2. Getting Started¶

2.1. Hello Proofs¶

The first step in using Why3 is to write a suitable input file. When one wants to learn a programming language, one starts by writing a basic program. Here is our first Why3 file, which is the file examples/logic/hello_proof.why of the distribution. It contains a small set of goals.

theory HelloProof

  goal G1: true

  goal G2: (true -> false) /\ (true \/ false)

  use int.Int

  goal G3: forall x:int. x * x >= 0

end

Any declaration must occur inside a theory, which is in that example called HelloProof. It contains three goals named G1, G2, G3. The first two are basic propositional goals, whereas the third involves some integer arithmetic, and thus it requires to import the theory of integer arithmetic from the Why3 standard library, which is done by the use declaration above.

We don’t give more details here about the syntax and refer to Section 3 for detailed explanations. In the following, we show how this file is handled in the Why3 GUI (Section 2.2) then in batch mode using the why3 executable (Section 2.3).

But before running any Why3 command, you should proceed with the automated detection of external provers (see also Section 4.2). This is done by running the config tool on the command line, as follows:

why3 config

2.2. Getting Started with the GUI¶

The graphical interface makes it possible to browse into a file or a set of files, and check the validity of goals with external provers, in a friendly way. This section presents the basic use of this GUI. Please refer to Section 5.3 for a more complete description.

Fig. 2.1 The GUI when started the very first time.¶

The GUI is launched on the file above as follows:

why3 ide hello_proof.why

When the GUI is started for the first time, you should get a window that looks like the screenshot of Fig. 2.1. The left part is a tree view that makes it possible to browse inside the files and their theories. The tree view shows that the example is made of a single file containing a single theory containing three goals. The top-right pane displays the content of this file. Now click on the row corresponding to goal G1, and then click on the “Task” tab of the top-right pane, so that it displays the corresponding task, as show on Fig. 2.2.

The GUI with goal ``G1`` selected. — Fig. 2.2 The GUI with goal `G1` selected.¶

2.2.1. Calling provers on goals¶

You are now ready to call provers on the goals. (If not done yet, you must perform prover autodetection using why3 config.) A prover is selected using the context menu (right-click). This prover is then called on the goal selected in the tree view. You can select several goals at a time, either by using multi-selection (typically by clicking while pressing the Shift or Control key) or by selecting the parent theory or the parent file.

Let us now select the theory “HelloProof” and run the Alt-Ergo prover. After a short time, you should get the display of Fig. 2.3.

Fig. 2.3 The GUI after running the Alt-Ergo prover on each goal.¶

Goals G1 and G3 are now marked with a green “checked” icon in the status column. This means that these goals have been proved by Alt-Ergo. On the contrary, goal G2 is not proved; it remains marked with a question mark. You could attempt to prove G2 using another prover, though it is obvious here it will not succeed.

2.2.2. Applying transformations¶

Instead of calling a prover on a goal, you can apply a transformation to it. Since G2 is a conjunction, a possibility is to split it into subgoals. You can do that by selecting Split VC in the context menu. Now you have two subgoals, and you can try again a prover on them, for example Alt-Ergo. We already have a lot of goals and proof attempts, so it is a good idea to close the sub-trees which are already proved. This can be done by the menu View ‣ Collapse proved goals, or even better by its shortcut !. You should now see what is displayed on Fig. 2.4.

The GUI after splitting goal ``G2``. — Fig. 2.4 The GUI after splitting goal `G2`.¶

The first part of goal G2 is still unproved. As a last resort, you can try to call the Coq proof assistant, by selecting it in the context menu. A new sub-row appear for Coq, and the Coq proof editor is launched. (It is coqide by default; see Section 5.3 for details on how to configure this). You get now a regular Coq file to fill in, as shown on Fig. 2.5. Please be mindful of the comments of this file. They indicate where Why3 expects you to fill the blanks. Note that the comments themselves should not be removed, as they are needed to properly regenerate the file when the goal is changed. See Section 10.3 for more details.

CoqIDE on subgoal 1 of ``G2``. — Fig. 2.5 CoqIDE on subgoal 1 of `G2`.¶

Of course, in that particular case, the goal cannot be proved since it is not valid. The only thing to do is to fix the input file, as explained below.

2.2.3. Modifying the input¶

You can edit the source file, using the corresponding tab in the top-right pane of the GUI. Change the goal G2 by replacing the first occurrence of true by false, e.g.,

goal G2 : (false -> false) /\ (true \/ false)

You can refresh the goals using menu File ‣ Save all and Refresh session, or the shortcut Control-r. You get the tree view shown on Fig. 2.6.

File reloaded after modifying goal ``G2``. — Fig. 2.6 File reloaded after modifying goal `G2`.¶

The important feature to notice first is that all the previous proof attempts and transformations were saved in a database — an XML file created when the Why3 file was opened in the GUI for the first time. Then, for all the goals that remain unchanged, the previous proofs are shown again. For the parts that changed, the previous proofs attempts are shown but marked with “(obsolete)” so that you know the results are not accurate. You can now retry to prove all the goals not yet proved using any prover.

2.2.4. Replaying obsolete proofs¶

Instead of pushing a prover’s button to rerun its proofs, you can replay the existing but obsolete proof attempts, using menu Tools ‣ Replay valid obsolete proofs. Notice that replaying can be done in batch mode, using the why3 replay command (see Section 5.4) For example, running the replayer on the hello_proof example is as follows (assuming G2 still is (true -> false) /\ (true \/ false)).

$ why3 replay hello_proof
 2/3 (replay OK)
   +--file ../hello_proof.why: 2/3
      +--theory HelloProof: 2/3
         +--goal G2 not proved

The last line tells us that no differences were detected between the current run and the run stored in the XML file. The tree above reminds us that G2 is not proved.

2.2.5. Cleaning¶

You may want to clean some of the proof attempts, e.g., removing the unsuccessful ones when a project is finally fully proved. A proof or a transformation can be removed by selecting it and using menu Tools ‣ Remove node or the Delete key. Menu Tools ‣ Clean node or shortcut C perform an automatic removal of all proofs attempts that are unsuccessful, while there exists a successful proof attempt for the same goal. Beware that there is no way to undo such a removal.

2.3. Getting Started with the Why3 Command¶

The why3 prove command makes it possible to check the validity of goals with external provers, in batch mode. This section presents the basic use of this tool. Refer to Section 5.2 for a more complete description of this tool and all its command-line options.

This prints some information messages on what detections are attempted. To know which provers have been successfully detected, you can do as follows.

$ why3 config list-provers
Alt-Ergo 1.30
CVC4 1.5
Coq 8.6

The first word of each line is a unique identifier for the associated prover. We thus have now the three provers Alt-Ergo [CC08], CVC4 [BCD+11], and Coq [BC04].

Let us assume that we want to run Alt-Ergo on the HelloProof example. The command to type and its output are as follows, where the why3 prove -P option is followed by the unique prover identifier (as shown by why3 config list-provers).

$ why3 prove -P Alt-Ergo hello_proof.why
hello_proof.why HelloProof G1: Valid (0.00s, 1 steps)
hello_proof.why HelloProof G2: Unknown (other) (0.01s)
hello_proof.why HelloProof G3: Valid (0.00s, 1 steps)

Unlike the Why3 GUI, the command-line tool does not save the proof attempts or applied transformations in a database.

We can also specify which goal or goals to prove. This is done by giving first a theory identifier, then goal identifier(s). Here is the way to call Alt-Ergo on goals G2 and G3.

$ why3 prove -P Alt-Ergo hello_proof.why -T HelloProof -G G2 -G G3
hello_proof.why HelloProof G2 : Unknown: Unknown (0.01s)
hello_proof.why HelloProof G3 : Valid (0.01s)

Finally, a transformation to apply to goals before proving them can be specified. To know the unique identifier associated to a transformation, do as follows.

$ why3 show transformations
Known non-splitting transformations:
  [...]

Known splitting transformations:
  [...]
  split_goal_right

Here is how you can split the goal G2 before calling Simplify on the resulting subgoals.

$ why3 prove -P Alt-Ergo hello_proof.why -a split_goal_right -T HelloProof -G G2
hello_proof.why HelloProof G2: Unknown (other) (0.01s)
hello_proof.why HelloProof G2: Valid (0.00s, 1 steps)

Section 12.5 gives the description of the various transformations available.