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e1ced61 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | """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"),
}}
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