mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
88 lines
2.3 KiB
Text
88 lines
2.3 KiB
Text
/-
|
|
Semantics/SLUG3.lean - Authoritative SLUG-3 Ternary Gate & Opcode Mapping
|
|
|
|
This module formalizes the 27 OISC opcodes derived from the SLUG-3 ternary
|
|
classification as specified in the N-Folded MMR Gossip EBML Schema.
|
|
|
|
Key mapping:
|
|
- Ternary: { -1, 0, 1 }
|
|
- Formula: k = 9*(y+1) + 3*(u+1) + (v+1)
|
|
- Range: [0, 26]
|
|
|
|
Lean is the source of truth.
|
|
-/
|
|
|
|
import Semantics.FixedPoint
|
|
|
|
namespace Semantics.SLUG3
|
|
|
|
open Semantics.Q16_16
|
|
|
|
/-- Binary-compatible 16-bit integer for operands -/
|
|
def OpVal := Q16_16
|
|
|
|
/-- SLUG-3 ternary states: -1 (Low), 0 (Mid), 1 (High) -/
|
|
inductive Ternary where
|
|
| low -- -1
|
|
| mid -- 0
|
|
| high -- 1
|
|
deriving DecidableEq, Repr, Inhabited
|
|
|
|
namespace Ternary
|
|
|
|
def toInt : Ternary → Int
|
|
| low => -1
|
|
| mid => 0
|
|
| high => 1
|
|
|
|
/-- Mapping to 0..2 for key calculation -/
|
|
def toIdx : Ternary → Nat
|
|
| low => 0
|
|
| mid => 1
|
|
| high => 2
|
|
|
|
end Ternary
|
|
|
|
/-- SLUG-3 Decision State (Y, U, V) -/
|
|
structure SLUG3State where
|
|
y : Ternary
|
|
u : Ternary
|
|
v : Ternary
|
|
deriving DecidableEq, Repr, Inhabited
|
|
|
|
namespace SLUG3State
|
|
|
|
/-- Authoritative key calculation: k = 9*(y+1) + 3*(u+1) + (v+1) -/
|
|
def key (s : SLUG3State) : Nat :=
|
|
9 * s.y.toIdx + 3 * s.u.toIdx + s.v.toIdx
|
|
|
|
end SLUG3State
|
|
|
|
/-- OISC Opcode Set (27 Instructions) -/
|
|
inductive OISCOp where
|
|
| nop | add | sub | mul | div
|
|
| min | max | abs | neg | shl
|
|
| shr | and | or | xor | eq
|
|
| lt | gt | load | store | jmp
|
|
| jz | jnz | call | ret | dup
|
|
| drop | halt
|
|
deriving DecidableEq, Repr, Inhabited
|
|
|
|
/-- Authoritative Decode Table (as per EBML Schema Section 3.1) -/
|
|
def decodeOp (k : Nat) : OISCOp :=
|
|
match k with
|
|
| 0 => .nop | 1 => .add | 2 => .sub | 3 => .mul
|
|
| 4 => .div | 5 => .min | 6 => .max | 7 => .abs
|
|
| 8 => .neg | 9 => .shl | 10 => .shr | 11 => .and
|
|
| 12 => .or | 13 => .xor | 14 => .eq | 15 => .lt
|
|
| 16 => .gt | 17 => .load | 18 => .store | 19 => .jmp
|
|
| 20 => .jz | 21 => .jnz | 22 => .call | 23 => .ret
|
|
| 24 => .dup | 25 => .drop | 26 => .halt | _ => .nop
|
|
|
|
/-- Entropy cost per operation in units of ln(2)
|
|
C_slug3 = log2(27) ≈ 4.755 bits
|
|
-/
|
|
def landauerCostBits : Q16_16 :=
|
|
Q16_16.ofFloat 4.755 -- log2(27) ≈ 4.755 bits in Q16.16 (placeholder)
|
|
|
|
end Semantics.SLUG3
|