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Proofs / zlib / The standard on valid input

rfc_trailing_bytes

For a stream that zlib's deflate made, followed by any bytes: when decompression returns Z_STREAM_END, it has consumed exactly the stream and none of the bytes after it.

spec
82 lines of C
with its headers
174 lines
status
Proved
21 of 62
On this page

The spec

The spec is the C program harness/rfc_trailing_bytes.c, 82 lines, shown whole as it is in the repository at 37189f4. It includes harness/laws_common.h (40 lines) and harness/laws_session.h (52 lines). Its first comment states the property in full, with every bound.

C
// Law rfc_trailing_bytes: For any data (any length the allocator provides) compressed with deflateInit2 (any level,
// windowBits, memLevel and strategy in zlib.h's ranges; it returns Z_OK) and deflate (all of it, in pieces of at most
// 2^32 - 1 bytes, Z_FINISH with the last, into deflateBound_z bytes; the run ends unless it reaches Z_STREAM_END),
// followed by any bytes (any number up to PTRDIFF_MAX minus the stream's length; none if the stream is longer),
// inflate() fed all of it and room for the data, in pieces of at most 2^32 - 1 bytes, with any flush, after
// inflateInit2 with the matching windowBits (it returns Z_OK), returns only Z_OK or Z_BUF_ERROR until Z_STREAM_END and
// stops where the stream ends: when it returns Z_STREAM_END it has read exactly the compressed bytes and none of the
// bytes after them (Z_MEM_ERROR ends the run).
#include "laws_common.h"
#include "laws_session.h"

int main(void) {
	size_t data_len = upto(PTRDIFF_MAX);
	unsigned char *data = alloc_any_bytes(data_len);
	unsigned char *out = malloc(data_len);
	if (data == NULL || out == NULL)
		return 0;
	int level = (int) nondet_u32();
	int window_bits = (int) nondet_u32();
	int mem_level = (int) nondet_u32();
	int strategy = (int) nondet_u32();
	gp_assume(deflate_params_ok(level, window_bits, mem_level, strategy));
	z_stream compressor;
	new_stream(&compressor);
	int code = deflateInit2(&compressor, level, Z_DEFLATED, window_bits, mem_level, strategy);
	if (code == Z_MEM_ERROR)
		return 0;
	gp_assert(code == Z_OK);
	size_t out_size = deflateBound_z(&compressor, data_len);
	unsigned char *compressed = malloc(out_size);
	if (compressed == NULL)
		return 0;
	compressor.next_in = data;
	compressor.next_out = compressed;
	do {
		size_t rest = data_len - (size_t) (compressor.next_in - data);
		int flush = Z_NO_FLUSH;
		if (rest <= UINT_MAX)
			flush = Z_FINISH;
		compressor.avail_in = clip(rest);
		compressor.avail_out = clip(out_size - (size_t) (compressor.next_out - compressed));

		code = deflate(&compressor, flush);
	} while (code == Z_OK);
	if (code != Z_STREAM_END)
		return 0;
	size_t compressed_len = (size_t) (compressor.next_out - compressed);
	// RFC 1950 2.2: "Any data which may appear after ADLER32 are not part of the zlib stream." zlib.h,
	// inflateInit2: "inflate() will return Z_STREAM_END at the end of the gzip member."
	size_t room = 0;
	if (compressed_len < PTRDIFF_MAX)
		room = PTRDIFF_MAX - compressed_len;
	size_t after = upto(room);
	unsigned char *input = alloc_any_bytes(compressed_len + after);
	if (input == NULL)
		return 0;
	for (size_t i = 0; i < compressed_len; i++)
		input[i] = compressed[i];
	z_stream decompressor;
	new_stream(&decompressor);
	// zlib.h, deflateInit2: "a request for 8 will result in 9"; "use 9 with inflateInit2()"
	if (window_bits == 8)
		window_bits = 9;
	code = inflateInit2(&decompressor, window_bits);
	if (code == Z_MEM_ERROR)
		return 0;
	gp_assert(code == Z_OK);
	decompressor.next_in = input;
	decompressor.next_out = out;
	do {
		decompressor.avail_in = clip(compressed_len + after - (size_t) (decompressor.next_in - input));
		decompressor.avail_out = clip(data_len - (size_t) (decompressor.next_out - out));

		code = inflate(&decompressor, (int) nondet_u32());

		if (code == Z_MEM_ERROR)
			return 0;
		gp_assert(code == Z_OK || code == Z_BUF_ERROR || code == Z_STREAM_END);
	} while (code != Z_STREAM_END);
	gp_assert(decompressor.next_in == input + compressed_len);
	return 0;
}
harness/laws_common.h, 40 lines
C
// laws_common.h: trivial helpers shared by the zlib laws (each law includes it once). No models, no algorithms.
#include <limits.h>
#include <stdlib.h>
#include "quickproof.h"
#include "zlib.h"
static size_t upto(size_t max) {
	size_t value = nondet_size();
	return value < max ? value : max;
}
static uInt clip(size_t n) { return n < UINT_MAX ? (uInt) n : UINT_MAX; }
static unsigned char *alloc_any_bytes(size_t n) {
	unsigned char *bytes = malloc(n);
	if (bytes != NULL)
		nondet_bytes(bytes, n);
	return bytes;
}
static unsigned char *copy_of(const unsigned char *source, size_t n) {
	unsigned char *copy = malloc(n);
	for (size_t i = 0; copy != NULL && i < n; i++)
		copy[i] = source[i];
	return copy;
}
static int bytes_eq(const unsigned char *a, const unsigned char *b, size_t n) {
	for (size_t i = 0; i < n; i++)
		if (a[i] != b[i])
			return 0;
	return 1;
}
static void set_buffer(z_stream *strm, unsigned char *in, size_t in_len, unsigned char *out, size_t out_len) {
	strm->next_in = in;
	strm->avail_in = (uInt) in_len;
	strm->next_out = out;
	strm->avail_out = (uInt) out_len;
}
static void new_stream(z_stream *strm) {
	strm->zalloc = Z_NULL;
	strm->zfree = Z_NULL;
	strm->opaque = Z_NULL;
	set_buffer(strm, Z_NULL, 0, Z_NULL, 0);
}
harness/laws_session.h, 52 lines
C
// laws_session.h: helpers of the laws that drive a z_stream, included after laws_common.h. No models, no algorithms.
static int deflate_params_ok(int level, int window_bits, int mem_level, int strategy) {
	// zlib.h, deflateInit2: level "Z_DEFAULT_COMPRESSION, or between 0 and 9"; memLevel 1..MAX_MEM_LEVEL (9,
	// zconf.h); strategy Z_DEFAULT_STRATEGY (0) .. Z_FIXED (4); windowBits 8..15, "-8..-15 for raw deflate", "Add 16
	// to windowBits to write a simple gzip header", but "For raw deflate or gzip encoding, a request for a 256-byte
	// window is rejected as invalid"
	int zlib_window = window_bits >= 8 && window_bits <= 15;
	int raw_window = window_bits >= -15 && window_bits <= -9;
	int gzip_window = window_bits >= 16 + 9 && window_bits <= 16 + 15;
	int valid = level >= -1 && level <= 9 && mem_level >= 1 && mem_level <= 9 && strategy >= 0 && strategy <= Z_FIXED;
	return valid && (zlib_window || raw_window || gzip_window);
}
static int inflate_window_ok(int window_bits) {
	// zlib.h, inflateInit2: windowBits "should be in the range 8..15", "can also be zero to request that inflate
	// use the window size in the zlib header", "can also be -8..-15 for raw inflate", "Add 32 to windowBits to
	// enable zlib and gzip decoding with automatic header detection, or add 16 to decode only the gzip format"
	int low = window_bits & 15;
	int raw = window_bits >= -15 && window_bits <= -8;
	int wrapped = window_bits >= 0 && window_bits < 48 && (low == 0 || low >= 8);
	return raw || wrapped;
}
struct position {
	unsigned char *next_in;
	uInt avail_in;
	unsigned char *next_out;
	uInt avail_out;
	uLong total_in;
	uLong total_out;
};
static void position_of(z_stream *strm, struct position *at) {
	at->next_in = strm->next_in;
	at->avail_in = strm->avail_in;
	at->next_out = strm->next_out;
	at->avail_out = strm->avail_out;
	at->total_in = strm->total_in;
	at->total_out = strm->total_out;
}
static int unmoved(z_stream *strm, struct position *at) {
	int in = strm->next_in == at->next_in && strm->avail_in == at->avail_in && strm->total_in == at->total_in;
	int out = strm->next_out == at->next_out && strm->avail_out == at->avail_out && strm->total_out == at->total_out;
	return in && out;
}
static int accounted(z_stream *strm, struct position *at) {
	int in = strm->avail_in <= at->avail_in && strm->next_in + strm->avail_in == at->next_in + at->avail_in;
	int out = strm->avail_out <= at->avail_out && strm->next_out + strm->avail_out == at->next_out + at->avail_out;
	return in && out;
}
static int counted(z_stream *strm, struct position *at) {
	int in = strm->total_in == at->total_in + (at->avail_in - strm->avail_in);
	int out = strm->total_out == at->total_out + (at->avail_out - strm->avail_out);
	return in && out;
}

The theorem

QuickProof generated this statement from the spec, in src/contracts/rfc_trailing_bytes.v:

Rocq
Theorem rfc_trailing_bytes : harness_safe whole_prog.

src/contracts/laws.v states it on the spec's own program, whole_prog (the spec linked with the code under test), with its proof:

Rocq
Theorem rfc_trailing_bytes : harness_safe Zlib.contracts.rfc_trailing_bytes.whole_prog.
Proof. exact (proj1 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 Zlib.contracts.suite.suite)))))))))))))))))))))))))). Qed.

Read as a statement about runs, it says that no run of the program has undefined behaviour or a failing check, for every value the spec can draw. That reading rests on VST's adequacy theorem, which is not yet instantiated in Rocq (formerly Coq) for QuickProof's environment.

The C files (units) its program links
  • adler32.c
  • crc32.c
  • deflate.c
  • trees.c
  • inflate.c
  • inffast.c
  • inftrees.c
  • zutil.c
  • quickproof/libc/libc.c

What it leaves out

  • What the first comment of the spec excludes, and its bounds.
  • Like every spec of this proof: termination (a run that never returns is not a counterexample), and binaries built by a compiler (the theorem is about the code as CompCert defines C for x86_64, LP64), one thread.
  • Where zlib reports Z_MEM_ERROR, most specs end the run and claim nothing about it; the first comment of the spec says so.
  • The edits to zlib's code, listed in the repository, are tested, not proved.

The summary page says what the proof as a whole covers.

How it was proved

AI agents wrote the proof, and Rocq checks it. qp verify passes on this repository: this statement is the one generated from the spec at the contract commit, and its proof uses only Rocq's standard axioms and VST's abstract malloc library.