7 releases (4 breaking)

0.5.2 Oct 8, 2021
0.5.1 Sep 28, 2021
0.4.0 Sep 26, 2021
0.3.0 Sep 3, 2021
0.1.0 Aug 28, 2021

#36 in Science

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MIT/Apache

36KB
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Mikino is a (relatively) simple induction and BMC engine. Its goal is to serve as a simple yet interesting tool for those interested in formal verification, especially SMT-based induction.

"Mikino" does not mean cinema. It is a contraction of "mini" and "kinō" (帰納: induction, recursion). It is a significantly simpler version of the now defunct kino k-induction engine on transition systems.

crates.io

Contents:

Installing

Make sure Rust is installed and up to date.

> rustup update

Use cargo to install mikino.

> cargo install mikino

That's it. Alternatively, you can build it from source.

Basics

You can run mikino in demo mode with mikino demo demo.mkn. This will write a heavily commented example system in demo.mkn. There is a discussion on transition systems below that goes into details on the input format, using this exact system as an example.

Running mikino help is also probably a good idea.

Note that mikino files are designed to work well with Rust syntax highlighting.

SMT Solver (Z3)

Mikino requires an SMT solver to run induction (and BMC). More precisely, it requires Z3 which you can download directly from the Z3 release page. You must either

  • make sure the Z3 binary is in your path, and is called z3, or
  • use mikino's --z3_cmd to specify how to call it, for instance:
    • mikino --z3_cmd my_z3 ... if my_z3 is in your path, or
    • mikino --z3_cmd ./path/to/my_z3 ... if path/to/my_z3 is where the Z3 binary is.

Building From Source

> cargo build --release
> ./target/release/mikino --version
mikino 0.5.0

Transition Systems

A (transition) system is composed of some variable declarations, of type bool, int or rat (rational). A valuation of these variables is usually called a state. (An int is a mathematical integer here: it cannot over/underflow. A rat is a fraction of ints.)

Let's use a simple counter system as an example. Say this system has two variables, cnt of type int and inc of type bool.

The definition of a system features an initial predicate. It is a boolean expression over the variables of the system that evaluate to true on the initial states of the system.

Assume now that we want to allow our counter's cnt variable's initial value to be anything as long as it is positive. Our initial predicate will be cnt ≥ 0. Note that variable inc is irrelevant in this predicate.

Next, the transition relation of the system is an expression over two versions of the variables: the current variables, and the next variables. The transition relation is a relation between the current state and the next state that evaluates to true if the next state is a legal successor of the current one. A the next version of a variable v is written 'v, and its current version is just written v.

Our counter should increase by 1 whenever variable inc is true, and maintain its value otherwise. There is several ways to write this, for instance

(inc ⋀ 'cnt = cnt + 1)(¬inc ⋀ 'cnt = cnt)

or

if inc { 'cnt = cnt + 1 } else { 'cnt = cnt }

or

'cnt = if inc { cnt + 1 } else { cnt }

Last, the transition system has a list of named candidates (candidate invariants) which are boolean expressions over the variables. The system is safe if and only if it is not possible to reach a falsification of any of these candidates from the initial states by applying the transition relation repeatedly.

A reasonable candidate for the counter system is (≥ cnt 0). The system is safe for this candidate as no reachable state of the counter can falsify it.

The candidate ¬(cnt = 7) does not hold in all reachable states, in fact the initial state { cnt: 7, inc: _ } falsifies it. But assume we change the initial predicate to be cnt = 0. Then the candidate is still falsifiable by applying the transition relation seven times to the (only) initial state { cnt: 0, inc: _ }. In all seven transitions, we need inc to be true so that cnt is actually incremented.

A falsification of a candidate is a concrete trace: a sequence of states i) that starts from an initial state, ii) where successors are valid by the transition relation and iii) such that the last state of the sequence falsifies the PO.

A falsification of ¬(cnt = 7) for the last system above with the modified initial predicate is

Step 0
| cnt: 0
Step 1
| cnt: 1
| inc: true
Step 2
| cnt: 2
| inc: true
Step 3
| cnt: 3
| inc: true
Step 4
| cnt: 4
| inc: true
Step 5
| cnt: 5
| inc: true
Step 6
| cnt: 6
| inc: true
Step 7
| cnt: 7
| inc: true

Dependencies

Mikino relies on the following stellar libraries:

License

Mikino is distributed under the terms of both the MIT license and the Apache License (Version 2.0).

See LICENSE-APACHE and LICENSE-MIT for details.


Copyright © OCamlPro SAS

Dependencies

~6.5MB
~125K SLoC

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