vdimir / py-refinement-lambda

Pyrefine – python code checker based on Hoare logic

Pyrefine

Python code checker based on Hoare logic to develop verified software with refinement types.

Z3 SMT-solver is used to prove statements about program.

Requirements

• Python 3.5+
• z3-solver
• pyparsing
• ast (build-in)

Supported language elements

• Function Definitions
• Lambda Functions
• If Statements
• While Loops

Usage

To run checker script run:

python -m pyrefine.__main__ ./examples/example.py

To use checker import module with stub-functions:

from pyrefine import *

Than you can use following code to create verified functions. Note that variables should be declared using c_ operator.

def func(<arg_list>):
    define_('<type_annotation>', 
            '<precondition>', 
            '<postcondition>')
    <statements>

func = define_('<type_annotation>', '<precondition>', '<postcondition>', 
               lambda x, y: ...)

constant = c_('<atomic_type>', <expr>)

while <expr>:
    loop_('<loop_invariant>', 
          '<bound_function>')
    <statements>

Explained example:

def gcd(x, y):
    define_('int -> int -> int', # define function type
            'x > 0 and y > 0',   # precondition
            'ret > 0')           # postcondition
    t = c_('int', 0)
    while x != y:
        loop_('x > 0 and y > 0', # loop invariant
              'x + y')           # bound function to prove loop termitation
        if x > y:
            y, x = x, y
        assert y > x             # assets also checked statically
        y = y - x
    assert x == y          
    return y                     # y > 0

Examples

You can find examples in example.py.

More examples in test folder.