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    1/*  Part of SWI-Prolog
    2
    3    Author:        Jan Wielemaker
    4    E-mail:        J.Wielemaker@vu.nl
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c)  2010-2011, VU University Amsterdam
    7    All rights reserved.
    8
    9    Redistribution and use in source and binary forms, with or without
   10    modification, are permitted provided that the following conditions
   11    are met:
   12
   13    1. Redistributions of source code must retain the above copyright
   14       notice, this list of conditions and the following disclaimer.
   15
   16    2. Redistributions in binary form must reproduce the above copyright
   17       notice, this list of conditions and the following disclaimer in
   18       the documentation and/or other materials provided with the
   19       distribution.
   20
   21    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   22    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   23    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   24    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
   25    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
   26    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
   27    BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   28    LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
   29    CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   30    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
   31    ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   32    POSSIBILITY OF SUCH DAMAGE.
   33*/
   34
   35:- module(coinduction,
   36          [ (coinductive)/1,
   37            op(1150, fx, (coinductive))
   38          ]).   39:- autoload(library(error),[instantiation_error/1,must_be/2]).

Co-Logic Programming

This simple module implements the directive coinductive/1 as described in "Co-Logic Programming: Extending Logic Programming with Coinduction" by Luke Simon et al. The idea behind coinduction is that a goal succeeds if it unifies to a parent goal. This enables some interesting programs, notably on infinite trees (cyclic terms).

:- use_module(library(coinduction)).

:- coinductive p/1.

p([1|T]) :- p(T).

This predicate is true for any cyclic list containing only 1-s, regardless of the cycle-length.

See also: - "Co-Logic Programming: Extending Logic Programming with Coinduction" by Luke Simon et al. */
bug: - Programs mixing normal predicates and coinductive predicates must be stratified. The theory does not apply to normal Prolog calling coinductive predicates, calling normal Prolog predicates, etc.
Stratification is not checked or enforced in any other way and thus left as a responsibility to the user.

   71:- multifile
   72    system:term_expansion/2,
   73    coinductive_declaration/2.      % Head, Module

head(+Term, -QHead) is semidet: Must be first to allow reloading!

   79head(Var, _) :-
   80    var(Var), !, fail.
   81head((H:-_B), Head) :-
   82    !,
   83    head(H, Head).
   84head(H, Head) :-
   85    (   H = _:_
   86    ->  Head = H
   87    ;   prolog_load_context(module, M),
   88        Head = M:H
   89    ).

coinductive(:Spec): The declaration :- coinductive name/arity, ... defines predicates as coinductive. The predicate definition is wrapped such that goals unify with their ancestors. This directive must precede all clauses of the predicate.

   98coinductive(Spec) :-
   99    throw(error(context_error(nodirective, coinductive(Spec)), _)).
  100
  101expand_coinductive_declaration(Spec, Clauses) :-
  102    prolog_load_context(module, Module),
  103    phrase(expand_specs(Spec, Module), Clauses).
  104
  105expand_specs(Var, _) -->
  106    { var(Var),
  107      !,
  108      instantiation_error(Var)
  109    }.
  110expand_specs(M:Spec, _) -->
  111    !,
  112    expand_specs(Spec, M).
  113expand_specs((A,B), Module) -->
  114    !,
  115    expand_specs(A, Module),
  116    expand_specs(B, Module).
  117expand_specs(Head, Module) -->
  118    { valid_pi(Head, Name, Arity),
  119      functor(GenHead, Name, Arity)
  120    },
  121    [ coinduction:coinductive_declaration(GenHead, Module) ].
  122
  123
  124valid_pi(Name/Arity, Name, Arity) :-
  125    must_be(atom, Name),
  126    must_be(integer, Arity).

wrap_coinductive(+Head, +Term, -Clauses) is det: Create a wrapper. The first clause deal with the case where we already created the wrapper. The second creates the wrapper and the first clause.

  135wrap_coinductive(Pred, Term, Clause) :-
  136    current_predicate(_, Pred),
  137    !,
  138    rename_clause(Term, 'coinductive ', Clause).
  139wrap_coinductive(Pred, Term, [Wrapper_1,Wrapper_2,FirstClause]) :-
  140    Pred = M:Head,
  141    functor(Head, Name, Arity),
  142    length(Args, Arity),
  143    GenHead =.. [Name|Args],
  144    atom_concat('coinductive ', Name, WrappedName),
  145    WrappedHead =.. [WrappedName|Args],
  146    Wrapper_1 = (GenHead :-
  147                    prolog_current_frame(F),
  148                    prolog_frame_attribute(F, parent, FP),
  149                    prolog_frame_attribute(FP, parent_goal, M:GenHead)),
  150    Wrapper_2 = (GenHead :- WrappedHead, coinduction:no_lco),
  151    rename_clause(Term, 'coinductive ', FirstClause).
  152
  153:- public no_lco/0.  154
  155no_lco.                                 % true, but do not optimize away

rename_clause(+Clause, +Prefix, -Renamed) is det: Rename a clause by prefixing its old name wit h Prefix.

  161rename_clause((Head :- Body), Prefix, (NewHead :- Body)) :-
  162    !,
  163    rename_clause(Head, Prefix, NewHead).
  164rename_clause(M:Head, Prefix, M:NewHead) :-
  165    rename_clause(Head, Prefix, NewHead).
  166rename_clause(Head, Prefix, NewHead) :-
  167    Head =.. [Name|Args],
  168    atom_concat(Prefix, Name, WrapName),
  169    NewHead =.. [WrapName|Args].
  170
  171
  172                 /*******************************
  173                 *        EXPANSION HOOKS       *
  174                 *******************************/
  175
  176system:term_expansion((:- coinductive(Spec)), Clauses) :-
  177    expand_coinductive_declaration(Spec, Clauses).
  178system:term_expansion(Term, Wrapper) :-
  179    head(Term, Module:Head),
  180    coinductive_declaration(Head, Module),
  181    wrap_coinductive(Module:Head, Term, Wrapper)