/-
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.DynamicCanal

namespace Semantics.SLUG3

open DynamicCanal

/-- Binary-compatible 16-bit integer for operands -/
def OpVal := Fix16

/-- 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 : Fix16 :=
  Fix16.mk 0x0004C160 -- log2(27) ≈ 4.755 bits in Q16.16 (placeholder)

end Semantics.SLUG3