ck_adler32

The spec#

The spec is the C program harness/ck_adler32.c, 23 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.

// Law ck_adler32: For any bytes (any length up to PTRDIFF_MAX that the allocator provides) and any Adler-32 value to
// continue from (both halves below 65521), adler32_z returns the Adler-32 of RFC 1950 as computed below.
#include "laws_common.h"

int main(void) {
	size_t len = upto(PTRDIFF_MAX);
	unsigned char *buf = alloc_any_bytes(len);
	if (buf == NULL)
		return 0;
	unsigned long s1 = upto(65520);
	unsigned long s2 = upto(65520);
	uLong start = s2 << 16 | s1;
	// RFC 1950 2.2: "s1 is the sum of all bytes, s2 is the sum of all s1 values. Both sums are done modulo 65521.
	// s1 is initialized to 1, s2 to zero. The Adler-32 checksum is stored as s2*65536 + s1"
	for (size_t i = 0; i < len; i++) {
		s1 = (s1 + buf[i]) % 65521;
		s2 = (s2 + s1) % 65521;
	}

	gp_assert(adler32_z(start, buf, len) == s2 * 65536 + s1);

	return 0;
}

// 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_adler32.v:

Theorem ck_adler32 : 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:

Theorem ck_adler32 : harness_safe Zlib.contracts.ck_adler32.whole_prog.
Proof. exact (proj1 (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.

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.