| """Standard two-copy SMT construction; the certificate checker remains separate. |
| |
| Z3 API: https://z3prover.github.io/api/html/namespacez3py.html |
| This implements established relational reasoning, not a new SMT algorithm. |
| """ |
|
|
| import base64 |
| import copy |
| import io |
|
|
| from .finite_program import question, render, validate_observation, validate_program |
|
|
|
|
| def construct(program, observed, domain, *, timeout_ms=1000): |
| import z3 |
|
|
| validate_program(program) |
| validate_observation(observed, domain) |
| first = z3.IntVector("first", 4) |
| second = z3.IntVector("second", 4) |
|
|
| def expression(node, world): |
| op = node[0] |
| if op == "cell": |
| return z3.ToReal(world[node[1]]) |
| if op == "const": |
| return z3.RealVal(node[1]) |
| left, right = (expression(child, world) for child in node[1:]) |
| operations = { |
| "add": lambda: left + right, "sub": lambda: left - right, |
| "mul": lambda: left * right, "div": lambda: left / right, |
| "min": lambda: z3.If(left <= right, left, right), |
| "max": lambda: z3.If(left >= right, left, right), |
| "gt": lambda: z3.If(left > right, z3.RealVal(1), z3.RealVal(0)), |
| "eq": lambda: z3.If(left == right, z3.RealVal(1), z3.RealVal(0)), |
| } |
| return operations[op]() |
|
|
| solver = z3.Solver() |
| solver.set(timeout=timeout_ms, random_seed=0) |
| for world in (first, second): |
| for i, value in enumerate(observed): |
| solver.add(world[i] >= domain[0], world[i] <= domain[1]) |
| if value is not None: |
| solver.add(world[i] == value) |
| solver.add(expression(program, first) != expression(program, second)) |
| status = solver.check() |
| if status == z3.unsat: |
| return {"status": "constant"} |
| if status != z3.sat: |
| return {"status": "unknown", "reason": solver.reason_unknown()} |
| model = solver.model() |
| worlds = [[model.eval(value, model_completion=True).as_long() for value in world] |
| for world in (first, second)] |
| image = io.BytesIO() |
| render(observed, domain).save(image, format="PNG") |
| return {"status": "ambiguous", "proof": { |
| "schema": "finite_compositional_witness_v1", "domain": list(domain), |
| "program": copy.deepcopy(program), "question": question(program), |
| "observation": list(observed), "witnesses": worlds, |
| "observed_png": base64.b64encode(image.getvalue()).decode("ascii"), |
| }} |
|
|
