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SilverSight/fortran/avm.f90
allaun 540236e617 feat(cartan-dna): Cartan-DNA bridge — derive spectral gap from encoder 
python/cartan_dna_bridge.py:
- Constructs 8×8 Cartan crossing matrix (block diagonal: 4×2 pairs)
- Each 2×2 block [273 256; 256 273] has eigenvalues {529, 17}
- σ = 273/1792 = 39/256 (normalized diagonal weight)
- τ = 256/1792 = 1/7 (normalized adjacent weight)
- ∆ = (273-256)/1792 = 17/1792 (difference)
- The min nonzero eigenvalue 17 IS the gap numerator

docs/cartan_dna_derivation.md:
- Step-by-step spec for modifying dna_codec.py
- Replace thermodynamic weights with Cartan weights
- Expected output and verification

All derived values match the Lean reference exactly.
The DNA encoder can now witness the spectral gap chain.
2026-06-30 20:06:38 -05:00

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Fortran
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! AVM ISA v1 — Fortran Port (Strict Functional Execution)
module avm
implicit none
! ── Constants ──────────────────────────────────────────────
integer, parameter :: AVM_CLAMP_MIN = -2147483647
integer, parameter :: AVM_CLAMP_MAX = 2147483647
integer, parameter :: AVM_Q0_MIN = -32767
integer, parameter :: AVM_Q0_MAX = 32767
integer, parameter :: Q16_SCALE = 65536
integer, parameter :: AVM_MAX_STACK = 1024
integer, parameter :: AVM_MAX_LOCALS = 256
! ── Types ──────────────────────────────────────────────────
integer, parameter :: TY_Q0 = 0, TY_Q16 = 1, TY_BOOL = 2
type :: AnyVal
integer :: ty = TY_Q0
integer :: i = 0
logical :: b = .false.
end type AnyVal
! ── Instruction encoding ───────────────────────────────────
integer, parameter :: OP_PUSH_Q16 = 0, OP_PUSH_BOOL = 1, OP_PUSH_Q0 = 2
integer, parameter :: OP_POP = 3, OP_DUP = 4, OP_SWAP = 5
integer, parameter :: OP_LOAD = 6, OP_STORE = 7
integer, parameter :: OP_JUMP = 8, OP_JUMP_IF = 9, OP_PRIM = 10, OP_HALT = 11
integer, parameter :: PRIM_ADD_Q0 = 0, PRIM_SUB_Q0 = 1
integer, parameter :: PRIM_ADD_Q16 = 2, PRIM_SUB_Q16 = 3
integer, parameter :: PRIM_MUL_Q16 = 4, PRIM_DIV_Q16 = 5
integer, parameter :: PRIM_LT_Q16 = 6, PRIM_EQ_Q16 = 7
integer, parameter :: PRIM_AND = 8, PRIM_OR = 9, PRIM_NOT = 10
type :: Instr
integer :: op = OP_HALT
integer :: arg = 0
logical :: arg2 = .false.
end type Instr
type :: State
integer :: pc = 0
type(AnyVal) :: stack(AVM_MAX_STACK)
integer :: sp = 0
type(AnyVal) :: locals(AVM_MAX_LOCALS)
logical :: local_set(AVM_MAX_LOCALS) = .false.
logical :: halted = .false.
end type State
contains
! ── Helpers ────────────────────────────────────────────────
function avm_clamp(x) result(r)
integer(kind=8), intent(in) :: x
integer :: r
if (x > AVM_CLAMP_MAX) then; r = AVM_CLAMP_MAX
else if (x < AVM_CLAMP_MIN) then; r = AVM_CLAMP_MIN
else; r = int(x); end if
end function avm_clamp
function avm_q0_clamp(x) result(r)
integer(kind=8), intent(in) :: x
integer :: r
if (x > AVM_Q0_MAX) then; r = AVM_Q0_MAX
else if (x < AVM_Q0_MIN) then; r = AVM_Q0_MIN
else; r = int(x); end if
end function avm_q0_clamp
function floor_div(a, b) result(r)
integer(kind=8), intent(in) :: a, b
integer :: r
integer(kind=8) :: q
q = a / b
if (mod(a, b) /= 0 .and. ieor(a, b) < 0) q = q - 1
r = int(q)
end function floor_div
function lt_q16_v6(a, b) result(r)
integer, intent(in) :: a, b
logical :: r
logical :: sa, sb
sa = a < 0; sb = b < 0
if (sa .neqv. sb) then; r = sa; else; r = a < b; end if
end function lt_q16_v6
! ── Primitive execution ────────────────────────────────────
function eval_prim(p, a, b) result(r)
integer, intent(in) :: p
type(AnyVal), intent(in) :: a, b
type(AnyVal) :: r
r%ty = TY_Q0; r%i = 0; r%b = .false.
if (p == PRIM_ADD_Q0) then
if (a%ty /= TY_Q0 .or. b%ty /= TY_Q0) return
r%ty = TY_Q0; r%i = avm_q0_clamp(int(a%i, 8) + int(b%i, 8))
else if (p == PRIM_SUB_Q0) then
if (a%ty /= TY_Q0 .or. b%ty /= TY_Q0) return
r%ty = TY_Q0; r%i = avm_q0_clamp(int(a%i, 8) - int(b%i, 8))
else if (p == PRIM_ADD_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16) return
r%ty = TY_Q16; r%i = avm_clamp(int(a%i, 8) + int(b%i, 8))
else if (p == PRIM_SUB_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16) return
r%ty = TY_Q16; r%i = avm_clamp(int(a%i, 8) - int(b%i, 8))
else if (p == PRIM_MUL_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16) return
r%ty = TY_Q16; r%i = avm_clamp(int(floor_div(int(a%i,8)*int(b%i,8), int(Q16_SCALE,8)), 8))
else if (p == PRIM_DIV_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16 .or. b%i == 0) return
r%ty = TY_Q16; r%i = avm_clamp(int(floor_div(int(a%i,8)*Q16_SCALE, int(b%i,8)), 8))
else if (p == PRIM_LT_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16) return
r%ty = TY_BOOL; r%b = lt_q16_v6(a%i, b%i)
else if (p == PRIM_EQ_Q16) then
if (a%ty /= TY_Q16 .or. b%ty /= TY_Q16) return
r%ty = TY_BOOL; r%b = (a%i == b%i)
else if (p == PRIM_AND) then
if (a%ty /= TY_BOOL .or. b%ty /= TY_BOOL) return
r%ty = TY_BOOL; r%b = a%b .and. b%b
else if (p == PRIM_OR) then
if (a%ty /= TY_BOOL .or. b%ty /= TY_BOOL) return
r%ty = TY_BOOL; r%b = a%b .or. b%b
else if (p == PRIM_NOT) then
if (a%ty /= TY_BOOL) return
r%ty = TY_BOOL; r%b = .not. a%b
end if
end function eval_prim
! ── Step ──────────────────────────────────────────────────
function step(s, prog, prog_len) result(err)
type(State), intent(inout) :: s
type(Instr), intent(in) :: prog(*)
integer, intent(in) :: prog_len
integer :: err, npc, arity
type(AnyVal) :: a, b, res
type(Instr) :: cur
err = 0
if (s%halted) then; err = -1; return; end if
if (s%pc < 0 .or. s%pc >= prog_len) then; s%halted = .true.; return; end if
cur = prog(s%pc + 1)
npc = s%pc + 1
! Stack depth check
if (cur%op <= OP_PUSH_Q0 .or. cur%op == OP_DUP .or. cur%op == OP_LOAD) then
if (s%sp >= AVM_MAX_STACK) then; err = -2; return; end if
end if
if (cur%op == OP_PUSH_Q16) then
s%sp = s%sp + 1; s%stack(s%sp)%ty = TY_Q16; s%stack(s%sp)%i = avm_clamp(int(cur%arg, 8))
else if (cur%op == OP_PUSH_BOOL) then
s%sp = s%sp + 1; s%stack(s%sp)%ty = TY_BOOL; s%stack(s%sp)%b = cur%arg2
else if (cur%op == OP_PUSH_Q0) then
s%sp = s%sp + 1; s%stack(s%sp)%ty = TY_Q0; s%stack(s%sp)%i = avm_q0_clamp(int(cur%arg, 8))
else if (cur%op == OP_POP) then
if (s%sp <= 0) then; err = -3; return; end if; s%sp = s%sp - 1
else if (cur%op == OP_DUP) then
if (s%sp <= 0) then; err = -3; return; end if
s%sp = s%sp + 1; s%stack(s%sp) = s%stack(s%sp - 1)
else if (cur%op == OP_SWAP) then
if (s%sp < 2) then; err = -4; return; end if
a = s%stack(s%sp); s%stack(s%sp) = s%stack(s%sp-1); s%stack(s%sp-1) = a
else if (cur%op == OP_LOAD) then
if (cur%arg < 0 .or. cur%arg >= AVM_MAX_LOCALS .or. .not. s%local_set(cur%arg+1)) then
err = -5; return
end if
s%sp = s%sp + 1; s%stack(s%sp) = s%locals(cur%arg+1)
else if (cur%op == OP_STORE) then
if (s%sp <= 0) then; err = -3; return; end if
if (cur%arg < 0 .or. cur%arg >= AVM_MAX_LOCALS) then; err = -5; return; end if
s%locals(cur%arg+1) = s%stack(s%sp); s%local_set(cur%arg+1) = .true.
s%sp = s%sp - 1
else if (cur%op == OP_JUMP) then
if (cur%arg < 0 .or. cur%arg >= prog_len) then; err = -6; return; end if
npc = cur%arg
else if (cur%op == OP_JUMP_IF) then
if (s%sp <= 0) then; err = -3; return; end if
a = s%stack(s%sp); s%sp = s%sp - 1
if (a%ty /= TY_BOOL) then; err = -7; return; end if
if (a%b) then
if (cur%arg < 0 .or. cur%arg >= prog_len) then; err = -6; return; end if
npc = cur%arg
end if
else if (cur%op == OP_PRIM) then
arity = 2; if (cur%arg == PRIM_NOT) arity = 1
if (s%sp < arity) then; err = -4; return; end if
if (arity >= 2) then; b = s%stack(s%sp); s%sp = s%sp - 1; end if
a = s%stack(s%sp); s%sp = s%sp - 1
res = eval_prim(cur%arg, a, b)
s%sp = s%sp + 1; s%stack(s%sp) = res
else if (cur%op == OP_HALT) then
s%halted = .true.
end if
s%pc = npc
end function step
end module avm
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