Sally

Sally is a model checker for infinite state systems described as transition systems. It is research software under development so the features and the input language may change rapidly.

The project is supported by NASA contract NNX14AI05A.

Prerequisites

In order to compile Sally you will need the following

A reasonable c++ compiler such as g++ or clang
```
sudo apt-get install g++
```
The CMake build system
```
sudo apt-get install cmake
```
The GMP library
```
sudo apt-get install libgmp-dev
```

Some Boost libraries

sudo apt-get install libboost-program-options-dev libboost-iostreams-dev libboost-test-dev libboost-thread-dev libboost-system-dev

A working Java runtime
```
sudo apt-get install default-jre
```

How to Compile

If you have Yices2 installed in the $YD directory, meaning that there are $YD/include and $YD/lib directories with Yices2 headers and libraries, then configure and build with

cd build
cmake .. -DYICES2_HOME=$YD
make
make check

If you have MathSAT5 installed in the $MD directory, meaning that there are $MD/include and $MD/lib directories with MathSAT5 headers and libraries, then configure and build with

cd build
cmake .. -DMATHSAT5_HOME=$MD
make
make check

Of course, you can use both Yices2 and MathSAT by adding both options to cmake as expected.

To compile sally in debug mode then configure and build with

cd build
cmake .. -DCMAKE_BUILD_TYPE=Debug
make
make check

Input Language

Transition System Definition

Sally takes as input a simple description of transition systems based on the SMT2 language. A transition system consists of a description of the state type, a formula describing the initial states of the system, and a formula describing the transitions from the current to the next state of the system.

State type is a list of variables that are part of the state, together with their types.

;; A definition of a state type called "my_state_type" with variables
;; x and y of type Real. 
(define-state-type my_state_type 
  ((x Real) (y Real))
)

With a defined state type, we can define sets of states and transitions over the state type.

We can describe a set of states with a state formula over the state type. A state formula is a first-order formula over the variables of the state type, written in SMT2 format.

;; Definition of a set of states "x_is_zero" capturing all states 
;; over the state type "my_state_type" where x is 0.
(define-states x_is_zero my_state_type
  (= x 0)
)

Once a state formula has been defined it can be reused in other state formulas over the same state type.

;; A definition of a set of states "initial_states" over 
;; "my_state_type" by a state formula. These are all states where 
;; both x and y are 0.
(define-states initial_states my_state_type
  (and x_is_zero (= y 0))
)

We can describe allowed state transitions by a first-order formula over the current (state) and next variables of the state type. We use the prefix state to denote current variables, and the prefix next to denote the variables in the next state. Previously defined state formulas over the same state type can be used as if they were variables (state or next). Similarly, previously defined transitions over the same type can be used directly.

;; Definition of a transition where the next value of x is the 
;; current value + 1.
(define-transition inc_x my_state_type
  (= next.x (+ state.x 1))
)   
    
;; Definition of a transition that increases both x and y
(define-transition inc_x_and_y my_state_type
  (and inc_x (= next.y (+ state.y 1)))
)
    
;; Definition of a transition that increases x and y if not 
;; exceeding 100, or goes back to the state with x = y = 0
(define-transition transition my_state_type
  (or 
    (and (< state.x 100) inc_x_and_y)
    next.initial_states
  ) 
)

We can define a state transition system by defining the state type, the initial states of the system and the transitions that the system can make.

;; Directly define a simple counter system that increases x and y
(define-transition-system T1 my_state_type
  ;; Initial states 
  (and (= x 0) (= y 0))
  ;; Transition 
  (and (= next.x (+ state.x 1)) (= next.y (+ state.y 1)))
)
    
;; Define a counter system that can reset to 0 by reusing defined
;; formulas 
(define-transition-system T2 my_state_type
   ;; Initial states
   initial_states
   ;; Transitions 
   transition
)

Queries

A query asks a question whether a state property is true in the given transition system. For example, in the system T1, it is clear that we the variables x and y will always be equal and non-negative. We can check these with the following queries.

;; Check whether x = y in T1
(query T1 (= x y))

;; Check whether x, y >= 0
(query T1 (and (>= x 0) (>= y 0)))

In the system T2, it should hold that both x and y will never exceed 20.

;; Check whether x, y <= 20
(query T2 (and (<= x 20) (<= y 20)))
    
;; Check whether x, y <= 19
(query T2 (and (<= x 19) (<= y 19)))

The example above is available in examples/example.mcmt.

Usage

To see the full set of options run sally -h. Some typical examples are as follows

Checking the properties with the bounded model-checking (BMC) engine

> sally --engine bmc examples/example.mcmt
unknown
unknown
unknown
unknown

Checking the property with BMC with a bigger bound and showing any counter-example traces

> sally --engine bmc --bmc-max 20 --show-trace examples/example.mcmt
unknown
unknown
unknown
invalid
(trace 
  (frame (x 0) (y 0))
  (frame (x 1) (y 1))
  ...
  (frame (x 20) (y 20))
)

Checking the properties with the k-induction engine

> sally --engine kind examples/example.mcmt
valid
valid
unknown
unknown 
> sally --engine kind --kind-max 20 examples/example.mcmt 
valid
valid
unknown
invalid

Checking the properties with the ic3 engine using the combination of yices2 and MathSAT5 as the reasoning engine
```
> sally --engine ic3 --solver y2m5 examples/example.mcmt 
valid
valid
valid
invalid
```

lememta / sally