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127 lines
4.4 KiB
Text
127 lines
4.4 KiB
Text
/-
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SLUQ.lean - SLUQ Decision Engine Formalization
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This module implements the SLUQ (Stability, Load, Quality) decision engine
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for dynamic system state evaluation. The engine uses a 16-bit accumulator
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and phi (phase) parameter to track system health and make allocation decisions.
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## State Machine:
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- Stable (00): acc < 0x4000 - Cool, reliable operation
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- Rising (01): 0x4000 ≤ acc < 0x8000 - Warming, monitor
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- Unstable (10): 0x8000 ≤ acc < 0xC000 - Overheating
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- Reset (11): acc ≥ 0xC000 - Snapped, requires reset
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## Mathematical Foundation:
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The accumulator represents a normalized 16-bit value where:
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- 0x0000 = 0.0 (minimum)
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- 0xFFFF = 1.0 (maximum)
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The phi parameter acts as a learning rate multiplier for state transitions.
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-/
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import Semantics.Bind
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namespace Semantics.SLUQ
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inductive SLUQState
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| Stable -- 00 : Cool, reliable
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| Rising -- 01 : Warming, monitor
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| Unstable -- 10 : Overheating
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| Reset -- 11 : Snapped
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deriving Repr, DecidableEq, Inhabited
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inductive CMYK
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| K
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| C
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| M
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| Y
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deriving Repr, DecidableEq, Inhabited
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structure SluqNode where
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acc : UInt16
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phi : UInt8
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selectionCount : UInt32
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deriving Repr, DecidableEq, Inhabited
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/-** Evaluate system state from accumulator value.
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Uses quadrant-based thresholds:
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- Stable: acc < 0x4000 (0.0 - 0.25)
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- Rising: 0x4000 ≤ acc < 0x8000 (0.25 - 0.5)
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- Unstable: 0x8000 ≤ acc < 0xC000 (0.5 - 0.75)
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- Reset: acc ≥ 0xC000 (0.75 - 1.0)
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Mathematical Expression:
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state(acc) =
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Stable if acc ∈ [0, 0x4000)
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Rising if acc ∈ [0x4000, 0x8000)
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Unstable if acc ∈ [0x8000, 0xC000)
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Reset if acc ∈ [0xC000, 0xFFFF]
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-/
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def evaluateState (acc : UInt16) : SLUQState :=
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if acc.toNat < 0x4000 then .Stable
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else if acc.toNat < 0x8000 then .Rising
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else if acc.toNat < 0xC000 then .Unstable
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else .Reset
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/-- Evaluate system state as integer (0-3) from accumulator value. -/
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def evaluateStateInt (acc : UInt16) : UInt8 :=
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if acc.toNat < 0x4000 then 0
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else if acc.toNat < 0x8000 then 1
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else if acc.toNat < 0xC000 then 2
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else 3
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/-** Update node state with new value.
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The accumulator increases by (value * phi).
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On Reset state, accumulator resets to 0 and selectionCount increments.
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Otherwise, accumulator updates and selectionCount increments.
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HIGH PRIORITY: Added overflow protection to prevent silent accumulator overflow.
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Mathematical Expression:
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newAcc = acc + (value × phi)
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If overflow occurs or state is Reset:
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acc = 0, selectionCount += 1
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Otherwise:
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acc = newAcc, selectionCount += 1
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-/
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def updateNode (node : SluqNode) (value : UInt8) : SluqNode :=
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let increase := value.toUInt16 * node.phi.toUInt16
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-- HIGH PRIORITY: Check for overflow before addition
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let newAcc := node.acc + increase
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let hasOverflow := node.acc.toNat + increase.toNat > 0xFFFF
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let state := evaluateState newAcc
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if hasOverflow || state == .Reset then
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{ node with acc := 0, selectionCount := node.selectionCount + 1 }
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else
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{ node with acc := newAcc, selectionCount := node.selectionCount + 1 }
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/-** Convert accumulator to Q16.16 fixed-point representation.
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Since max acc is 65535 (0xFFFF), we place acc in the fractional portion.
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Result: 0x0000 → 0x00000000, 0xFFFF → 0xFFFF0000 (~1.0 in Q16.16)
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CRITICAL FIX: Must shift left by 16 bits to place in fractional portion.
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Previous implementation was incorrect and caused 65536x numerical errors.
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-/
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def tempQ16 (acc : UInt16) : UInt32 :=
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-- Normalize to Q16.16 (65536 is 1.0)
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-- CRITICAL: Place 16-bit value in fractional portion via left shift
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-- 0xFFFF << 16 = 0xFFFF0000 (~1.0 in Q16.16)
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acc.toUInt32 << 16
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/-- Compute cost between two SLUQ nodes as absolute accumulator difference.
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The cost is the absolute difference in accumulator values, converted to Q16.16.
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This represents the distance between two system states in the SLUQ framework. -/
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def sluqCost (nodeA nodeB : SluqNode) (_metric : Metric) : Q16_16 :=
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let diff := if nodeB.acc > nodeA.acc then nodeB.acc - nodeA.acc else nodeA.acc - nodeB.acc
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Q16_16.ofNat diff.toNat
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/-- Invariant string for SLUQ node state. -/
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def sluqInvariant (node : SluqNode) : String :=
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let st := evaluateStateInt node.acc
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s!"state={st},acc={node.acc}"
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/-- Bind two SLUQ nodes using thermodynamic binding. -/
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def sluqBind (nodeA nodeB : SluqNode) (metric : Metric) : Bind SluqNode SluqNode :=
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thermodynamicBind nodeA nodeB metric sluqCost sluqInvariant sluqInvariant
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#eval updateNode { acc := 0x3FFF, phi := 10, selectionCount := 5 } 1
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end Semantics.SLUQ
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