Simplify

## What is Simplify?

Simplify is the constraint simplification engine of Mistral, which implements the algorithm described in this paper. It brings formulas to a so-called "simplified form" which has the guarantee that no subpart of the formula is redundant. Simplification can be useful either to make the constraint more readable by humans or in contexts where it is desirable or beneficial to keep formulas as concise and as non-redundant as possible.

## How to Use Simplify

Using the simplification functionality of constraint is very simple: It simplifies formulas every time you make a satsfiability or validity query using sat() or valid(). The following example illustrates how simplification works:

```     Term* x = VariableTerm::make("x");
Term* y = VariableTerm::make("y");

Constraint c1(x, ConstantTerm::make(0), ATOM_GT);
Constraint c2(y, ConstantTerm::make(1), ATOM_EQ);
Constraint c3 = (c1 | (!c1 & c2));

cout << "Redundant constraint: " << c3 << endl;
c3.sat();
cout << "Simplified constraint: " << c3 << endl;
```

Here, we construct a constraint c3, which represents the formula x>0 | (x<=0 & y=1). However, as a result of the satisfiability query c3.sat(), c3 gets simplified, and the formula that is printed at the last line is the simpler constraint x>0| y=1. Simplify guarantees that any formula that is valid gets simplified to true, and any unsatisfiable formula simplifies to false. If simplification is not desired or needed, use the sat_discard() and valid_discard() methods.

Another functionality that Simplify provides is to simplify a formula with respect to another one. This is achieved using the assume function provided in Constraint.h. Here is an example illustrating the use of assume:

```     Term* x = VariableTerm::make("x");
Term* y = VariableTerm::make("y");

Constraint c1(x, ConstantTerm::make(1), ATOM_GT);
Constraint c2(y, ConstantTerm::make(2), ATOM_EQ );
Constraint c3 = c1 | c2;

cout << "Original constraint: " << c3 << endl;
c3.assume(!c1);
cout << "After assuming !c1: " << c3 << endl;

```

Here, we first construct a constraint c3, which represents (x > 1 | y = 2). After the assume operation at the last line, the new constraint c3 now becomes y=2, since we are assuming that x <=1.