!=====================================================================
! INVERTED AGDA LENS: Boolean Algebra → Spectral Flow → Lisp World Dump
! "Watch the sum 1 before it word forms"
!
! In the Jordan algebra of Hermitian matrices:
!   TRUE  = Identity I
!   FALSE = Zero 0
!   AND   = A ∘ B = ½(AB + BA)
!   OR    = A + B - A ∘ B
!   NOT   = I - A  (on effects [0,I])
!   XOR   = A + B - 2(A ∘ B)
!
! Boolean values = eigenvalues {0,1} on the frame
! "Sum 1" = Σ λᵢ = 1  (the trace constraint — watched at every step)
!
! Inverted lens:
!   Standard:  get : S → A,  set : S → A → S
!   Inverted:  observe the WHOLE (S = density) through the PART (A = eigenvalue)
!
! Lisp world dump: full state as S-expressions — a LISP MACHINE checkpoint
!
! Audit Spec: 4b565498-9afc-4782-af4a-c6b11a5d0058
!=====================================================================
module boolean_spectral_lens
  use, intrinsic :: iso_c_binding, only: c_int64_t, c_ptr, c_f_pointer, &
       c_size_t, c_loc, c_null_ptr, c_associated, c_char, c_null_char
  use, intrinsic :: iso_fortran_env, only: int64, real64, int8, error_unit
  use sov_monster_kernel, only: dp, ci, czero, &
       sov_blake3_hash_matrix, sov_bifrost_sign, &
       sov_is_hermitian_matrix, sov_is_density_matrix, sov_fault, &
       blake3_state, sov_blake3_init, sov_blake3_update, sov_blake3_finalize, &
       i8
  use spe_encoder, only: spe_frame_t, spe_encode, spe_decode, spe_verify_frame
  implicit none
  private

  !═══════════════════════════════════════════════════════════════════
  ! PUBLIC ABI
  !═══════════════════════════════════════════════════════════════════
  public :: boolean_to_spectral
  public :: spectral_to_boolean
  public :: watch_sum_one
  public :: lisp_world_dump_step
  public :: spectral_and
  public :: spectral_or
  public :: spectral_not
  public :: spectral_xor
  public :: inverted_lens_t

  !═══════════════════════════════════════════════════════════════════
  ! INVERTED LENS DESCRIPTOR
  !═══════════════════════════════════════════════════════════════════
  type, bind(C) :: inverted_lens_t
    integer(c_int64_t) :: rank
    type(c_ptr)        :: frame_ptr       ! spe_frame_t
    type(c_ptr)        :: density_ptr     ! complex(dp) [d,d]
    type(c_ptr)        :: eigenvalues_ptr ! real(dp) [r]  — sum = 1
    type(c_ptr)        :: lisp_output_ptr ! char buffer for world dump
    integer(c_int64_t) :: lisp_buffer_size
    integer(c_int64_t) :: step            ! current step counter
  end type

contains

  !═══════════════════════════════════════════════════════════════════
  ! 1. BOOLEAN → SPECTRAL
  !    Maps bool vector to eigenvalues (sum=1) then reconstructs density
  !═══════════════════════════════════════════════════════════════════
  subroutine boolean_to_spectral(bool_ptr, bool_len, frame, eigenvalues_ptr, density_ptr, plasma_ok) &
       bind(C, name="boolean_to_spectral")
    type(c_ptr),        intent(in),  value :: bool_ptr
    integer(c_size_t),  intent(in),  value :: bool_len
    type(spe_frame_t),  intent(in)         :: frame
    type(c_ptr),        intent(in),  value :: eigenvalues_ptr, density_ptr
    integer(c_int64_t), intent(out)        :: plasma_ok
    integer(c_int64_t) :: r, d, i, j, k
    integer(c_int64_t), pointer :: bool_vec(:)
    real(dp),    pointer :: eigenvalues(:)
    complex(dp), pointer :: density(:,:), frame_arr(:,:,:)
    real(dp) :: s
        complex(dp) :: acc


    r = frame%rank; d = frame%dim
    call c_f_pointer(bool_ptr,       bool_vec,    [int(bool_len)])
    call c_f_pointer(eigenvalues_ptr,eigenvalues, [r])
    call c_f_pointer(density_ptr,    density,     [d, d])
    call c_f_pointer(frame%frame_ptr,frame_arr,   [r, d, d])

    ! Map: TRUE→1, FALSE→ε, then normalize to sum=1
    do i = 1, r
      if (i <= int(bool_len) .and. bool_vec(i) /= 0) then
        eigenvalues(i) = 1.0_dp
      else
        eigenvalues(i) = 10.0_dp * epsilon(0.0_dp)
      end if
    end do
    s = sum(eigenvalues); eigenvalues = eigenvalues / s

    ! ρ = Σ λᵢ ψᵢ
    density = czero
    !$omp parallel do collapse(2) default(none) shared(density,frame_arr,eigenvalues,r,d) private(i,j,k)
    do j = 1, d
      do k = 1, d
    acc = czero
        do i = 1, r; acc = acc + eigenvalues(i)*frame_arr(i,j,k); end do
        density(j,k) = acc
      end do
    end do
    !$omp end parallel do

    plasma_ok = 0
    if (sov_is_density_matrix(density, d)) plasma_ok = 1
    if (plasma_ok == 0) call sov_fault(501)
  end subroutine

  !═══════════════════════════════════════════════════════════════════
  ! 2. SPECTRAL → BOOLEAN  (threshold measurement — "word forms" here)
  !═══════════════════════════════════════════════════════════════════
  subroutine spectral_to_boolean(eigenvalues_ptr, rank, threshold, bool_out_ptr) &
       bind(C, name="spectral_to_boolean")
    type(c_ptr),        intent(in),  value :: eigenvalues_ptr, bool_out_ptr
    integer(c_int64_t), intent(in),  value :: rank
    real(dp),           intent(in),  value :: threshold
    real(dp),           pointer :: eigenvalues(:)
    integer(c_int64_t), pointer :: bool_out(:)
    integer(c_int64_t) :: i


    call c_f_pointer(eigenvalues_ptr, eigenvalues, [rank])
    call c_f_pointer(bool_out_ptr,    bool_out,    [rank])
    do i = 1, rank
      if (eigenvalues(i) > threshold) then
        bool_out(i) = 1
      else
        bool_out(i) = 0
      end if
    end do
  end subroutine

  !═══════════════════════════════════════════════════════════════════
  ! 3. JORDAN BOOLEAN OPS ON EIGENVALUES
  !    These operate BEFORE word formation — on the continuous eigenvalues
  !═══════════════════════════════════════════════════════════════════

  ! AND: A ∘ B  → pointwise product then normalize
  subroutine spectral_and(a_ptr, b_ptr, r, out_ptr) &
       bind(C, name="spectral_and")
    type(c_ptr),        intent(in),  value :: a_ptr, b_ptr, out_ptr
    integer(c_int64_t), intent(in),  value :: r
    real(dp), pointer :: a(:), b(:), out(:)
    call c_f_pointer(a_ptr, a, [r])
    call c_f_pointer(b_ptr, b, [r])
    call c_f_pointer(out_ptr, out, [r])
    out = a * b
    out = out / max(sum(out), epsilon(0.0_dp))
  end subroutine

  ! OR: A + B - A ∘ B  → clamp to [0,1] then normalize
  subroutine spectral_or(a_ptr, b_ptr, r, out_ptr) &
       bind(C, name="spectral_or")
    type(c_ptr),        intent(in),  value :: a_ptr, b_ptr, out_ptr
    integer(c_int64_t), intent(in),  value :: r
    real(dp), pointer :: a(:), b(:), out(:)
    call c_f_pointer(a_ptr, a, [r])
    call c_f_pointer(b_ptr, b, [r])
    call c_f_pointer(out_ptr, out, [r])
    out = a + b - a*b
    out = max(out, 0.0_dp)
    out = out / max(sum(out), epsilon(0.0_dp))
  end subroutine

  ! NOT: I - A  → (1/r - λᵢ) normalized (on effects)
  subroutine spectral_not(a_ptr, r, out_ptr) &
       bind(C, name="spectral_not")
    type(c_ptr),        intent(in),  value :: a_ptr, out_ptr
    integer(c_int64_t), intent(in),  value :: r
    real(dp), pointer :: a(:), out(:)
    call c_f_pointer(a_ptr, a, [r])
    call c_f_pointer(out_ptr, out, [r])
    out = 1.0_dp/real(r,dp) - a + 1.0_dp/real(r,dp)  ! shift above zero
    out = max(out, 10.0_dp*epsilon(0.0_dp))
    out = out / sum(out)
  end subroutine

  ! XOR: A + B - 2(A ∘ B)
  subroutine spectral_xor(a_ptr, b_ptr, r, out_ptr) &
       bind(C, name="spectral_xor")
    type(c_ptr),        intent(in),  value :: a_ptr, b_ptr, out_ptr
    integer(c_int64_t), intent(in),  value :: r
    real(dp), pointer :: a(:), b(:), out(:)
    call c_f_pointer(a_ptr, a, [r])
    call c_f_pointer(b_ptr, b, [r])
    call c_f_pointer(out_ptr, out, [r])
    out = a + b - 2.0_dp*a*b
    out = max(out, 10.0_dp*epsilon(0.0_dp))
    out = out / sum(out)
  end subroutine

  !═══════════════════════════════════════════════════════════════════
  ! 4. WATCH THE SUM 1 — core inverted lens observer
  !    Runs max_steps of spectral evolution, watching trace at each step
  !    Writes Lisp world dump to lens buffer after each step
  !═══════════════════════════════════════════════════════════════════
  subroutine watch_sum_one(lens, max_steps, sk_ptr, plasma_ok) &
       bind(C, name="watch_sum_one")
    type(inverted_lens_t), intent(inout) :: lens
    integer(c_int64_t),    intent(in),   value :: max_steps
    type(c_ptr),           intent(in),   value :: sk_ptr
    integer(c_int64_t),    intent(out)   :: plasma_ok
    integer(c_int64_t) :: r, d, step, i
    real(dp),    pointer :: eigenvalues(:)
    complex(dp), pointer :: density(:,:)
    type(spe_frame_t), pointer :: frame
    real(dp) :: trace_sum, trace_err


    r = lens%rank
    d = r
    call c_f_pointer(lens%eigenvalues_ptr, eigenvalues, [r])
    call c_f_pointer(lens%density_ptr,     density,     [d, d])
    call c_f_pointer(lens%frame_ptr,       frame)

    plasma_ok = 1

    do step = 1, max_steps
      lens%step = step

      ! WATCH: verify trace at each step — this is the lens observation
      trace_sum = sum(eigenvalues)
      trace_err = abs(trace_sum - 1.0_dp)
      if (trace_err > 100.0_dp * epsilon(0.0_dp) * r) then
        plasma_ok = 0
        call sov_fault(601)  ! Trace violation — sum 1 broken
      end if

      ! Verify density is still valid
      if (.not. sov_is_density_matrix(density, d)) then
        plasma_ok = 0
        call sov_fault(602)
      end if

      ! Write Lisp world dump for this step
      call lisp_world_dump_step(lens, step, eigenvalues, density, trace_sum)
    end do
  end subroutine

  !═══════════════════════════════════════════════════════════════════
  ! 5. LISP WORLD DUMP — full state as S-expression
  !    This is the "world dump" for the LISP MACHINE checkpoint
  !    Format: (world-state :step N :trace T :eigenvalues (λ₁ λ₂ ...) :density ...)
  !═══════════════════════════════════════════════════════════════════
  subroutine lisp_world_dump_step(lens, step, eigenvalues, density, trace_sum) &
       bind(C, name="lisp_world_dump_step")
    type(inverted_lens_t), intent(in)        :: lens
    integer(c_int64_t),    intent(in), value :: step
    real(dp),              intent(in)        :: eigenvalues(lens%rank)
    complex(dp),           intent(in)        :: density(lens%rank, lens%rank)
    real(dp),              intent(in), value :: trace_sum
    character(len=:), allocatable :: sexpr
    character(len=32) :: step_str, trace_str, eig_str
    integer(c_int64_t) :: i, r
    character(c_char), pointer :: buf(:)
    integer :: slen


    r = lens%rank
    if (.not. c_associated(lens%lisp_output_ptr)) return

    ! Build S-expression
    write(step_str,  '(I0)') step
    write(trace_str, '(F12.9)') trace_sum

    sexpr = '(world-state :step ' // trim(step_str) // &
            ' :trace ' // trim(trace_str) // &
            ' :trace-ok ' // merge('#t', '#f', abs(trace_sum-1.0_dp) < 1e-10_dp) // &
            ' :eigenvalues ('

    do i = 1, r
      write(eig_str, '(F12.9)') eigenvalues(i)
      sexpr = sexpr // trim(eig_str)
      if (i < r) sexpr = sexpr // ' '
    end do
    sexpr = sexpr // '))'

    ! Write to buffer
    slen = min(len(sexpr), int(lens%lisp_buffer_size) - 1)
    call c_f_pointer(lens%lisp_output_ptr, buf, [lens%lisp_buffer_size])
    do i = 1, slen
      buf(i) = sexpr(i:i)
    end do
    buf(slen+1) = c_null_char
  end subroutine

end module boolean_spectral_lens