provably

Z3-backed formal verification for Python — via decorators and refinement types.

An awkronos library. The Python sibling of provably for Rust.

from provably import verified

@verified(
    pre=lambda val, lo, hi: lo <= hi,
    post=lambda val, lo, hi, result: (result >= lo) & (result <= hi),
)
def clamp(val: float, lo: float, hi: float) -> float:
    if val < lo:
        return lo
    elif val > hi:
        return hi
    else:
        return val

clamp.__proof__.verified   # True — for ALL inputs where lo <= hi
str(clamp.__proof__)       # "[Q.E.D.] clamp"

verified=True is a mathematical proof. Z3 determined that no input satisfying the precondition can violate the postcondition.

Install

pip install provably
# or: uv add provably

Examples

Pre/post contracts

@verified(
    pre=lambda a, b: b > 0,
    post=lambda a, b, result: (result >= 0) & (result < b),
)
def modulo(a: int, b: int) -> int:
    return a % b

modulo.__proof__.verified        # True
modulo.__proof__.solver_time_ms  # ~2ms

Refinement types

from typing import Annotated
from provably.types import Between, Gt, NonNegative

@verified(post=lambda p, x, result: result >= 0)
def scale(
    p: Annotated[float, Between(0, 1)],
    x: Annotated[float, Gt(0)],
) -> NonNegative:
    return p * x

scale.__proof__.verified  # True

Counterexample extraction

@verified(
    pre=lambda n: n >= 0,
    post=lambda n, result: result * result == n,  # wrong
)
def bad_sqrt(n: int) -> int:
    return n // 2

bad_sqrt.__proof__.counterexample  # {'n': 3, '__return__': 1}

Compositionality

@verified(
    contracts={"my_abs": my_abs.__contract__},
    post=lambda x, y, result: result >= 0,
)
def manhattan(x: float, y: float) -> float:
    return my_abs(x) + my_abs(y)

manhattan.__proof__.verified  # True

While loops

Bounded while loops are unrolled (up to 256 iterations), just like for loops:

@verified(
    pre=lambda n: (n >= 0) & (n <= 10),
    post=lambda n, result: result == n * (n + 1) // 2,
)
def triangle(n: int) -> int:
    total = 0
    i = 0
    while i < n:  # variant: n - i
        i += 1
        total += i
    return total

triangle.__proof__.verified  # True

Walrus operator

@verified(
    post=lambda x, result: (result >= 0) & ((result == x) | (result == -x)),
)
def my_abs(x: float) -> float:
    return (neg := -x) if x < 0 else x

my_abs.__proof__.verified  # True

Match/case (Python 3.10+)

match/case statements are desugared to if/elif/else for Z3:

@verified(
    pre=lambda code: (code >= 0) & (code <= 3),
    post=lambda code, result: (result >= 10) & (result <= 40),
)
def dispatch(code: int) -> int:
    match code:
        case 0: return 10
        case 1: return 20
        case 2: return 30
        case _: return 40

dispatch.__proof__.verified  # True

Tuple returns

@verified(
    post=lambda x, y, result: result >= 0,
)
def sum_and_diff(x: float, y: float) -> tuple:
    return (x + y, x - y)

Lean 4 backend

Cross-check Z3 results with an independent proof assistant:

from provably import verify_with_lean4, export_lean4

cert = verify_with_lean4(clamp, pre=lambda v, lo, hi: lo <= hi,
                         post=lambda v, lo, hi, r: (r >= lo) & (r <= hi))

lean_code = export_lean4(clamp, output_path="clamp.lean")

Supported constructs

Construct	Supported
+, -, *, //, /, %, **n	Yes
<, <=, >, >=, ==, !=	Yes
and, or, not, &, |, ~	Yes
if/elif/else/ternary	Yes
match/case (Python 3.10+)	Yes (desugared to if/elif/else)
min, max, abs	Yes
pow, bool, int, float, len, round	Yes
sum, any, all	Yes
Annotated refinement types	Yes
Calls via contracts=	Yes
Walrus operator (:=)	Yes
Tuple returns + constant subscript (t[0])	Yes
while loops (bounded, max 256 iterations)	Yes (unrolled)
for i in range(N) (literal N, max 256)	Yes (unrolled)
assert statements	Yes (become proof obligations)
Lean 4 backend (verify_with_lean4)	Yes (requires Lean 4)
Recursion	No
str, list, dict	No
Unbounded loops, generators, async	No

Comparison

Library	Approach	Proof strength	Call-site overhead
provably	SMT / Z3	Mathematical proof	Zero solver overhead
deal	Runtime contracts	Bug finding	Per-call
icontract	Runtime contracts	Bug finding	Per-call
CrossHair	Symbolic execution	Property testing	Test-time
beartype	Runtime types	Type checking	Per-call

Links

• Documentation
• Getting started
• How it works
• Self-proof
• API reference
• Changelog · License (MIT)

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awkronos — a small penguin with snow on its head. We prove the math you've been meaning to do.

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