Mercury: This predicate works if declared at the top level, but not as a lambda

Question

(The excerpt below is from this test suite, which is half of the two-file program found here.)

I've defined an auxiliary predicate in two ways: once at the top level (called helper), and once as a lambda (called Helper). In the last three lines of the code below, I use that auxiliary predicate. If I use helper it works, but if I use Helper I get an error (below).

I suspect the problem might be that I am able to specify a type signature as well as a mode signature for the type-level predicate, but only a mode signature for the lambda. (If that's the problem, I don't know what to do about it.)

Here's the relevant code:

:- pred helper( query, int ).
:- mode helper( in, out ) is nondet.
helper( Q, F ) :-
  inQuery( fiveNumberSpace, Q, F ).

testQAnd = Res :-
    QQF = qqFind( qFind( list.filter( <(3) ) ) )
  , QQC = qqCond( qCond( func( Int )
                         = (if Int > 4 then no else yes) ) )
  , Helper = ( pred( Q :: in, F :: out ) is nondet :-
               inQuery( fiveNumberSpace, Q, F ) )

  % TODO Why can't I use Helper instead of helper for these?
  , solutions( helper( qqAnd( [QQF     ] ) ) , F1 )
  , solutions( helper( qqAnd( [QQF, QQC] ) ) , F2 )
  , solutions( helper( qqAnd( [     QQC] ) ) , F3 )

Here's the error I get from using Helper:

Making Mercury/cs/test.c
test.m:098: In clause for function `testQAnd'/0:
test.m:098:   in argument 1 of call to predicate `solutions'/2:
test.m:098:   in unification of argument
test.m:098:   and term `Helper(V_34)':
test.m:098:   type error in argument(s) of higher-order term (with arity 1).
test.m:098:   Functor (Helper) has type `pred(query.query, int)',
test.m:098:   expected type was `((func V_13) = V_14)'.
** Error making `Mercury/cs/test.c'.

Answer 1

I don't have a complete answer to your question, but I believe this has something to do with currying the predicate. I wrote some test code which queries a small database of fish.

:- pred fish(string::out, int::out) is multi.
fish("Red", 1).
fish("Blue", 2).
fish("Green", 3).

This helper produces the same error as above:

Helper = (pred(S::in, L::out) is nondet :- fish(S, L)),
solutions(Helper("Red"), Sols)

This helper works fine:

Helper2 = (pred(X::out) is nondet :- fish("Red", X)),
solutions(Helper2, Sols)

I also tried wrapping the solutions function. This works fine:

:- func solutions_to(string) = list(int).
solutions_to(Color) = Answers :-
  P = (pred(X::out) is nondet :- fish(Color, X)),
  solutions(P, Answers).

I was able to write a predicate that returned a lambda predicate, however I was unable to write a function to do the same. This is where I start to get confused. According to this page it is only possible to return a predicate with mode information if you wrap the predicate in a discriminated union type. The following code isn't really useful, but it manages to both

1. implement a poor-man's currying of a lambda
2. returns a lambda predicate from a function

See:

:- type inner
  ---> inner(pred(string:: out, int::out) is multi).
:- type wrapper
  ---> wrapper(pred(int::out) is nondet).

:- func make_pred(inner, string) = wrapper.
make_pred(Inner, Param) = P :-
  Inner = inner(I),
  P = wrapper(pred(X::out) is nondet :- I(Param, X)).

And then to use it:

Inner = inner((pred(X::out, Y::out) is multi :- fish(X, Y))),
WP = make_pred(Inner, "Red"),
WP = wrapper(P),
solutions(P, Sols),