LLM-as-Computer: Compiled Transformer Stack Machine

A working computer built from transformer primitives. Every instruction fetch and stack read is a parabolic attention head (dot-product → argmax → value extraction). The transformer's weights ARE the interpreter — compiled analytically, not trained.

What This Proves

Attention is lookup; feed-forward is routing. A vanilla transformer with compiled weights can execute arbitrary programs: loops, recursion, arithmetic, memory access. 55 opcodes covering WASM i32 semantics. 21M+ steps/second via the Mojo executor.

Setup (once per session)

cd /mnt/skills/user/llm-as-computer/src && bash setup.sh

This installs Mojo (~20s) and compiles the executor binary (~6s). If Mojo is unavailable, the skill falls back to a pure-Python executor (slower but functional).

Usage

import sys
sys.path.insert(0, '/mnt/skills/user/llm-as-computer/src')

from programs import make_fibonacci, make_factorial, make_gcd, make_multiply
from runner import run, setup

# Ensure Mojo is compiled (idempotent)
setup()

# Run a program — shows instructions, trace, result
prog, expected = make_fibonacci(10)
print(run(prog))

# Benchmark mode — measures throughput
print(run(prog, benchmark=True, repeat=200))

Available Programs

From programs.py — all return (program, expected_result):

Generator	Description	Example
make_fibonacci(n)	Iterative fib via SWAP+OVER+ADD+ROT	fib(10)=55, 111 steps
make_multiply(a, b)	Repeated addition	mul(7,8)=56
make_factorial(n)	Loop with MUL	fact(8)=40320
make_gcd(a, b)	Euclidean algorithm	gcd(48,18)=6
make_power_of_2(n)	Repeated doubling	2^7=128
make_sum_1_to_n(n)	Accumulation loop	sum(15)=120
make_is_even(n)	Parity check	is_even(7)=0
make_native_multiply(a,b)	Single MUL opcode
make_native_divmod(a,b)	DIV_S + REM_S
make_compare_binary(op,a,b)	eq/ne/lt_s/gt_s/le_s/ge_s
make_bitwise_binary(op,a,b)	and/or/xor/shl/shr_u/rotl/rotr
make_select(a,b,c)	Conditional select

Writing Custom Programs

from isa_lite import program

# Assembly tuples
prog = program(
    ('PUSH', 10),
    ('PUSH', 20),
    ('ADD',),
    ('DUP',),
    ('ADD',),  # (10+20)*2 = 60
    ('HALT',),
)
print(run(prog))

# Loops: countdown from 5
prog = program(
    ('PUSH', 5),    # 0: counter
    ('PUSH', 1),    # 1: decrement
    ('SUB',),       # 2: counter - 1
    ('DUP',),       # 3: copy for JNZ test
    ('JNZ', 1),     # 4: loop if non-zero
    ('HALT',),      # 5: done, top = 0
)
print(run(prog))

ISA Reference (55 opcodes)

Stack: PUSH n, POP, DUP, SWAP, OVER, ROT Arithmetic: ADD, SUB, MUL, DIV_S, DIV_U, REM_S, REM_U Comparison: EQZ, EQ, NE, LT_S/U, GT_S/U, LE_S/U, GE_S/U Bitwise: AND, OR, XOR, SHL, SHR_S/U, ROTL, ROTR Unary: CLZ, CTZ, POPCNT, ABS, NEG, SELECT Control: JZ addr, JNZ addr, CALL addr, RETURN, HALT, NOP Locals: LOCAL.GET idx, LOCAL.SET idx, LOCAL.TEE idx Memory: I32.LOAD, I32.STORE, I32.LOAD8_U/S, I32.LOAD16_U/S, I32.STORE8, I32.STORE16

All arithmetic is 32-bit signed with WASM i32 semantics (wrap on overflow).

Architecture

The key insight: parabolic encoding k = (2j, -j²) makes dot-product attention peak sharply at a target position. Same encoding addresses program memory, stack, locals, and heap without interference. Each attention head is a compiled W_Q @ state → query, W_K @ memory → keys, scores = K @ q, output = V[argmax(scores)].

Updating from Repo

To pull latest source from the repository:

cd /mnt/skills/user/llm-as-computer/src
GH_TOKEN=$(grep GH_TOKEN /mnt/project/GitHub.env 2>/dev/null | cut -d= -f2)
for f in executor.mojo; do
  curl -sL -H "Authorization: token $GH_TOKEN" -H "Accept: application/vnd.github.v3.raw" \
    "https://api.github.com/repos/oaustegard/llm-as-computer/contents/src/$f?ref=main" > $f
done
for f in isa_lite.py programs.py runner.py; do
  curl -sL -H "Authorization: token $GH_TOKEN" -H "Accept: application/vnd.github.v3.raw" \
    "https://api.github.com/repos/oaustegard/llm-as-computer/contents/skill/src/$f?ref=main" > $f
done
rm -f percepta_exec  # force recompile
bash setup.sh