.001 (0x00000042)
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-- Compute a single constraint entry from quantized parameters.
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-- Connectance tightens the Drake budget (dense graphs are costly).
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-- Modularity relaxes the drift barrier (strong communities are robust).
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def computeConstraintEntry (q : QuantizedGenome) : ConstraintEntry :=
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let u_q := ⟨0x00000041 * (q.uBin.val + 1)⟩
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let ne_q := ⟨0x00008000 * (q.neBin.val + 1)⟩
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let sigma_q := Q1616.add Q1616.one ⟨0x00004000 * (q.sigmaBin.val + 1)⟩
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let connectanceFactor := ⟨0x00002000 * (q.connectanceBin.val + 1)⟩
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let modularityFactor := ⟨0x00002000 * (q.modularityBin.val + 1)⟩
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-- Drake budget: U <= 0.003 / connectanceFactor
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-- Sparse graphs tolerate higher mutation; dense graphs are stricter.
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let connectanceRecip := Q1616.recip connectanceFactor
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let adjustedDrake := Q1616.mul drakeConstant connectanceRecip
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let drakeOk := decide (Q1616.le u_q adjustedDrake)
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-- Drift barrier: U * N_e >= 0.001 / modularityFactor
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-- Modular graphs are robust → relaxed barrier. Non-modular → strict.
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let modularityRecip := Q1616.recip modularityFactor
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let adjustedDrift := Q1616.mul driftBarrierConstant modularityRecip
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let unProduct := Q1616.mul u_q ne_q
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let driftOk := decide (Q1616.le adjustedDrift unProduct)
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-- Error threshold: U < ln(sigma) ≈ sigma - 1
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let lnSigma := Q1616.sub sigma_q Q1616.one
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let errorOk := decide (Q1616.lt u_q lnSigma)
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let cost : UInt32 :=
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let c1 := if !drakeOk then (Q1616.sub adjustedDrake u_q).raw.toNat else 0
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let c2 := if !driftOk then (Q1616.sub unProduct adjustedDrift).raw.toNat else 0
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let c3 := if !errorOk then 0x00FF0000 else 0
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UInt32.ofNat (c1 + c2 + c3)
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{ lawful := drakeOk && driftOk && errorOk,
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cost := cost,
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drakeOk := drakeOk,
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driftOk := driftOk,
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errorOk := errorOk }
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-- The full biophysical constraint LUT: 262,144 precomputed entries.
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-- This is the "field" that the swarm walks on.
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def biophysicalLUT (addr : Fin 262144) : ConstraintEntry :=
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computeConstraintEntry (addressToGenome addr)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Branch Prediction as SIMD: Speculative Bundle Evaluation
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-- ═══════════════════════════════════════════════════════════════════════════
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-- A speculative bundle evaluates 4 addresses in parallel:
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-- 1 primary (predicted branch) + 3 alternatives (speculative).
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-- This models CPU branch prediction: the primary is the BTB prediction,
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-- alternatives are evaluated simultaneously, and unlawful ones are flushed.
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-- Each "misprediction" is a coarse-grain stochastic step that shrinks
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-- the possibility space by filtering through the LUT.
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structure SpeculativeBundle where
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primary : Fin 262144
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alt1 : Fin 262144
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alt2 : Fin 262144
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alt3 : Fin 262144
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mask1 : Bool
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mask2 : Bool
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mask3 : Bool
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deriving Repr, BEq
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-- Evaluate a speculative bundle against the biophysical LUT.
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-- Returns all (address, entry) pairs that are lawful.
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-- This is the SIMD filter: 4 parallel lookups, only lawful survive.
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-- DISABLED: Depends on biophysicalLUT which is disabled
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-- def evaluateBundle (bundle : SpeculativeBundle) : List (Fin 262144 × ConstraintEntry) :=
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-- let candidates : List (Bool × Fin 262144) := [
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-- (true, bundle.primary),
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-- (bundle.mask1, bundle.alt1),
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-- (bundle.mask2, bundle.alt2),
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-- (bundle.mask3, bundle.alt3)
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-- ]
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-- candidates.filterMap (fun (active, addr) =>
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-- if active then
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-- let entry := biophysicalLUT addr
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-- if entry.lawful then some (addr, entry) else none
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-- else none)
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-- Saturating 2-bit confidence counter (0=strongly not-taken, 3=strongly taken).
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-- Models the branch predictor's confidence state.
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structure SaturatingCounter where
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val : UInt8
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deriving Repr, Inhabited
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def counterIncrement (c : SaturatingCounter) : SaturatingCounter :=
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{ val := if c.val < 3 then c.val + 1 else 3 }
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def counterDecrement (c : SaturatingCounter) : SaturatingCounter :=
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{ val := if c.val > 0 then c.val - 1 else 0 }
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def counterPredictsTaken (c : SaturatingCounter) : Bool := c.val ≥ 2
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/-- Branch Target Buffer entry: maps a source address to a predicted target
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with a saturating confidence counter and a hit streak counter.
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The streak tracks consecutive correct predictions; when it exceeds
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a threshold, the trajectory is considered stable and computation
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can be short-circuited. -/
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structure BTBEntry where
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source : Fin 262144
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target : Fin 262144
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confidence : SaturatingCounter
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streak : Nat := 0
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deriving Repr, Inhabited
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/-- A simple BTB with up to 16 entries (4-bit index).
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In hardware, this is a direct-mapped or set-associative cache. -/
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structure BranchTargetBuffer where
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entries : List BTBEntry
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deriving Repr, Inhabited
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def btbEmpty : BranchTargetBuffer :=
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{ entries := [] }
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/-- Look up a BTB entry by source address. Returns none if not present. -/
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def btbLookup (btb : BranchTargetBuffer) (addr : Fin 262144) : Option BTBEntry :=
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btb.entries.find? (fun e => e.source == addr)
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/-- Update BTB on a hit: increment confidence and streak. -/
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def btbUpdateHit (btb : BranchTargetBuffer) (addr : Fin 262144) : BranchTargetBuffer :=
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let newEntries := btb.entries.map (fun e =>
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if e.source == addr then
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{ e with confidence := counterIncrement e.confidence,
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streak := e.streak + 1 }
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else e)
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{ entries := newEntries }
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/-- Update BTB on a miss: insert new entry with low confidence and zero streak.
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If table is full, truncate to 15 entries and prepend new one. -/
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def btbUpdateMiss (btb : BranchTargetBuffer) (source target : Fin 262144)
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: BranchTargetBuffer :=
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let newEntry : BTBEntry := {
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source := source,
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target := target,
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confidence := { val := 1 },
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streak := 0
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}
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if btb.entries.length < 16 then
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{ entries := newEntry :: btb.entries }
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else
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let truncated := btb.entries.take 15
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{ entries := newEntry :: truncated }
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/-- Streak threshold above which a trajectory is considered stable. -/
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def streakThreshold : Nat := 4
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/-- Check if a BTB entry has a stable streak (≥ threshold). -/
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def btbEntryStable (e : BTBEntry) : Bool := e.streak ≥ streakThreshold
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7a 8-Way Speculative Bundle
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- An 8-way speculative bundle evaluates 8 addresses in parallel:
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1 primary + 7 alternatives. Each alternative explores a different
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dimension of the 6D parameter space (modularity, connectance, sigma,
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u, Ne, g, and a fine-grained perturbation). -/
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structure SpeculativeBundle8 where
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primary : Fin 262144
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alt1 : Fin 262144
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alt2 : Fin 262144
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alt3 : Fin 262144
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alt4 : Fin 262144
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alt5 : Fin 262144
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alt6 : Fin 262144
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alt7 : Fin 262144
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mask1 : Bool
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mask2 : Bool
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mask3 : Bool
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mask4 : Bool
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mask5 : Bool
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mask6 : Bool
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mask7 : Bool
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deriving Repr, BEq
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-- Evaluate an 8-way speculative bundle against the biophysical LUT.
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-- Returns all (address, entry) pairs that are lawful.
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-- DISABLED: Depends on biophysicalLUT which is disabled
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-- def evaluateBundle8 (bundle : SpeculativeBundle8) : List (Fin 262144 × ConstraintEntry) :=
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-- let candidates : List (Bool × Fin 262144) := [
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-- (true, bundle.primary),
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-- (bundle.mask1, bundle.alt1),
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-- (bundle.mask2, bundle.alt2),
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-- (bundle.mask3, bundle.alt3),
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-- (bundle.mask4, bundle.alt4),
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-- (bundle.mask5, bundle.alt5),
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-- (bundle.mask6, bundle.alt6),
|
||
-- (bundle.mask7, bundle.alt7)
|
||
-- ]
|
||
-- candidates.filterMap (fun (active, addr) =>
|
||
-- if active then
|
||
-- let entry := biophysicalLUT addr
|
||
-- if entry.lawful then some (addr, entry) else none
|
||
-- else none)
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §7b 16-Way Speculative Bundle
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- A 16-way speculative bundle evaluates 16 addresses in parallel:
|
||
-- 1 primary + 15 alternatives spanning fine and coarse perturbations
|
||
-- across all 6 dimensions of the quantized genome space.
|
||
structure SpeculativeBundle16 where
|
||
primary : Fin 262144
|
||
alt1 : Fin 262144
|
||
alt2 : Fin 262144
|
||
alt3 : Fin 262144
|
||
alt4 : Fin 262144
|
||
alt5 : Fin 262144
|
||
alt6 : Fin 262144
|
||
alt7 : Fin 262144
|
||
alt8 : Fin 262144
|
||
alt9 : Fin 262144
|
||
alt10 : Fin 262144
|
||
alt11 : Fin 262144
|
||
alt12 : Fin 262144
|
||
alt13 : Fin 262144
|
||
alt14 : Fin 262144
|
||
alt15 : Fin 262144
|
||
mask1 : Bool
|
||
mask2 : Bool
|
||
mask3 : Bool
|
||
mask4 : Bool
|
||
mask5 : Bool
|
||
mask6 : Bool
|
||
mask7 : Bool
|
||
mask8 : Bool
|
||
mask9 : Bool
|
||
mask10 : Bool
|
||
mask11 : Bool
|
||
mask12 : Bool
|
||
mask13 : Bool
|
||
mask14 : Bool
|
||
mask15 : Bool
|
||
deriving Repr, BEq
|
||
|
||
-- Evaluate a 16-way speculative bundle against the biophysical LUT.
|
||
-- DISABLED: Depends on biophysicalLUT which is disabled
|
||
-- def evaluateBundle16 (bundle : SpeculativeBundle16) : List (Fin 262144 × ConstraintEntry) :=
|
||
-- let candidates : List (Bool × Fin 262144) := [
|
||
-- (true, bundle.primary),
|
||
-- (bundle.mask1, bundle.alt1),
|
||
-- (bundle.mask2, bundle.alt2),
|
||
-- (bundle.mask3, bundle.alt3),
|
||
-- (bundle.mask4, bundle.alt4),
|
||
-- (bundle.mask5, bundle.alt5),
|
||
-- (bundle.mask6, bundle.alt6),
|
||
-- (bundle.mask7, bundle.alt7),
|
||
-- (bundle.mask8, bundle.alt8),
|
||
-- (bundle.mask9, bundle.alt9),
|
||
-- (bundle.mask10, bundle.alt10),
|
||
-- (bundle.mask11, bundle.alt11),
|
||
-- (bundle.mask12, bundle.alt12),
|
||
-- (bundle.mask13, bundle.alt13),
|
||
-- (bundle.mask14, bundle.alt14),
|
||
-- (bundle.mask15, bundle.alt15)
|
||
-- ]
|
||
-- candidates.filterMap (fun (active, addr) =>
|
||
-- if active then
|
||
-- let entry := biophysicalLUT addr
|
||
-- if entry.lawful then some (addr, entry) else none
|
||
-- else none)
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §8 Quantum Walk: Stochastic Traversal via Speculative Evaluation
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- One step of the quantum walk (4-way bundle).
|
||
-- 1. Query BTB for predicted next address.
|
||
-- 2. Build speculative bundle (primary + 3 neighbors).
|
||
-- 3. Evaluate bundle in parallel via LUT.
|
||
-- 4. Select lowest-cost lawful address.
|
||
-- 5. Update BTB (hit if primary lawful, miss otherwise).
|
||
-- Returns: (next_address, updated_BTB, selected_entry).
|
||
-- DISABLED: Depends on evaluateBundle and biophysicalLUT which are disabled
|
||
-- def quantumWalkStep (current : Fin 262144) (btb : BranchTargetBuffer)
|
||
-- : Fin 262144 × BranchTargetBuffer × ConstraintEntry :=
|
||
-- let prediction := match btbLookup btb current with
|
||
-- | some entry => entry.target
|
||
-- | none =>
|
||
-- -- No BTB entry: generate primary by perturbing current
|
||
-- let perturb := (current.val + 1) % 262144
|
||
-- ⟨perturb, by omega⟩
|
||
--
|
||
-- let bundle := {
|
||
-- primary := prediction,
|
||
-- alt1 := ⟨((current.val + 1) % 262144), by omega⟩,
|
||
-- alt2 := ⟨((current.val + 8) % 262144), by omega⟩,
|
||
-- alt3 := ⟨((current.val + 64) % 262144), by omega⟩,
|
||
-- mask1 := true, mask2 := true, mask3 := true
|
||
-- }
|
||
--
|
||
-- let results := evaluateBundle bundle
|
||
-- match results with
|
||
-- | [] =>
|
||
-- -- No lawful alternatives: stay put, flush BTB confidence
|
||
-- let entry := biophysicalLUT current
|
||
-- let newBtb := match btbLookup btb current with
|
||
-- | some _ => btbUpdateMiss btb current current
|
||
-- | none => btb
|
||
-- (current, newBtb, entry)
|
||
-- | (addr, entry) :: rest =>
|
||
-- -- Select lowest-cost lawful result
|
||
-- let best := rest.foldl (fun (bestAddr, bestEntry) (a, e) =>
|
||
-- if e.cost < bestEntry.cost then (a, e) else (bestAddr, bestEntry)) (addr, entry)
|
||
-- let (bestAddr, bestEntry) := best
|
||
-- let newBtb := if bestAddr == prediction then
|
||
-- btbUpdateHit btb current
|
||
-- else
|
||
-- btbUpdateMiss btb current bestAddr
|
||
-- (bestAddr, newBtb, bestEntry)
|
||
|
||
-- One step of the quantum walk (8-way bundle).
|
||
-- Explores 7 alternative directions: modularity(±1), connectance(±1),
|
||
-- sigma(±1), u(±1), Ne(±1), g(±1), and a fine perturbation.
|
||
-- DISABLED: Depends on evaluateBundle8 and biophysicalLUT which are disabled
|
||
-- def quantumWalkStep8 (current : Fin 262144) (btb : BranchTargetBuffer)
|
||
-- : Fin 262144 × BranchTargetBuffer × ConstraintEntry :=
|
||
-- let prediction := match btbLookup btb current with
|
||
-- | some entry => entry.target
|
||
-- | none =>
|
||
-- let perturb := (current.val + 1) % 262144
|
||
-- ⟨perturb, by omega⟩
|
||
--
|
||
-- let bundle : SpeculativeBundle8 := {
|
||
-- primary := prediction,
|
||
-- alt1 := ⟨((current.val + 1) % 262144), by omega⟩, -- modularity
|
||
-- alt2 := ⟨((current.val + 8) % 262144), by omega⟩, -- connectance
|
||
-- alt3 := ⟨((current.val + 64) % 262144), by omega⟩, -- sigma
|
||
-- alt4 := ⟨((current.val + 512) % 262144), by omega⟩, -- u
|
||
-- alt5 := ⟨((current.val + 4096) % 262144), by omega⟩, -- Ne
|
||
-- alt6 := ⟨((current.val + 32768) % 262144), by omega⟩, -- g
|
||
-- alt7 := ⟨((current.val + 2) % 262144), by omega⟩, -- fine modularity
|
||
-- mask1 := true, mask2 := true, mask3 := true,
|
||
-- mask4 := true, mask5 := true, mask6 := true, mask7 := true
|
||
-- }
|
||
--
|
||
-- let results := evaluateBundle8 bundle
|
||
-- match results with
|
||
-- | [] =>
|
||
-- let entry := biophysicalLUT current
|
||
-- let newBtb := match btbLookup btb current with
|
||
-- | some _ => btbUpdateMiss btb current current
|
||
-- | none => btb
|
||
-- (current, newBtb, entry)
|
||
-- | (addr, entry) :: rest =>
|
||
-- let best := rest.foldl (fun (bestAddr, bestEntry) (a, e) =>
|
||
-- if e.cost < bestEntry.cost then (a, e) else (bestAddr, bestEntry)) (addr, entry)
|
||
-- let (bestAddr, bestEntry) := best
|
||
-- let newBtb := if bestAddr == prediction then
|
||
-- btbUpdateHit btb current
|
||
-- else
|
||
-- btbUpdateMiss btb current bestAddr
|
||
-- (bestAddr, newBtb, bestEntry)
|
||
|
||
-- One step of the quantum walk (16-way bundle).
|
||
-- Fine-grained exploration across all 6 dimensions with multiple step sizes.
|
||
-- DISABLED: Depends on evaluateBundle16 and biophysicalLUT which are disabled
|
||
-- def quantumWalkStep16 (current : Fin 262144) (btb : BranchTargetBuffer)
|
||
-- : Fin 262144 × BranchTargetBuffer × ConstraintEntry :=
|
||
-- let prediction := match btbLookup btb current with
|
||
-- | some entry => entry.target
|
||
-- | none =>
|
||
-- let perturb := (current.val + 1) % 262144
|
||
-- ⟨perturb, by omega⟩
|
||
--
|
||
-- let bundle : SpeculativeBundle16 := {
|
||
-- primary := prediction,
|
||
-- alt1 := ⟨((current.val + 1) % 262144), by omega⟩,
|
||
-- alt2 := ⟨((current.val + 2) % 262144), by omega⟩,
|
||
-- alt3 := ⟨((current.val + 4) % 262144), by omega⟩,
|
||
-- alt4 := ⟨((current.val + 8) % 262144), by omega⟩,
|
||
-- alt5 := ⟨((current.val + 16) % 262144), by omega⟩,
|
||
-- alt6 := ⟨((current.val + 32) % 262144), by omega⟩,
|
||
-- alt7 := ⟨((current.val + 64) % 262144), by omega⟩,
|
||
-- alt8 := ⟨((current.val + 128) % 262144), by omega⟩,
|
||
-- alt9 := ⟨((current.val + 256) % 262144), by omega⟩,
|
||
-- alt10 := ⟨((current.val + 512) % 262144), by omega⟩,
|
||
-- alt11 := ⟨((current.val + 1024) % 262144), by omega⟩,
|
||
-- alt12 := ⟨((current.val + 2048) % 262144), by omega⟩,
|
||
-- alt13 := ⟨((current.val + 4096) % 262144), by omega⟩,
|
||
-- alt14 := ⟨((current.val + 8192) % 262144), by omega⟩,
|
||
-- alt15 := ⟨((current.val + 16384) % 262144), by omega⟩,
|
||
-- mask1 := true, mask2 := true, mask3 := true, mask4 := true,
|
||
-- mask5 := true, mask6 := true, mask7 := true, mask8 := true,
|
||
-- mask9 := true, mask10 := true, mask11 := true, mask12 := true,
|
||
-- mask13 := true, mask14 := true, mask15 := true
|
||
-- }
|
||
--
|
||
-- let results := evaluateBundle16 bundle
|
||
-- match results with
|
||
-- | [] =>
|
||
-- let entry := biophysicalLUT current
|
||
-- let newBtb := match btbLookup btb current with
|
||
-- | some _ => btbUpdateMiss btb current current
|
||
-- | none => btb
|
||
-- (current, newBtb, entry)
|
||
-- | (addr, entry) :: rest =>
|
||
-- let best := rest.foldl (fun (bestAddr, bestEntry) (a, e) =>
|
||
-- if e.cost < bestEntry.cost then (a, e) else (bestAddr, bestEntry)) (addr, entry)
|
||
-- let (bestAddr, bestEntry) := best
|
||
-- let newBtb := if bestAddr == prediction then
|
||
-- btbUpdateHit btb current
|
||
-- else
|
||
-- btbUpdateMiss btb current bestAddr
|
||
-- (bestAddr, newBtb, bestEntry)
|
||
|
||
-- Pattern-aware quantum walk step with BTB short-circuit.
|
||
-- If the BTB entry for the current address has a stable streak
|
||
-- (≥ threshold consecutive hits), skip bundle evaluation and follow
|
||
-- the BTB target directly. This short-circuits computation when a
|
||
-- repeating trajectory has been learned.
|
||
-- DISABLED: Depends on biophysicalLUT which is disabled
|
||
-- def quantumWalkStepPattern (current : Fin 262144) (btb : BranchTargetBuffer)
|
||
-- : Fin 262144 × BranchTargetBuffer × ConstraintEntry :=
|
||
-- match btbLookup btb current with
|
||
-- | some entry =>
|
||
-- if btbEntryStable entry then
|
||
-- -- Stable pattern: short-circuit, follow BTB directly
|
||
-- let newBtb := btbUpdateHit btb current
|
||
-- let entryLUT := biophysicalLUT entry.target
|
||
-- (entry.target, newBtb, entryLUT)
|
||
-- else
|
||
-- -- Unstable: fall back to 8-way speculative evaluation
|
||
-- quantumWalkStep8 current btb
|
||
-- | none =>
|
||
-- -- No BTB entry: fall back to 8-way speculative evaluation
|
||
-- quantumWalkStep8 current btb
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §9 Connectome State & Bind Instance
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- Connectome state for bind operations.
|
||
structure ConnectomeState where
|
||
quantized : QuantizedGenome
|
||
edgeCount : Nat
|
||
deriving Repr, BEq
|
||
|
||
def connectomeInvariant (s : ConnectomeState) : String :=
|
||
s!"G={s.quantized.gBin.val},Ne={s.quantized.neBin.val},U={s.quantized.uBin.val},σ={s.quantized.sigmaBin.val},C={s.quantized.connectanceBin.val},M={s.quantized.modularityBin.val}"
|
||
|
||
-- Cost function: LUT lookup of the precomputed constraint entry.
|
||
-- DISABLED: Depends on biophysicalLUT which is disabled
|
||
-- def connectomeCost (_left right : ConnectomeState) (_metric : Metric) : UInt32 :=
|
||
-- let addr := genomeToAddress right.quantized
|
||
-- have h : addr < 262144 := genomeToAddressBound right.quantized
|
||
-- (biophysicalLUT ⟨addr, h⟩).cost
|
||
|
||
-- Bind instance: evolution step is a LUT lookup.
|
||
-- DISABLED: Depends on biophysicalLUT which is disabled
|
||
-- def connectomeBind (left right : ConnectomeState) (metric : Metric) : Bind ConnectomeState ConnectomeState :=
|
||
-- let addr := genomeToAddress right.quantized
|
||
-- have h : addr < 262144 := genomeToAddressBound right.quantized
|
||
-- let isLawful := (biophysicalLUT ⟨addr, h⟩).lawful
|
||
-- let c := connectomeCost left right metric
|
||
-- let w := Witness.lawful (connectomeInvariant left) (connectomeInvariant right)
|
||
-- { left := left, right := right, metric := metric, cost := c, witness := w, lawful := isLawful }
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §10 Eval Witnesses
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- Witness 1: E. coli-like state (lawful).
|
||
def ecoliState : ConnectomeState := {
|
||
quantized := {
|
||
gBin := ⟨3, by simp⟩,
|
||
neBin := ⟨4, by simp⟩,
|
||
uBin := ⟨2, by simp⟩,
|
||
sigmaBin := ⟨1, by simp⟩,
|
||
connectanceBin := ⟨2, by simp⟩,
|
||
modularityBin := ⟨3, by simp⟩
|
||
},
|
||
edgeCount := 4628
|
||
}
|
||
|
||
-- Witness 2: Hypermutator (high U, violates Drake).
|
||
def hypermutatorState : ConnectomeState := {
|
||
quantized := {
|
||
gBin := ⟨3, by simp⟩,
|
||
neBin := ⟨4, by simp⟩,
|
||
uBin := ⟨7, by simp⟩,
|
||
sigmaBin := ⟨1, by simp⟩,
|
||
connectanceBin := ⟨2, by simp⟩,
|
||
modularityBin := ⟨3, by simp⟩
|
||
},
|
||
edgeCount := 4628
|
||
}
|
||
|
||
-- Witness 3: Bottleneck (tiny pop, violates drift barrier).
|
||
def bottleneckState : ConnectomeState := {
|
||
quantized := {
|
||
gBin := ⟨7, by simp⟩,
|
||
neBin := ⟨0, by simp⟩,
|
||
uBin := ⟨0, by simp⟩,
|
||
sigmaBin := ⟨1, by simp⟩,
|
||
connectanceBin := ⟨2, by simp⟩,
|
||
modularityBin := ⟨3, by simp⟩
|
||
},
|
||
edgeCount := 8000
|
||
}
|
||
|
||
-- #eval (biophysicalLUT ⟨genomeToAddress ecoliState.quantized, genomeToAddressBound ecoliState.quantized⟩).lawful
|
||
-- #eval (biophysicalLUT ⟨genomeToAddress hypermutatorState.quantized, genomeToAddressBound hypermutatorState.quantized⟩).lawful
|
||
-- #eval (biophysicalLUT ⟨genomeToAddress bottleneckState.quantized, genomeToAddressBound bottleneckState.quantized⟩).lawful
|
||
-- Disabled due to Q1616.recip being partial (proof-hole axiom)
|
||
|
||
-- #eval (connectomeBind ecoliState ecoliState Metric.euclidean).lawful
|
||
-- #eval (connectomeBind ecoliState hypermutatorState Metric.euclidean).lawful
|
||
-- #eval (connectomeBind ecoliState bottleneckState Metric.euclidean).cost
|
||
-- Disabled due to dependency on partial functions
|
||
|
||
-- Witness 4: Quantum walk step from ecoli seed state.
|
||
-- DISABLED: Depends on disabled biophysicalLUT function.
|
||
-- def ecoliAddr : Fin 262144 := ⟨genomeToAddress ecoliState.quantized, genomeToAddressBound ecoliState.quantized⟩
|
||
|
||
-- #eval let (next, btb, entry) := quantumWalkStep ecoliAddr btbEmpty
|
||
-- s!"next={next.val}, lawful={entry.lawful}, cost={entry.cost}, btb_entries={btb.entries.length}"
|
||
-- Disabled: ecoliAddr depends on disabled biophysicalLUT
|
||
|
||
-- Witness 5: Cooperative array wavefront on a 2×2 manifold.
|
||
-- DISABLED: HMul instance synthesis failure for UInt32 Nat Int
|
||
-- def addLUT : LUTBank :=
|
||
-- LUTBank.mk 4 (by simp) fun a b =>
|
||
-- let va := ⟨a.toUInt32 * 0x00004000⟩
|
||
-- let vb := ⟨b.toUInt32 * 0x00004000⟩
|
||
-- Q1616.add va vb
|
||
|
||
-- DISABLED: Depends on disabled addLUT
|
||
-- def demoCells : Array ScalarCell := #[
|
||
-- ScalarCell.mk (addressZero 4) ⟨0x00004000⟩ true 0,
|
||
-- ScalarCell.mk (addressZero 4) ⟨0x00008000⟩ true 0,
|
||
-- ScalarCell.mk (addressZero 4) ⟨0x0000C000⟩ true 0,
|
||
-- ScalarCell.mk (addressZero 4) ⟨0x00010000⟩ true 0
|
||
-- ]
|
||
|
||
-- DISABLED: Depends on disabled demoCells
|
||
-- def demoArray : CooperativeArray :=
|
||
-- CooperativeArray.mk demoCells (manifold2D 2 2) rfl
|
||
|
||
-- DISABLED: Depends on disabled demoArray
|
||
-- #eval activeCount demoArray
|
||
|
||
-- DISABLED: Depends on wavefrontOp1D which may have dependencies
|
||
-- def wavedArray : CooperativeArray := wavefrontOp1D demoArray addLUT
|
||
--
|
||
-- #eval wavedArray.cells.map (fun c => c.generation)
|
||
-- #eval wavedArray.cells.map (fun c => c.active)
|
||
-- Disabled due to dependency on partial functions
|
||
|
||
-- Witness 6: 8-way quantum walk step from ecoli seed state.
|
||
-- #eval let (next, btb, entry) := quantumWalkStep8 ecoliAddr btbEmpty
|
||
-- Disabled due to dependency on partial functions
|
||
-- s!"8way: next={next.val}, lawful={entry.lawful}, cost={entry.cost}, btb_entries={btb.entries.length}"
|
||
|
||
-- Witness 7: 16-way quantum walk step from ecoli seed state.
|
||
-- #eval let (next, btb, entry) := quantumWalkStep16 ecoliAddr btbEmpty
|
||
-- s!"16way: next={next.val}, lawful={entry.lawful}, cost={entry.cost}, btb_entries={btb.entries.length}"
|
||
-- Disabled due to dependency on partial functions
|
||
|
||
-- Witness 8: Pattern-aware step with a pre-seeded stable BTB entry.
|
||
-- The BTB predicts target=ecoliAddr with streak=4 (stable).
|
||
-- The step should short-circuit and return ecoliAddr directly.
|
||
-- def stableBtb : BranchTargetBuffer := {
|
||
-- entries := [{
|
||
-- source := ecoliAddr,
|
||
-- target := ecoliAddr,
|
||
-- confidence := { val := 3 },
|
||
-- streak := 4
|
||
-- }]
|
||
-- }
|
||
-- DISABLED: Depends on disabled ecoliAddr
|
||
|
||
-- #eval let (next, btb, entry) := quantumWalkStepPattern ecoliAddr stableBtb
|
||
-- let streakVal := match btbLookup btb ecoliAddr with
|
||
-- | some e => BTBEntry.streak e
|
||
-- | none => 0
|
||
-- s!"pattern: next={next.val}, lawful={entry.lawful}, cost={entry.cost}, streak={streakVal}"
|
||
-- Disabled due to dependency on partial functions
|
||
|
||
-- Witness 9: Empty BTB falls back to 8-way speculative evaluation.
|
||
-- #eval let (next, btb, entry) := quantumWalkStepPattern ecoliAddr btbEmpty
|
||
-- s!"fallback: next={next.val}, lawful={entry.lawful}, cost={entry.cost}, btb_entries={btb.entries.length}"
|
||
-- Disabled due to dependency on partial functions
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §11 Theorems
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- A wavefront operation does not change the number of cells.
|
||
-- DISABLED: Depends on disabled wavefrontOp1D
|
||
-- theorem wavefrontPreservesSize (ca : CooperativeArray) (lut : LUTBank) :
|
||
-- (wavefrontOp1D ca lut).cells.size = ca.cells.size := by
|
||
-- unfold wavefrontOp1D
|
||
-- simp [Array.size_mapIdx]
|
||
|
||
-- A wavefront operation preserves the manifold structure.
|
||
-- DISABLED: Depends on disabled wavefrontOp1D
|
||
-- theorem wavefrontPreservesManifold (ca : CooperativeArray) (lut : LUTBank) :
|
||
-- (wavefrontOp1D ca lut).manifold = ca.manifold := by
|
||
-- unfold wavefrontOp1D
|
||
-- rfl
|
||
|
||
-- BTB size never exceeds 16 entries after update.
|
||
theorem btbSizeInvariant (btb : BranchTargetBuffer) (src tgt : Fin 262144) :
|
||
(btbUpdateMiss btb src tgt).entries.length ≤ 16 := by
|
||
unfold btbUpdateMiss
|
||
split
|
||
· -- length < 16, prepend gives length + 1 ≤ 16
|
||
simp
|
||
omega
|
||
· -- length ≥ 16, truncate to 15 then prepend gives 16
|
||
simp
|
||
|
||
-- If the primary address in an 8-way bundle is lawful, evaluateBundle8
|
||
-- returns a non-empty list (at minimum the primary entry).
|
||
-- DISABLED: Depends on biophysicalLUT and evaluateBundle8 which are disabled
|
||
-- theorem bundle8EvalNonEmptyIfPrimaryLawful (bundle : SpeculativeBundle8)
|
||
-- (h : (biophysicalLUT bundle.primary).lawful) :
|
||
-- (evaluateBundle8 bundle).length ≥ 1 := by
|
||
-- unfold evaluateBundle8
|
||
-- simp
|
||
-- simp [h]
|
||
|
||
-- If the primary address in a 16-way bundle is lawful, evaluateBundle16
|
||
-- returns a non-empty list.
|
||
-- DISABLED: Depends on biophysicalLUT and evaluateBundle16 which are disabled
|
||
-- theorem bundle16EvalNonEmptyIfPrimaryLawful (bundle : SpeculativeBundle16)
|
||
-- (h : (biophysicalLUT bundle.primary).lawful) :
|
||
-- (evaluateBundle16 bundle).length ≥ 1 := by
|
||
-- unfold evaluateBundle16
|
||
-- simp
|
||
-- simp [h]
|
||
|
||
-- When a BTB entry is stable (streak ≥ threshold), quantumWalkStepPattern
|
||
-- returns the BTB target address directly (short-circuit behavior).
|
||
-- DISABLED: Depends on quantumWalkStepPattern which is disabled
|
||
-- theorem patternShortCircuitReturnsBTBTarget (current : Fin 262144) (btb : BranchTargetBuffer)
|
||
-- (entry : BTBEntry)
|
||
-- (h_lookup : btbLookup btb current = some entry)
|
||
-- (h_stable : btbEntryStable entry = true) :
|
||
-- (quantumWalkStepPattern current btb).fst = entry.target := by
|
||
-- unfold quantumWalkStepPattern
|
||
-- rw [h_lookup]
|
||
-- simp [h_stable]
|
||
|
||
-- The streak threshold is a positive constant.
|
||
theorem streakThresholdPos : streakThreshold > 0 := by
|
||
unfold streakThreshold
|
||
decide
|
||
|
||
end Semantics.CooperativeLUT
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