import Mathlib.Data.Fin.Basic

namespace Semantics

/-- Genome18: 18-bit semantic micro-ISA for equation forest routing state.

Structure: 6 bins × 3 bits = 18 bits (8^6 = 262,144 states)

Bin meanings:
- muBin: mutation / drift bin (routing load)
- rhoBin: verification pressure bin (routing efficiency)
- cBin: connectance bin (geometry / route neighborhood)
- mBin: compression residue / modularity bin (entropy)
- neBin: observer mass / effective sample bin (entropy)
- sigmaBin: sigma / fitness proxy bin (entropy)

This represents the routing state class:
- Where this object is in the forest
- How risky it is
- How compressed it is
- How lawful it appears
- Which route moves are worth trying next

This is the FPGA LUT address layer.
-/
structure Genome18 where
  muBin    : Fin 8  -- mutation / drift (routing load)
  rhoBin   : Fin 8  -- verification pressure (routing efficiency)
  cBin     : Fin 8  -- connectance (geometry / route neighborhood)
  mBin     : Fin 8  -- compression residue / modularity (entropy)
  neBin    : Fin 8  -- observer mass / effective sample (entropy)
  sigmaBin : Fin 8  -- sigma / fitness proxy (entropy)

namespace Genome18

/-- Compute 18-bit address from Genome18 state.

Address calculation:
  addr = muBin * 32768 + rhoBin * 4096 + cBin * 512 + mBin * 64 + neBin * 8 + sigmaBin

This is the O(1) LUT route lookup address for FPGA routing.
-/
def addr (g : Genome18) : Nat :=
  g.muBin.val * 32768 +
  g.rhoBin.val * 4096 +
  g.cBin.val * 512 +
  g.mBin.val * 64 +
  g.neBin.val * 8 +
  g.sigmaBin.val

/-- Theorem: addr is injective (Theorem 5 - 18-bit injective encoding).

This proves that distinct Genome18 states map to distinct addresses,
which is required for correct LUT lookup.
-/
theorem addr_injective : Function.Injective addr := by
  intro g h h_eq
  cases g with
  | mk mu rho c m ne sigma =>
    cases h with
    | mk mu' rho' c' m' ne' sigma' =>
      simp only [addr] at h_eq
      have h1 : mu = mu' := by apply Fin.ext; omega
      have h2 : rho = rho' := by apply Fin.ext; omega
      have h3 : c = c' := by apply Fin.ext; omega
      have h4 : m = m' := by apply Fin.ext; omega
      have h5 : ne = ne' := by apply Fin.ext; omega
      have h6 : sigma = sigma' := by apply Fin.ext; omega
      simp [h1, h2, h3, h4, h5, h6]

/-- Theorem: addr values are in range [0, 262143].

This proves the address fits in 18 bits.
-/
theorem addr_range (g : Genome18) : g.addr < 262144 := by
  simp only [addr]
  have mu_bound : g.muBin.val ≤ 7 := Fin.is_le g.muBin
  have rho_bound : g.rhoBin.val ≤ 7 := Fin.is_le g.rhoBin
  have c_bound : g.cBin.val ≤ 7 := Fin.is_le g.cBin
  have m_bound : g.mBin.val ≤ 7 := Fin.is_le g.mBin
  have ne_bound : g.neBin.val ≤ 7 := Fin.is_le g.neBin
  have sigma_bound : g.sigmaBin.val ≤ 7 := Fin.is_le g.sigmaBin
  omega

/-- Default Genome18 state (all zeros). -/
def default : Genome18 :=
  { muBin := 0, rhoBin := 0, cBin := 0, mBin := 0, neBin := 0, sigmaBin := 0 }

end Genome18

end Semantics