Chapter 3  The Why3 API

• Building Propositional Formulas
• Building Tasks
• Calling External Provers
• Building Terms
• Building Quantified Formulas
• Building Theories
• Operations on Terms and Formulas, Transformations
• Proof Sessions
• ML Programs

This chapter is a tutorial for the users who want to link their own OCaml code with the Why3 library. We progressively introduce the way one can use the library to build terms, formulas, theories, proof tasks, call external provers on tasks, and apply transformations on tasks. The complete documentation for API calls is given at this URL.

We assume the reader has a fair knowledge of the OCaml language. Notice that the Why3 library must be installed, see Section 4.1.2. The OCaml code given below is available in the source distribution in directory examples/use_api/ together with a few other examples.

3.1  Building Propositional Formulas

The first step is to know how to build propositional formulas. The module Term gives a few functions for building these. Here is a piece of OCaml code for building the formula true ∨ false.

The library uses the common type term both for terms (i.e. expressions that produce a value of some particular type) and formulas (i.e. boolean-valued expressions).

Such a formula can be printed using the module Pretty providing pretty-printers.

Assuming the lines above are written in a file f.ml, it can be compiled using

ocamlfind ocamlc -package why3 -linkpkg f.ml -o f

Running the generated executable f results in the following output.

formula 1 is: true \/ false

Let us now build a formula with propositional variables: A ∧ B → A. Propositional variables must be declared first before using them in formulas. This is done as follows.

The type lsymbol is the type of function and predicate symbols (which we call logic symbols for brevity). Then the atoms A and B must be built by the general function for applying a predicate symbol to a list of terms. Here we just need the empty list of arguments.

As expected, the output is as follows.

formula 2 is: A /\ B -> A

Notice that the concrete syntax of Why3 forbids function and predicate names to start with a capital letter (except for the algebraic type constructors which must start with one). This constraint is not enforced when building those directly using library calls.

3.2  Building Tasks

Let us see how we can call a prover to prove a formula. As said in previous chapters, a prover must be given a task, so we need to build tasks from our formulas. Task can be build incrementally from an empty task by adding declaration to it, using the functions add_*_decl of module Task. For the formula true ∨ false above, this is done as follows.

To make the formula a goal, we must give a name to it, here “goal1”. A goal name has type prsymbol, for identifiers denoting propositions in a theory or a task. Notice again that the concrete syntax of Why3 requires these symbols to be capitalized, but it is not mandatory when using the library. The second argument of add_prop_decl is the kind of the proposition: Paxiom, Plemma or Pgoal. Notice that lemmas are not allowed in tasks and can only be used in theories.

Once a task is built, it can be printed.

The task for our second formula is a bit more complex to build, because the variables A and B must be added as abstract (i.e. not defined) propositional symbols in the task.

Execution of our OCaml program now outputs:

task 1 is:
theory Task
  goal Goal1 : true \/ false
end

task 2 is:
theory Task
  predicate A

  predicate B

  goal Goal2 : A /\ B -> A
end

3.3  Calling External Provers

To call an external prover, we need to access the Why3 configuration file why3.conf, as it was built using the why3config command line tool or the Detect Provers menu of the graphical IDE. The following API calls allow to access the content of this configuration file.

The type ’a Whyconf.Mprover.t is a map indexed by provers. A prover is a record with a name, a version, and an alternative description (to differentiate between various configurations of a given prover). Its definition is in the module Whyconf:

The map provers provides the set of existing provers. In the following, we directly attempt to access a prover named “Alt-Ergo”, any version.

We could also get a specific version with :

The next step is to obtain the driver associated to this prover. A driver typically depends on the standard theories so these should be loaded first.

We are now ready to call the prover on the tasks. This is done by a function call that launches the external executable and waits for its termination. Here is a simple way to proceed:

This way to call a prover is in general too naive, since it may never return if the prover runs without time limit. The function prove_task has an optional parameter limit, a record defined in module Call_provers:

where the field limit_time is the maximum allowed running time in seconds, and limit_mem is the maximum allowed memory in megabytes. The type prover_result is a record defined in module Call_provers:

with in particular the fields:

• pr_answer: the prover answer, explained below;
• pr_time : the time taken by the prover, in seconds.

A pr_answer is the sum type defined in module Call_provers:

corresponding to these kinds of answers:

• Valid: the task is valid according to the prover.
• Invalid: the task is invalid.
• Timeout: the prover exceeds the time limit.
• OutOfMemory: the prover exceeds the memory limit.
• Unknown msg: the prover can’t determine if the task is valid; the string parameter msg indicates some extra information.
• Failure msg: the prover reports a failure, e.g. it was unable to read correctly its input task.
• HighFailure: an error occurred while trying to call the prover, or the prover answer was not understood (e.g. none of the given regular expressions in the driver file matches the output of the prover).

Here is thus another way of calling the Alt-Ergo prover, on our second task.

The output of our program is now as follows.

On task 1, alt-ergo answers Valid (0.01s)
On task 2, alt-ergo answers Valid in  0.01 seconds

3.4  Building Terms

An important feature of the functions for building terms and formulas is that they statically guarantee that only well-typed terms can be constructed.

Here is the way we build the formula 2+2=4. The main difficulty is to access the internal identifier for addition: it must be retrieved from the standard theory Int of the file int.why.

An important point to notice as that when building the application of + to the arguments, it is checked that the types are correct. Indeed the constructor t_app_infer infers the type of the resulting term. One could also provide the expected type as follows.

When building a task with this formula, we need to declare that we use theory Int:

3.5  Building Quantified Formulas

To illustrate how to build quantified formulas, let us consider the formula ∀ x:int. x*x ≥ 0. The first step is to obtain the symbols from Int.

The next step is to introduce the variable x with the type int.

The formula x*x ≥ 0 is obtained as in the previous example.

To quantify on x, we use the appropriate smart constructor as follows.

3.6  Building Theories

We illustrate now how one can build theories. Building a theory must be done by a sequence of calls:

• creating a theory “under construction”, of type Theory.theory_uc;
• adding declarations, one at a time;
• closing the theory under construction, obtaining something of type Theory.theory.

Creation of a theory named My_theory is done by

First let us add formula 1 above as a goal:

Note that we reused the goal identifier goal_id1 that we already defined to create task 1 above.

Adding formula 2 needs to add the declarations of predicate variables A and B first:

Adding formula 3 is a bit more complex since it uses integers, thus it requires to “use” the theory int.Int. Using a theory is indeed not a primitive operation in the API: it must be done by a combination of an “export” and the creation of a namespace. We provide a helper function for that:

Addition of formula 3 is then

Addition of goal 4 is nothing more complex:

Finally, we close our theory under construction as follows.

We can inspect what we did by printing that theory:

which outputs

my new theory is as follows:

theory My_theory
  (* use BuiltIn *)

  goal goal1 : true \/ false

  predicate A

  predicate B

  goal goal2 : A /\ B -> A

  (* use int.Int *)

  goal goal3 : (2 + 2) = 4

  goal goal4 : forall x:int. (x * x) >= 0
end

From a theory, one can compute at once all the proof tasks it contains as follows:

Note that the tasks are returned in reverse order, so we reverse the list above.

We can check our generated tasks by printing them:

One can run provers on those tasks exactly as we did above.

3.7  Operations on Terms and Formulas, Transformations

The following code illustrates a simple recursive functions of formulas. It explores the formula and when a negation is found, it tries to push it down below a conjunction, a disjunction or a quantifier.

The following illustrates how to turn such an OCaml function into a transformation in the sense of the Why3 API. Moreover, it registers that transformation to make it available for example in Why3 IDE.

The directory src/transform contains the code for the many transformations that are already available in Why3.

3.8  Proof Sessions

See the example examples/use_api/create_session.ml of the distribution for an illustration on how to manipulate proof sessions from an OCaml program.

3.9  ML Programs

The simplest way to build WhyML programs from OCaml is to build untyped syntax trees for such programs, and then call the Why3 typing procedure to build typed declarations.

The examples of this section are available in the file examples/use_api/mlw_tree.ml of the distribution.

The first step is to build an environment as already illustrated in Section 3.3, and open the OCaml module Ptree which contains most of the OCaml functions we need in this section.

To contain all the example programs we are going to build we need a module. We start the creation of that module using the following declarations, that first introduces a pseudo “file” to hold the module, then the module itself called Program.

Notice the use of a first simple helper function mk_ident to build an identifier without any attributes nor any location.

To write our programs, we need to import some other modules from the standard library. The following introduces two helper functions for building qualified identifiers and importing modules, and finally imports int.Int.

We want now to build a program equivalent to the following code in concrete Why3 syntax.

The OCaml code that programmatically build this Why3 function is as follows.

This code makes uses of helper functions that are given in Figure 3.1.

---

let mk_expr e = { expr_desc = e; expr_loc = Loc.dummy_position } let mk_term t = { term_desc = t; term_loc = Loc.dummy_position } let mk_pat p = { pat_desc = p; pat_loc = Loc.dummy_position } let pat_var id = mk_pat (Pvar id) let mk_var id = mk_term (Tident (Qident id)) let param0 = [Loc.dummy_position, None, false, Some (PTtuple [])] let param1 id ty = [Loc.dummy_position, Some id, false, Some ty] let mk_tconst s = mk_term (Tconst Number.(ConstInt { ic_negative = false ; ic_abs = int_literal_dec s })) let mk_econst s = mk_expr (Econst Number.(ConstInt { ic_negative = false ; ic_abs = int_literal_dec s })) let mk_tapp f l = mk_term (Tidapp(f,l)) let mk_eapp f l = mk_expr (Eidapp(f,l)) let mk_evar x = mk_expr(Eident(Qident x))

Figure 3.1: Helper functions for building WhyML programs

---

We want now to build a program equivalent to the following code in concrete Why3 syntax.

We need to import the ref.Ref module first. The rest is similar to the first example, the code is as follows

The next example makes use of arrays.

The corresponding OCaml code is as follows

Having declared all the programs we wanted to write, we can now close the module and the file, and get as a result the set of modules of our file, under the form of a map of module names to modules.

We can then construct the proofs tasks for our module, and then try to call the Alt-Ergo prover. The rest of that code is using OCaml functions that were already introduced before.