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Proofs / zlib / Checksums

ck_crc32_combine

The same for CRC-32, with each of zlib's three combine functions.

spec
26 lines of C
with its headers
66 lines
status
Proved
44 of 62
On this page

The spec

The spec is the C program harness/ck_crc32_combine.c, 26 lines, shown whole as it is in the repository at 37189f4. It includes harness/laws_common.h (40 lines). Its first comment states the property in full, with every bound.

C
// Law ck_crc32_combine: For any bytes (any length up to PTRDIFF_MAX that the allocator provides), any split of them
// into a first and a second part and any CRC-32 value to start from, combining the first part's CRC (from start) with
// the second part's (from 0) gives the CRC of all the bytes (from start), with crc32_combine as with crc32_combine_op
// and crc32_combine_gen.
#include "laws_common.h"

int main(void) {
	size_t len = upto(PTRDIFF_MAX);
	size_t split = upto(len);
	unsigned char *buf = alloc_any_bytes(len);
	if (buf == NULL)
		return 0;
	uLong start = nondet_u32();

	uLong first = crc32_z(start, buf, split);
	uLong second = crc32_z(0, buf + split, len - split);
	uLong whole = crc32_z(start, buf, len);

	// zlib.h, crc32_combine: "crc32_combine() returns the CRC-32 check value of seq1 and seq2 concatenated,
	// requiring only crc1, crc2, and len2"; crc32_combine_gen: "Return the operator corresponding to length len2,
	// to be used with crc32_combine_op()".
	gp_assert(crc32_combine(first, second, (z_off_t) (len - split)) == whole);
	uLong op = crc32_combine_gen((z_off_t) (len - split));
	gp_assert(crc32_combine_op(first, second, op) == whole);
	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);
}

The theorem

QuickProof generated this statement from the spec, in src/contracts/ck_crc32_combine.v:

Rocq
Theorem ck_crc32_combine : 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 ck_crc32_combine : harness_safe Zlib.contracts.ck_crc32_combine.whole_prog.
Proof. exact (proj1 (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
  • crc32.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.