HOPES is a prototype interpreter for a higher-order PROLOG-like language.
The syntax of the language extends that of PROLOG by supporting higher-order constructs (such as higher-order predicate variables, partial application and lambda terms). In particular, the syntax allows clauses (and queries) that contain uninstantiated predicate variables. The interpreter implements a higher-order top-down SLD-resolution proof procedure described in CKRW13 together with the semantics of the language.
HOPES has all the advantages of a higher-order system but continues to keep the flavor of classical PROLOG programming.
In HOPES one can express popular functional operators such as map:
map(R,[],[]).
map(R,[X|Xs],[Y|Ys]) :- R(X,Y), map(R,Xs,Ys).Apart from using functional operators in a logic programming context, we can also express naturally relational operators and graph operators:
join(R,Q)(X) :- R(X), Q(X).
union(R,Q)(X) :- R(X).
union(R,Q)(X) :- Q(X).
singleton(Y)(X) :- X = Y.
diff(R,Q)(X) :- R(X), not(Q(X)).
tc(G)(X,Y) :- G(X,Y).
tc(G)(X,Y) :- G(X,Z), tc(G)(Z,Y).The definition of higher-order predicates together with the use of partial
applications can lead to a different programming style that blends the
functional and the logic programming. The following HOPES snipset shows how we
can define except (i.e. the predicate that succeeds for all elements of R
except Y) by reusing (possibly) partially applied operators.
except(R,Y)(X) :- diff(R, singleton(Y)).As in classical PROLOG it is not required to use in a query some variables as input and some variables as output. Along that lines, HOPES also support queries that may have unbound predicate variables. For example, one can query
?- tc(G)(a,b).
to ask for potential graphs G whose transitive closure contains (a,b). In
that case the interpreter will systematically (and in a sophisticated way)
investigate all finite instantiations of these variables. The answers will be
sets that represent the extension of G even if no such predicate is
currently defined in the program. For example, potential answers of the
aforementioned query will be:
G = { (a,b) } ;
G = { (a,X1), (X1,b) } ;
G = { (a,X1), (X1,X2), (X2,b) };
In order to build HOPES you must should install haskell stack.
$ curl -sSL https://get.haskellstack.org/ | sh
$ stack buildMicrosoft Windows compilations are not yet tested but there should be no problem as far as GHC and cabal are installed in the system.
In pl/examples directory there are some hopes examples to getting started. To load an example you must type
-? :l pl/examples/file.pl