Datasets:

turtlecannon
/

bf-rasp-minimal-13

"""bf-rasp v0: a compact RASP variant written as stack (postfix) strings. Language reference: README.md.
A program is a string over ALPHABET. Reading left to right, each symbol pops its inputs from a stack of columns
(one value per position, bytes mod 256) and pushes its result. A valid program type-checks and leaves exactly one
column; at each position its value is the next token. Generation starts from the single token 0 and has no input.
This module holds the language definition and three evaluators that must agree:
  evaluate     reference: whole columns from the definitions, plain lists, O(n^2) attention; obviously correct
  generate     incremental: one position at a time with running state, O(length) per token (used for outputs)
  evaluate_np  numpy over a batch of sequences (used by the enumerator to fingerprint columns)
"""
import numpy as np

ALPHABET = "T0123+-%=<!&?CPMDS"      # also the (length, lexicographic) order of programs
NUM, BOOL = "N", "B"                 # a boolean is a number that is 0 or 1; it can be used wherever a number can
ATTENTION = frozenset("CPM")
ARITY = {**{s: 0 for s in "T0123"}, **{s: 1 for s in "!CP"}, **{s: 2 for s in "+-%=<&"}, **{s: 3 for s in "?M"}}


def result_type(sym, arg_types):
    """Type of sym applied to arg_types (in push order), or None when the types do not fit."""
    if sym == "T" or sym in "23":
        return NUM
    if sym in "01":
        return BOOL
    if sym in "+-%":
        return NUM
    if sym in "=<":
        return BOOL
    if sym in "!&":
        return BOOL if all(t == BOOL for t in arg_types) else None
    if sym == "?":
        c, a, b = arg_types
        if c != BOOL:
            return None
        return BOOL if a == b == BOOL else NUM
    if sym == "C":
        return NUM if arg_types[0] == BOOL else None
    if sym == "P":
        return arg_types[0]
    if sym == "M":
        return arg_types[2]
    raise ValueError(sym)


def compile_program(prog):
    """Program string -> (nodes, types, top). nodes[i] = (symbol, input node indices in push order); D and S only
    rewire the stack and make no node. Raises ValueError for an invalid program."""
    nodes, types, stack = [], [], []
    for pos, s in enumerate(prog):
        if s == "D":
            if not stack:
                raise ValueError(f"D on an empty stack at {pos}")
            stack.append(stack[-1])
        elif s == "S":
            if len(stack) < 2:
                raise ValueError(f"S needs two columns at {pos}")
            stack[-1], stack[-2] = stack[-2], stack[-1]
        elif s in ARITY:
            k = ARITY[s]
            if len(stack) < k:
                raise ValueError(f"{s} needs {k} columns at {pos}")
            args = tuple(stack[len(stack) - k:]) if k else ()
            del stack[len(stack) - k:]
            t = result_type(s, [types[a] for a in args])
            if t is None:
                raise ValueError(f"{s} has the wrong input types at {pos}")
            nodes.append((s, args)); types.append(t); stack.append(len(nodes) - 1)
        else:
            raise ValueError(f"unknown symbol {s!r} at {pos}")
    if len(stack) != 1:
        raise ValueError(f"program leaves {len(stack)} columns")
    return nodes, types, stack[0]


def is_valid(prog):
    try:
        compile_program(prog)
        return True
    except ValueError:
        return False


def measures(prog):
    """length; depth = most attention symbols on any path to the output (transformer layers); n_attn = attention
    symbols; width = most attention symbols at one depth (heads per layer)."""
    nodes, _, top = compile_program(prog)
    depth = []
    for s, args in nodes:
        d = max((depth[a] for a in args), default=0)
        depth.append(d + (s in ATTENTION))
    per_layer = {}
    for (s, _), d in zip(nodes, depth):
        if s in ATTENTION:
            per_layer[d] = per_layer.get(d, 0) + 1
    return {"length": len(prog), "depth": depth[top], "n_attn": sum(per_layer.values()),
            "width": max(per_layer.values(), default=0)}


# ---------------------------------------------------------------- reference evaluator (definitions, plain lists)

def evaluate(prog, seq):
    """Output column (one value per position) of prog on the token sequence seq."""
    nodes, _, top = compile_program(prog)
    n, cols = len(seq), []
    for s, args in nodes:
        x = [cols[a] for a in args]
        if s == "T":
            c = [int(v) % 256 for v in seq]
        elif s in "0123":
            c = [int(s)] * n
        elif s == "+":
            c = [(a + b) % 256 for a, b in zip(*x)]
        elif s == "-":
            c = [(a - b) % 256 for a, b in zip(*x)]
        elif s == "%":
            c = [a % b if b else a for a, b in zip(*x)]
        elif s == "=":
            c = [int(a == b) for a, b in zip(*x)]
        elif s == "<":
            c = [int(a < b) for a, b in zip(*x)]
        elif s == "!":
            c = [1 - a for a in x[0]]
        elif s == "&":
            c = [a & b for a, b in zip(*x)]
        elif s == "?":
            c = [a if t else b for t, a, b in zip(*x)]
        elif s == "C":                        # count of k <= q where b[k] is true
            c = [sum(x[0][:q + 1]) % 256 for q in range(n)]
        elif s == "P":                        # value one position back; 0 at position 0
            c = [0] + x[0][:-1]
        elif s == "M":                        # V at the latest k < q with K[k] = Q[q]; 0 if there is none
            K, Q, V = x
            c = []
            for q in range(n):
                v = 0
                for k in range(q):
                    if K[k] == Q[q]:
                        v = V[k]
                c.append(v)
        cols.append(c)
    return cols[top]


def generate_reference(prog, T):
    """The first T generated tokens, re-evaluating the whole sequence at every step (slow; for tests)."""
    seq = [0]
    for _ in range(T):
        seq.append(evaluate(prog, seq)[-1])
    return seq[1:]


def produces(prog, y):
    """Teacher forcing: prog generates y (as its first len(y) tokens) iff its column on 0, y[:-1] equals y."""
    return evaluate(prog, [0] + list(y[:-1])) == list(y)


# ---------------------------------------------------------------- incremental generator

def generate(prog, T):
    """The first T generated tokens, as bytes. Keeps per-node running state: a count for C, the previous input
    value for P, and for M a table from key to the value at its latest position (updated after the lookup, so only
    k < q are visible)."""
    nodes, _, top = compile_program(prog)
    state = [0 if s in "CP" else ({} if s == "M" else None) for s, _ in nodes]
    out, x, v = bytearray(), 0, [0] * len(nodes)
    for _ in range(T):
        for i, (s, args) in enumerate(nodes):
            if s == "T":
                r = x
            elif s in "0123":
                r = ord(s) - 48
            elif s == "+":
                r = (v[args[0]] + v[args[1]]) & 255
            elif s == "-":
                r = (v[args[0]] - v[args[1]]) & 255
            elif s == "%":
                b = v[args[1]]
                r = v[args[0]] % b if b else v[args[0]]
            elif s == "=":
                r = int(v[args[0]] == v[args[1]])
            elif s == "<":
                r = int(v[args[0]] < v[args[1]])
            elif s == "!":
                r = 1 - v[args[0]]
            elif s == "&":
                r = v[args[0]] & v[args[1]]
            elif s == "?":
                r = v[args[1]] if v[args[0]] else v[args[2]]
            elif s == "C":
                r = state[i] = (state[i] + v[args[0]]) & 255
            elif s == "P":
                r = state[i]; state[i] = v[args[0]]
            else:                              # M
                table = state[i]
                r = table.get(v[args[1]], 0)
                table[v[args[0]]] = v[args[2]]
            v[i] = r
        x = v[top]
        out.append(x)
    return bytes(out)


# ---------------------------------------------------------------- numpy evaluator over a batch of sequences

def apply_np(sym, args, seqs):
    """Column of sym on numpy uint8 input columns args (each [batch, n]); seqs is the token batch (for T)."""
    shape = seqs.shape
    if sym == "T":
        return seqs
    if sym in "0123":
        return np.full(shape, int(sym), np.uint8)
    if sym == "+":
        return args[0] + args[1]                       # uint8 arithmetic wraps mod 256
    if sym == "-":
        return args[0] - args[1]
    if sym == "%":
        a, b = args
        return np.where(b == 0, a, a % np.maximum(b, 1)).astype(np.uint8)
    if sym == "=":
        return (args[0] == args[1]).astype(np.uint8)
    if sym == "<":
        return (args[0] < args[1]).astype(np.uint8)
    if sym == "!":
        return 1 - args[0]
    if sym == "&":
        return args[0] & args[1]
    if sym == "?":
        return np.where(args[0] != 0, args[1], args[2])
    if sym == "C":
        return (np.cumsum(args[0], axis=1, dtype=np.int64) & 255).astype(np.uint8)
    if sym == "P":
        out = np.zeros(shape, np.uint8)
        out[:, 1:] = args[0][:, :-1]
        return out
    if sym == "M":
        # Sort the keys by (row, value, position); a query (row, Q[q], q) lands just after the latest k < q with the
        # same row and value, if there is one. O(n log n) per row, so long sequences are fine.
        K, Q, V = args
        b, n = shape
        base = (np.arange(b, dtype=np.int64)[:, None] * 256 * n)
        pos = np.arange(n, dtype=np.int64)[None, :]
        keys = (base + K.astype(np.int64) * n + pos).ravel()
        order = np.argsort(keys, kind="stable")
        sk = keys[order]
        queries = (base + Q.astype(np.int64) * n + pos).ravel()
        j = np.searchsorted(sk, queries, side="left") - 1          # last key strictly below the query
        jj = np.maximum(j, 0)
        hit = (j >= 0) & (sk[jj] // n == queries // n)              # same row and value, and position < q
        return np.where(hit, V.ravel()[order[jj]], 0).reshape(shape).astype(np.uint8)
    raise ValueError(sym)


def evaluate_np(prog, seqs):
    nodes, _, top = compile_program(prog)
    cols = []
    for s, args in nodes:
        cols.append(apply_np(s, [cols[a] for a in args], seqs))
    return cols[top]

	"""bf-rasp v0: a compact RASP variant written as stack (postfix) strings. Language reference: README.md.

	A program is a string over ALPHABET. Reading left to right, each symbol pops its inputs from a stack of columns
	(one value per position, bytes mod 256) and pushes its result. A valid program type-checks and leaves exactly one
	column; at each position its value is the next token. Generation starts from the single token 0 and has no input.

	This module holds the language definition and three evaluators that must agree:
	evaluate reference: whole columns from the definitions, plain lists, O(n^2) attention; obviously correct
	generate incremental: one position at a time with running state, O(length) per token (used for outputs)
	evaluate_np numpy over a batch of sequences (used by the enumerator to fingerprint columns)
	"""
	import numpy as np

	ALPHABET = "T0123+-%=<!&?CPMDS" # also the (length, lexicographic) order of programs
	NUM, BOOL = "N", "B" # a boolean is a number that is 0 or 1; it can be used wherever a number can
	ATTENTION = frozenset("CPM")
	ARITY = {{s: 0 for s in "T0123"}, {s: 1 for s in "!CP"}, {s: 2 for s in "+-%=<&"}, {s: 3 for s in "?M"}}


	def result_type(sym, arg_types):
	"""Type of sym applied to arg_types (in push order), or None when the types do not fit."""
	if sym == "T" or sym in "23":
	return NUM
	if sym in "01":
	return BOOL
	if sym in "+-%":
	return NUM
	if sym in "=<":
	return BOOL
	if sym in "!&":
	return BOOL if all(t == BOOL for t in arg_types) else None
	if sym == "?":
	c, a, b = arg_types
	if c != BOOL:
	return None
	return BOOL if a == b == BOOL else NUM
	if sym == "C":
	return NUM if arg_types[0] == BOOL else None
	if sym == "P":
	return arg_types[0]
	if sym == "M":
	return arg_types[2]
	raise ValueError(sym)


	def compile_program(prog):
	"""Program string -> (nodes, types, top). nodes[i] = (symbol, input node indices in push order); D and S only
	rewire the stack and make no node. Raises ValueError for an invalid program."""
	nodes, types, stack = [], [], []
	for pos, s in enumerate(prog):
	if s == "D":
	if not stack:
	raise ValueError(f"D on an empty stack at {pos}")
	stack.append(stack[-1])
	elif s == "S":
	if len(stack) < 2:
	raise ValueError(f"S needs two columns at {pos}")
	stack[-1], stack[-2] = stack[-2], stack[-1]
	elif s in ARITY:
	k = ARITY[s]
	if len(stack) < k:
	raise ValueError(f"{s} needs {k} columns at {pos}")
	args = tuple(stack[len(stack) - k:]) if k else ()
	del stack[len(stack) - k:]
	t = result_type(s, [types[a] for a in args])
	if t is None:
	raise ValueError(f"{s} has the wrong input types at {pos}")
	nodes.append((s, args)); types.append(t); stack.append(len(nodes) - 1)
	else:
	raise ValueError(f"unknown symbol {s!r} at {pos}")
	if len(stack) != 1:
	raise ValueError(f"program leaves {len(stack)} columns")
	return nodes, types, stack[0]


	def is_valid(prog):
	try:
	compile_program(prog)
	return True
	except ValueError:
	return False


	def measures(prog):
	"""length; depth = most attention symbols on any path to the output (transformer layers); n_attn = attention
	symbols; width = most attention symbols at one depth (heads per layer)."""
	nodes, _, top = compile_program(prog)
	depth = []
	for s, args in nodes:
	d = max((depth[a] for a in args), default=0)
	depth.append(d + (s in ATTENTION))
	per_layer = {}
	for (s, _), d in zip(nodes, depth):
	if s in ATTENTION:
	per_layer[d] = per_layer.get(d, 0) + 1
	return {"length": len(prog), "depth": depth[top], "n_attn": sum(per_layer.values()),
	"width": max(per_layer.values(), default=0)}


	# ---------------------------------------------------------------- reference evaluator (definitions, plain lists)

	def evaluate(prog, seq):
	"""Output column (one value per position) of prog on the token sequence seq."""
	nodes, _, top = compile_program(prog)
	n, cols = len(seq), []
	for s, args in nodes:
	x = [cols[a] for a in args]
	if s == "T":
	c = [int(v) % 256 for v in seq]
	elif s in "0123":
	c = [int(s)] * n
	elif s == "+":
	c = [(a + b) % 256 for a, b in zip(*x)]
	elif s == "-":
	c = [(a - b) % 256 for a, b in zip(*x)]
	elif s == "%":
	c = [a % b if b else a for a, b in zip(*x)]
	elif s == "=":
	c = [int(a == b) for a, b in zip(*x)]
	elif s == "<":
	c = [int(a < b) for a, b in zip(*x)]
	elif s == "!":
	c = [1 - a for a in x[0]]
	elif s == "&":
	c = [a & b for a, b in zip(*x)]
	elif s == "?":
	c = [a if t else b for t, a, b in zip(*x)]
	elif s == "C": # count of k <= q where b[k] is true
	c = [sum(x[0][:q + 1]) % 256 for q in range(n)]
	elif s == "P": # value one position back; 0 at position 0
	c = [0] + x[0][:-1]
	elif s == "M": # V at the latest k < q with K[k] = Q[q]; 0 if there is none
	K, Q, V = x
	c = []
	for q in range(n):
	v = 0
	for k in range(q):
	if K[k] == Q[q]:
	v = V[k]
	c.append(v)
	cols.append(c)
	return cols[top]


	def generate_reference(prog, T):
	"""The first T generated tokens, re-evaluating the whole sequence at every step (slow; for tests)."""
	seq = [0]
	for _ in range(T):
	seq.append(evaluate(prog, seq)[-1])
	return seq[1:]


	def produces(prog, y):
	"""Teacher forcing: prog generates y (as its first len(y) tokens) iff its column on 0, y[:-1] equals y."""
	return evaluate(prog, [0] + list(y[:-1])) == list(y)


	# ---------------------------------------------------------------- incremental generator

	def generate(prog, T):
	"""The first T generated tokens, as bytes. Keeps per-node running state: a count for C, the previous input
	value for P, and for M a table from key to the value at its latest position (updated after the lookup, so only
	k < q are visible)."""
	nodes, _, top = compile_program(prog)
	state = [0 if s in "CP" else ({} if s == "M" else None) for s, _ in nodes]
	out, x, v = bytearray(), 0, [0] * len(nodes)
	for _ in range(T):
	for i, (s, args) in enumerate(nodes):
	if s == "T":
	r = x
	elif s in "0123":
	r = ord(s) - 48
	elif s == "+":
	r = (v[args[0]] + v[args[1]]) & 255
	elif s == "-":
	r = (v[args[0]] - v[args[1]]) & 255
	elif s == "%":
	b = v[args[1]]
	r = v[args[0]] % b if b else v[args[0]]
	elif s == "=":
	r = int(v[args[0]] == v[args[1]])
	elif s == "<":
	r = int(v[args[0]] < v[args[1]])
	elif s == "!":
	r = 1 - v[args[0]]
	elif s == "&":
	r = v[args[0]] & v[args[1]]
	elif s == "?":
	r = v[args[1]] if v[args[0]] else v[args[2]]
	elif s == "C":
	r = state[i] = (state[i] + v[args[0]]) & 255
	elif s == "P":
	r = state[i]; state[i] = v[args[0]]
	else: # M
	table = state[i]
	r = table.get(v[args[1]], 0)
	table[v[args[0]]] = v[args[2]]
	v[i] = r
	x = v[top]
	out.append(x)
	return bytes(out)


	# ---------------------------------------------------------------- numpy evaluator over a batch of sequences

	def apply_np(sym, args, seqs):
	"""Column of sym on numpy uint8 input columns args (each [batch, n]); seqs is the token batch (for T)."""
	shape = seqs.shape
	if sym == "T":
	return seqs
	if sym in "0123":
	return np.full(shape, int(sym), np.uint8)
	if sym == "+":
	return args[0] + args[1] # uint8 arithmetic wraps mod 256
	if sym == "-":
	return args[0] - args[1]
	if sym == "%":
	a, b = args
	return np.where(b == 0, a, a % np.maximum(b, 1)).astype(np.uint8)
	if sym == "=":
	return (args[0] == args[1]).astype(np.uint8)
	if sym == "<":
	return (args[0] < args[1]).astype(np.uint8)
	if sym == "!":
	return 1 - args[0]
	if sym == "&":
	return args[0] & args[1]
	if sym == "?":
	return np.where(args[0] != 0, args[1], args[2])
	if sym == "C":
	return (np.cumsum(args[0], axis=1, dtype=np.int64) & 255).astype(np.uint8)
	if sym == "P":
	out = np.zeros(shape, np.uint8)
	out[:, 1:] = args[0][:, :-1]
	return out
	if sym == "M":
	# Sort the keys by (row, value, position); a query (row, Q[q], q) lands just after the latest k < q with the
	# same row and value, if there is one. O(n log n) per row, so long sequences are fine.
	K, Q, V = args
	b, n = shape
	base = (np.arange(b, dtype=np.int64)[:, None] * 256 * n)
	pos = np.arange(n, dtype=np.int64)[None, :]
	keys = (base + K.astype(np.int64) * n + pos).ravel()
	order = np.argsort(keys, kind="stable")
	sk = keys[order]
	queries = (base + Q.astype(np.int64) * n + pos).ravel()
	j = np.searchsorted(sk, queries, side="left") - 1 # last key strictly below the query
	jj = np.maximum(j, 0)
	hit = (j >= 0) & (sk[jj] // n == queries // n) # same row and value, and position < q
	return np.where(hit, V.ravel()[order[jj]], 0).reshape(shape).astype(np.uint8)
	raise ValueError(sym)


	def evaluate_np(prog, seqs):
	nodes, _, top = compile_program(prog)
	cols = []
	for s, args in nodes:
	cols.append(apply_np(s, [cols[a] for a in args], seqs))
	return cols[top]