Safer type tests in Prolog

Question

ISO-Prolog (ISO/IEC 13211-1:1995 including Cor.1:2007, Cor.2:2012) offers the following built-in predicates for testing the type of a term:

8.3 Type testing

1 var/1. 2 atom/1. 3 integer/1. 4 float/1. 5 atomic/1. 6 compound/1. 7 nonvar/1. 8 number/1. 9 callable/1. 10 ground/1. 11 acyclic_term/1.

Within this group there are those whose purpose is solely to test for a certain instantiation, that is 8.3.1 var/1, 8.3.7 nonvar/1, 8.3.10 ground/1, and those that assume that a term is sufficiently instantiated such that the type test is safe. Unfortunately, they are combined with testing for a concrete instantiation.

Consider the goal integer(X) which fails if X is a nonvar term that is not an integer and when X is a variable. This destroys many desirable declarative properties:

?- X = 1, integer(X).
   true.
?- integer(X), X = 1.
   false.

Ideally the second query would either succeed using some form of coroutining ; or it would issue an instantiation error¹ according to the error classification. After all:

7.12.2 Error classification

Errors are classified according to the form of Error_term:

a) There shall be an Instantiation Error when an
argument or one of its components is a variable, and an
instantiated argument or component is required. It has
the form instantiation_error.

...

Note that this implicit combination of instantiation testing and type testing leads to many errors in Prolog programs and also here on SO.

A quick fix to this situation would be to add an explicit test in front of every test built-in, either verbosely as

   ( nonvar(T) -> true ; throw(error(instantiation_error,_)) ),
   integer(T), ....

or more compactly as

functor(T, _,_),
integer(T), ....

it could be even

T =.. _,
integer(T), ...

My question is twofold:

How to provide this functionality on the user level?

and, to make this also a bit challenging:

What is the most compact implementation of a safer atomic/1 written in ISO-Prolog?

---

^{1 Other less desirable options would be to loop or to produce a resource error. Still preferable to an incorrect result.}

Answer 1

The testing for types needs to distinguish itself from the traditional "type testing" built-ins that implicitly also test for a sufficient instantiation. So we effectively test only for sufficiently instantiated terms (si). And if they are not sufficiently instantiated, an appropriate error is issued.

For a type nn, there is thus a type testing predicate nn_si/1 with the only error condition

a) If there is a θ and σ such that nn_si(Xθ) is true and nn_si(Xσ) is false
— instantiation_error.

atom_si(A) :-
   functor(A, _, 0),    % for the instantiation error
   atom(A).

integer_si(I) :-
   functor(I, _, 0),
   integer(I).

atomic_si(AC) :-
   functor(AC,_,0).

list_si(L) :-
   \+ \+ length(L, _),  % for silent failure
   sort(L, _).          % for the instantiation error

character_si(Ch) :-
   functor(Ch,Ch,0),
   atom(Ch),
   atom_length(Ch,1).

chars_si(Chs) :-
   \+ \+ length(Chs,_),
   \+ ( once(length(Chs,_)), member(Ch,Chs), nonvar(Ch), \+ character_si(Ch) ),
   \+ ( member(Ch,Chs), \+ character_si(Ch) ). % for the instantiation error

This is available as library(si) in Scryer.

In SWI, due to its differing behavior in length/2, use rather:

list_si(L) :-
    '$skip_list'(_, L, T),
    functor(T,_,_),
    T == [].

Answer 2

This is a very naive attempt at implementing both your suggested solutions.

First, has_type(Type, Var) that succeeds, or fails with an instantiation error:

has_type(Type, X) :-
    var(X), !,
    throw(error(instantiation_error, _)).
has_type(Type, X) :-
    nonvar_has_type(Type, X).

nonvar_has_type(atom, X) :- atom(X).
nonvar_has_type(integer, X) :- integer(X).
nonvar_has_type(compound, X) :- compound(X).
% etc

Second, a could_be(Type, Var) (analogy to must_be/2) that uses coroutining to allow the query to succeed at some point in the future:

could_be(Type, X) :-
    var(X), !,
    freeze_type(Type, X).
could_be(Type, X) :-
    nonvar_has_type(Type, X).

freeze_type(integer, X) :- freeze(X, integer(X)).
freeze_type(atom, X) :- freeze(X, atom(X)).
freeze_type(compound, X) :- freeze(X, compound(X)).
% etc

There are several weak points to this approach but your comments might help me understand the use cases better.

EDIT: On "types" in Prolog

Types in Prolog, as I understand them, are not "types": they are just information that can be queried at run time, and which exists because it is a useful leaky abstraction of the underlying implementation.

The only way I have been able to make practical use of a "type" has been to "tag" my variables, as in the compound terms number(1), number(pi), operator(+), date(2015, 1, 8), and so on. I can then put variables in there, write deterministic or semi-deterministic predicates, understand what my code means when I see it a week later....

So a free variable and an integer are just terms; mostly because, as your question very smartly points out, a free variable can become an integer, or an atom, or a compound term. You could use coroutining to make sure that a free variable can only become a certain "type" of term later, but this is still inferior to using compound terms, from a practical point of view.

It highly likely that I am confounding very different issues here; and to be honest, my experience with Prolog is limited at best. I just read the documentation of the implementation I am using, and try to find out the best way to use it to my advantage.