arbitrary

The arbitrary library defines an arbitrary category providing predicates for generating random values for selected types to the type object, complementing its type checking predicates. Both the object and the category predicates can be extended by the user with definitions for new types by defining clauses for multifile predicates. This library is notably used in the QuickCheck implementation by the lgtunit tool. See also the documentation of the mutations library for related functionality.

API documentation

Open the ../../docs/library_index.html#arbitrary link in a web browser.

Loading

To load all entities in this library, load the loader.lgt file:

| ?- logtalk_load(arbitrary(loader)).

Testing

To test this library predicates, load the tester.lgt file:

| ?- logtalk_load(arbitrary(tester)).

Pre-defined types

This library defines random generators for most common Logtalk and Prolog types. See the API documentation for a listing of all the pre-defined types.

Usage

The arbitrary category complements the type object and thus its predicates are accessed via this object. For example:

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = -816
yes

To define a generator of arbitrary values for a type, define a clause for the arbitrary::arbitrary/1 multifile predicate specifying the type and a clause for the arbitrary::arbitrary/2 multifile predicate generating an arbitrary term of the specified type. As a simple example, assume that we want to define an “odd integer type”. We start by defining both the type checker and the arbitrary generator:

:- multifile(type::type/1).
type::type(odd).

:- multifile(type::check/2).
type::check(odd, Term) :-
    (   var(Term) ->
        throw(instantiation_error)
    ;   integer(Term),
        Term mod 2 =:= 1 ->
        true
    ;   throw(type_error(odd, Term))
    ).

:- multifile(arbitrary::arbitrary/1).
arbitrary::arbitrary(odd).

:- multifile(arbitrary::arbitrary/2).
arbitrary::arbitrary(odd, Arbitrary) :-
    type::arbitrary(integer, Arbitrary0),
    (   Arbitrary0 mod 2 =:= 1 ->
        Arbitrary = Arbitrary0
    ;   Arbitrary is Arbitrary0 + 1
    ).

We can also define a clause for the arbitrary::shrinker/1 multifile predicate to declare a new shrinker and a arbitrary::shrink/3 multifile predicate for shrinking arbitrary values for QuickCheck usage:

:- multifile(arbitrary::shrinker/1).
arbitrary::shrinker(odd).

:- multifile(arbitrary::shrink/3).
arbitrary::shrink(odd, Large, Small) :-
    integer(Large),
    (   Large < -1 ->
        Small is Large + 2
    ;   Large > 1,
        Small is Large - 2
    ).

Definitions for the shrink/3 predicate should either succeed or fail but never throw an exception.

It is also possible to define edge cases for a given type for use with QuickCheck implementations. For example:

:- multifile(arbitrary::edge_case/2).
arbitrary::edge_case(odd,  1).
arbitrary::edge_case(odd, -1).

Edge cases are tried before resorting to generating arbitrary values for a type.

A more complex example is generating arbitrary values for a recursive type. A simple example of a recursive type is a binary tree. Assuming that we are working with a binary tree holding integers where each node is represented by a node(Left, Right) compound term, we can define a node(Depth) type where Depth is the maximum depth of the tree. This argument allows us to prevent excessively deep trees:

:- category(binary_tree).

    :- multifile(type::type/1).
    type::type(node(_)).

    :- multifile(type::check/2).
    type::check(node(_), Term) :-
        (   check(Term) ->
            true
        ;   var(Term) ->
            throw(instantiation_error)
        ;   throw(type_error(node(_), Term))
        ).

    check(Term) :-
        (   integer(Term) ->
            true
        ;   compound(Term),
            Term = node(Left, Right),
            check(Left),
            check(Right)
        ).

    :- multifile(arbitrary::arbitrary/1).
    arbitrary::arbitrary(node(_)).

    :- multifile(arbitrary::arbitrary/2).
    arbitrary::arbitrary(node(Depth), Arbitrary) :-
    (   Depth > 1 ->
        NewDepth is Depth - 1,
        type::arbitrary(
            types_frequency([
                integer - 1,
                compound(
                    node,
                    [
                        types([node(NewDepth), integer]),
                        types([node(NewDepth), integer])
                    ]
                ) - 3
            ]),
            Arbitrary
        )
    ;   type::arbitrary(
    integer, Arbitrary)
    ).

:- end_category.

In this second example, we use some of the pre-defined types provided by the library. The types_frequency(Pairs) type supports generating random terms for a type in the Type-Frequency pairs list where the type ie randomly chosen after the types relative frequency. The compound(Name, Types) type supports generating compound term with a given name and random arguments after the given types:

| ?- type::arbitrary(node(4), Arbitrary).
Arbitrary = 907
yes

| ?- type::arbitrary(node(4), Arbitrary).
Arbitrary = node(node(node(522, 509), node(83, 453)), node(454, -197))
yes

| ?- type::arbitrary(node(4), Arbitrary).
Arbitrary = node(node(-875, -866), -254)
yes

| ?- type::arbitrary(node(4), Arbitrary).
Arbitrary = node(-133, -831)
yes

The source code of these examples can be found in the test_files/custom.lgt file. Other examples of arbitrary term generators can be found in the implementation of the optionals and expecteds libraries.

Reproducing sequences of arbitrary terms

The arbitrary category provides access to the pseudo-random generator it uses via the get_seed/1 and set_seed/1. This allows sequences of arbitrary values to be reproduced. For example:

| ?- type::get_seed(Seed).
Seed = seed(3172, 9814, 20125)
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = -816
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = -113
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = 446

| ?- type::set_seed(seed(3172, 9814, 20125)).
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = -816
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = -113
yes

| ?- type::arbitrary(integer, Arbitrary).
Arbitrary = 446
yes

The seed should be regarded as an opaque term and handled using the get_seed/1 and set_seed/1 predicates. These predicates are notably used in the QuickCheck implementation provided by the lgtunit tool.

Known issues

Some Prolog systems either don’t support the null character or provide buggy results when calling char_code/2 with a code of zero. When that’s the case, the null character is excluded when generating arbitrary characters or character codes.

Generating arbitrary Unicode characters (instead of Unicode codepoints) is inherently problematic as the process first generates codepoints and then tries to use the standard char_code/2 to convert them to characters. But, depending on the backend Prolog system and its internal (if any) Unicode normalization, it may not be possible to convert a codepoint to a single character.