% --------------- GRIND ----------------
% (Prolog Grammar Rules IN Depth)
%
%  An investigation of grammar rules for 
%  standard Prolog (ISO/IEC 13211-3)

% (1) Load a file to simulate any features
% of Standard Prolog that are not in the
% system being tested, for example
%    consult(r382sics38).
% or
%    consult(r382sics21).
% or
%    consult(r382bim).
% 
% This file must also define a procedure
%    system_tested(A)
% where A is an atom identifying the
% system being tested. 

% (2) Load this file
%    consult(r382).

% (3) Run all tests (which sends the
% results to r382r1)
%    run_all_tests.

% (4) Check the results of the tests
% by running the program r382check

% Known errors
%   1) None

% To be done
%   xxx

% ----------- Define operators ---------
 
% None yet required
 
% -------- Utility predicates ---------

% ---------- Output predicates ---------

% write_list(L) outputs a message defined by L
write_list([]).
write_list([T | Tail]) :-
   ( T == nl ->
     nl  
   ; write(T)
   ),
   write_list(Tail).

% -------------------

% write_list_as_table(H, L)
%  outputs the heading H using
%  write_list/2 and then outputs each
%  element of L on a line by itself
%  using write_list/2
write_list_as_table(H, _) :-
   write_list(H),
   write_list([nl]),
   fail.
write_list_as_table(_, L) :-
   write_each_line_of_table(L).
write_each_line_of_table([]).
write_each_line_of_table([H | T]) :-
   write_list([H]),
   write_list([nl]),
   write_each_line_of_table(T).

% ---------- Run all tests -------------

% Test expand_term/2

run_1 :-
  test_gr(GR),
  expand_term(GR, EGR),
  write_list(['gr(( ']),
  writeq(GR),
  write_list([' ), ', nl, '    (']),
  writeq(EGR),
  write_list([')).', nl, nl]),
  fail.
run_1.

% Test whether required built-in procedures exist

run_2 :-
  test_gr_procs(GRP),
  findall(P, predicate_property(GRP, P),
    L),
  write_list(['grp(( ']),
  writeq(GRP),
  write_list([' ), ', nl, '    (']),
  writeq(L),
  write_list([')).', nl, nl]),
  fail.
run_2.

% Are grammar rule clauses consistent
%  with expand_term/2

run_3 :-
  clause(a(N, S0, S1), B1),
  write_list([nl]),
  writeq(( a(N, S0, S1) :- B1 )),
  write_list(['.', nl]),
  fail.
run_3 :-
   write_list([nl]).

run_all_tests :-
  open('r382r1', write, S),
  set_output(S),
  write_list([nl, ' :- dynamic (grind/1,
    gr/2, grp/2).', nl]),
  system_tested(SYS),
  write_list(['grind(']),
  writeq(SYS),
  write_list([').', nl]),
  run_1,
  run_2,
  write_list([nl, ':- dynamic a/3.',
    nl]),
  run_3,
  write_list([nl]),
  close(S, []).

% ----------- Test cases -----------

% Test cases (1) expand_term

test_gr(( a(1) --> b )).
test_gr(( a(2) --> [b] )).
test_gr(( a(3) --> [] )).
test_gr(( a(4) --> "b" )).
test_gr(( a(5) --> {b} )).
test_gr(( a(6) --> b, c )).
test_gr(( a(7) --> b ; c )).
test_gr(( a(8) --> b -> c )).
test_gr(( a(9) --> b1, b2 -> c ; d )).
test_gr(( a(10) --> b -> c1, c2 ; d )).
test_gr(( a(11) --> b -> c ; d1, d2 )).
test_gr(( a(12) --> b, !, c, d )).
test_gr(( a(13) --> b, !, c ; d )).
test_gr(( a(14) --> [abc, xyz] )).
test_gr(( a(15) --> [abc | xyz] )).
test_gr(( a(16) --> [_] )).
test_gr(( a(17) --> [[], {}, 3, 3.2,
    a(b)] )).
test_gr(( a(18) --> _ )).
test_gr(( a(19) --> '{}'((c,d)) )).
test_gr(( a(20) --> {c,d} )).
test_gr(( a(21), [t] --> b, c )).
test_gr(( a(22), [t] --> b, [t] )).
test_gr(( a(23), [t] --> b, [s, t] )).
test_gr(( a(24), [t] --> b, [s], [t] )).
test_gr(( a(25), [t], [t2] --> b, c )).
test_gr(( a(26), b --> c )).
test_gr(( [b], a(27) --> c )).
test_gr(( a(28) --> \+ b, c )).
test_gr(( a(29) --> true, c )).
test_gr(( a(30) --> false, c )).
test_gr(( a(31) --> b, \+ c, d )).
test_gr(( a(32, X) --> call(X), c )).
test_gr(( '[' --> b, c )).
test_gr(( '=' --> b, c )).
test_gr(( c(X) --> b(X) )).

% Test cases (2) Built-in predicates and 
%   user defined procedures 

test_gr_procs('C'(_, _, _)).
test_gr_procs(term_expansion(_, _)).
test_gr_procs(expand_term(_, _)).
test_gr_procs(phrase(_, _)).
test_gr_procs(phrase(_, _,_)).

% Test cases (3) Consulting grammar
%   rules

:- dynamic a/3.
:- dynamic '['/2.
:- dynamic a/4.

a(1) --> b.
a(2) --> [b].
a(3) --> [].
a(4) --> "b".
a(5) --> {b}.
a(6) --> b, c.
a(7) --> b ; c.
a(8) --> b -> c.
a(9) --> b1, b2 -> c ; d.
a(10) --> b -> c1, c2 ; d.
a(11) --> b -> c ; d1, d2.
a(12) --> b, !, c, d.
a(13) --> b, !, c ; d.
a(14) --> [abc, xyz].
a(15) --> [abc | xyz].
a(16) --> [_].
a(17) --> [[], {}, 3, 3.2, a(b)].
a(18) --> _.
a(19) --> '{}'((c,d)).
a(20) --> {c,d}.
a(21), [t] --> b, c.
a(22), [t] --> b, [t].
a(23), [t] --> b, [s, t].
a(24), [t] --> b, [s], [t].
a(25), [t], [t2] --> b, c.
a(26), b --> c.
[b], a(27) --> c.
a(28) --> \+ b, c.
a(29) --> true, c.
a(30) --> false, c.
a(31) --> b, \+ c, d.
a(32, X) --> call(X), c.

'[' --> b, c .
'=' --> b, c .
c(X) --> b(X) .

% A.2 Example of a file defining the required predicates (r382sics21)
% This file defines the system_tested/1 procedure and those built-in predicates that are defined in ISO standard Prolog, but not in the system being tested.
% system_tested('SICStus 2.1 # 9').

close(S, _) :-
  close(S).

% A.3 Check results from running GRIND (r382check)
% ----------- Check GRIND ------------
% (Prolog Grammar Rules IN Depth)
%
% Check an investigation of grammar
%  rules for  standard Prolog
%    (ISO/IEC 13211-3)

% (1) Load a file to simulate any
%  features of Standard Prolog that are
%  not in the system being tested, for
%  example
%   consult(r382sics38).
% or
%   consult(r382sics21).
% or
%   consult(r382bim).
%
% This file must also define a procedure
%   system_tested(A)
% where A is an atom identifying the
% system being tested. 

% (2) Load this file
%   consult(r382check).

% (3) Load the file of results obtained
% from running GRIND
%   consult(r382r1).

% (4) Checking the results.
%   run_all_checks.

% Known errors
%  1) None

% To be done
%  xxx

% --------- Define operators ---------

% None yet required

% --------- Utility predicates -------

% --------- Output predicates -------

% write_list(L) outputs a message
%   defined by L
write_list([]).
write_list([T | Tail]) :-
  ( T == nl ->
    nl  
  ; write(T)
  ),
  write_list(Tail).

% -------------------

% write_list_as_table(H, L)
%  outputs the heading H using
%  write_list/2 and then outputs each
%  element of L on a line by itself
%  using write_list/2
write_list_as_table(H, _) :-
  write_list(H),
  write_list([nl]),
  fail.
write_list_as_table(_, L) :-
  write_each_line_of_table(L).
write_each_line_of_table([]).
write_each_line_of_table([H | T]) :-
  write_list([H]),
  write_list([nl]),
  write_each_line_of_table(T).

% -------------------

expand(( a(1)-->b ), 
   (a(1, S0, S1):-b( S0, S1))).

expand(( a(2)-->[b] ), 
   (a(2, S0, S1):- 'C'( S0,b, S1))).

expand(( a(3)-->[] ),
   (a(3, S1, S2):- S2= S1)).

expand(( a(4)-->[98] ), 
   (a(4, S0, S1):- 'C'( S0,98, S1))).

expand(( a(5)-->{b} ), 
   (a(5, S0, S1):-b, S1= S0)).

expand(( a(6)-->b,c ), 
   (a(6, S1, S3):-b( S1, S2),c( S2, S3))).

expand(( a(7)-->b;c ), 
   (a(7, S1, S3):-b( S1, S3);c( S1, S3))).

expand(( a(8)-->b->c ), 
   (a(8, S1, S3):-b( S1, S2)->c( S2, S3))).

expand(( a(9)-->b1,b2->c;d ), 
   (a(9, S2, S5):-b1( S2, S3),b2( S3, S4)->c( S4, S5);d( S2, S5))).

expand(( a(10)-->b->c1,c2;d ), 
   (a(10, S2, S5):-b( S2, S3)->c1( S3, S4),c2( S4, S5);d( S2, S5))).

expand(( a(11)-->b->c;d1,d2 ), 
   (a(11, S2, S5):-b( S2, S3)->c( S3, S5);d1( S2, S4),d2( S4, S5))).

expand(( a(12)-->b,!,c,d ), 
   (a(12, S2, S5):-b( S2, S3),!,c( S3, S4),d( S4, S5))).

expand(( a(13)-->b,!,c;d ), 
   (a(13, S2, S5):-b( S2, S4),!,c( S4, S5);d( S2, S5))).

expand(( a(14)-->[abc,xyz] ),
   (a(14, T1, T3):-'C'( T1,abc, T2),'C'( T2,xyz, T3))).

expand(( a(15)-->[abc|xyz] ),
   (a(15,_1361,_1362):-'C'(_1361,abc, T2),xyz( T2,_1362))).

expand(( a(16)-->[_1343] ),
   (a(16,_1361,_1362):-'C'(_1361,_1343,_1362))).
 
expand(( a(17)-->[[],{},3,3.2,a(b)] ),
   (a(17,_1375,_1376):-'C'(_1375,[],_1396),'C'(_1396,{},_1389),'C'(_1389,3,_1382),'C'(_1382,3.2,_1378),'C'(_1378,a(b),_1376))).
 
expand(( a(18)-->_1347 ),
   (a(18, S1, S2):-phrase(_1347, S1, S2))).
 
expand(( a(19)-->{c,d} ),
   (a(19, T3,_1365):-(c,d),_1365= T3)).
 
expand(( a(20)-->{c,d} ),
   (a(20, T3,_1365):-(c,d),_1365= T3)).
 
expand(( a(21),[t]-->b,c ), 
   (a(21,_189, S2):-(b(_189,_195),c(_195,_200)), 'C'( S2,t,_200))).

expand(( a(22),[t]-->b,[t] ),
   (a(22,_1372,_1373):-
      (b(_1372,_1378),'C'(_1378,t,_1382)),'C'(_1373,t,_1382))).
 
expand(( a(23),[t]-->b,[s,t] ),
   (a(23,_1374,_1375):-
     (b(_1374,_1380),
     'C'(_1380,s,_1382),'C'(_1382,t,_1384)),'C'(_1375,t,_1384))).
 
expand(( a(24),[t]-->b,[s],[t] ),
   (a(24,_1377,_1378):-
     (b(_1377,_1383),
     'C'(_1383,s,_1387),'C'(_1387,t,_1391)),'C'(_1378,t,_1391))).

expand(( a(25),[t],[t2]-->b,c ), 
   (a(25,_194,_195):-
     (b(_194,_200),c(_200,_205)), 'C'(_195,t,_212), 'C'(_212,t2,_205))).

expand(( a(26),b-->c ),
   (a(26,_1365, T2):-c(_1365,_1371),b( T2,_1371))).
 
expand(( [b],a(27)-->c ),
   ('.'(b,[],_1368,_1369):-c(_1368,_1374),a(27,_1369,_1374))).

expand(( a(28)--> \+b,c ),
   (a(28,_608,_609):-(b(_608,_619)->fail;_617=_608),c(_617,_609))).
 
expand(( a(29)-->true,c ),
   (a(29,_606,_607):-true(_606,_612),c(_612,_607))).
 
expand(( a(30)-->false,c ),
   (a(30,_606,_607):-false(_606,_612),c(_612,_607))).
 
expand(( a(31)-->b,\+c,d ),
   (a(31,_611,_612):-
      b(_611,_617),(c(_617,_627)->fail;_625=_617),d(_625,_612))).
 
expand(( a(32,_574)-->call(_574),c ),
   (a(32,_574,_610,_611):-call(_574,_610,_617),c(_617,_611))).
 

expand(( '[' -->b,c ), 
   ('['( S1, S3):-b( S1, S2),c( S2, S3))).

expand(( '=' -->b,c ), 
   ('='( S1, S3):-b( S1, S2),c( S2, S3))).

expand(( c(_168)-->b(_168) ), 
   (c(_168,_183,_184):-b(_168,_183,_184))).

bip( 'C'(_175,_176,_177) ).

bip( term_expansion(_175,_176) ). 

bip( expand_term(_175,_176) ). 

bip( phrase(_175,_176) ). 

bip( phrase(_175,_176,_177) ). 

% ---------------- ----------------

% Check the results 

% ---------------- ----------------

output_system_tested :-
  grind(Sys),
  system_tested(S),
  write_list([nl,
    'Checking Grammar Rules in ']),
  write_list(['system ', Sys, nl,
    '   using ']),
  write_list(['system ', S, nl]).

check_expand_term :-
  write_list([nl, 
    '(1) - Does expand_term/3']),
  write_list([' work as expected?',
     nl]),
  clause(gr(T, ET1), true),
  ( expand(T, ET) ->
    ( ET = ET1 ->
      write_list(['  ok - expanding ',
        T, nl])
    ;
      write_list([' fail- expanding ',
        T, nl]),
      write_list(['   correct = ', ET,
        nl]),
      write_list(['   wrong   = ', ET1,
        nl])
    )
  ;
    write_list(['  ?? - expanding ', T,
        nl])
  ),
  fail.
check_expand_term :-
  expand(T, _),
  \+ clause(gr(T, _), true),
  write_list([
    ' not tested - expanding ', T, nl]),
  fail.
check_expand_term.

check_existence_of_procedures :-
  write_list([nl, 
    '(2a) - The following procedures']),
  write_list([' exist in the system',
     nl]),
  grp(BIP, Property_list),
  functor(BIP, F, N),
  write_list([' ', F, '/', N, ' - ']),
  write_list([Property_list, nl]),
  fail.
check_existence_of_procedures :-
  write_list([nl,
    '(2b) - The following procedures ',
    'do not exist in the system', nl]),
  bip(BIP),
  \+ grp(BIP, _),
  functor(BIP, F, N),
  write_list([' ', F, '/', N]),
  fail.
check_existence_of_procedures.

check_grammar_rule_clauses :-
  write_list([nl, '(3) - Are grammar ',
    'rule clauses consistent ',
    'with expand_term/3?', nl]),
  check_grammar_rule_clauses(_).
check_grammar_rule_clauses.

check_grammar_rule_clauses(N) :-
  clause(a(N, S0, S1), ET),
  expand((a(N) --> B), EB),
  ( ( a(N, S0, S1) :- EB ) = ET ->
    write_list([nl, '  ok - a(', N,
      ')'])
  ; write_list([nl, ' fail- ', a(N),
      ' --> ', B]),
    write_list([nl, '   expected:',
      a(N, S0, S1), ' :- ', EB]),
    write_list([nl, '   expanded:', ET])
  ),
  fail.

run_all_checks :-
  open('r382c1', write, S),
  set_output(S),
  output_system_tested,
  check_expand_term,
  check_existence_of_procedures,
  check_grammar_rule_clauses,
  write_list([nl]),
  close(S, []).

% A.3 Running GRIND - An example
% GRIND was run on SICStus 3.8 with the following results. It was necessary to comment out tests 15, 25, 26, 27 because they gave errors. The following results show what happened after this was done.
% A.3.1 Define system_tested/1 for SICStus 3.8 (r382sics38)
% system_tested('SICStus 3.8 (sparc-solaris-5.5.1)').
% A.3.2 Results from GRIND (r382r1)

:- dynamic (grind/1, gr/2, grp/2).
grind('SICStus 3.8 (sparc-solaris-5.5.1)').
gr(( a(1)-->b ), 
   (a(1,_603,_604):-b(_603,_604))).

gr(( a(2)-->[b] ), 
   (a(2,_605,_606):-'C'(_605,b,_606))).

gr(( a(3)-->[] ), 
   (a(3,_603,_604):-_604=_603)).

gr(( a(4)-->[98] ), 
   (a(4,_605,_606):-'C'(_605,98,_606))).

gr(( a(5)-->{b} ), 
   (a(5,_605,_606):-b,_606=_605)).

gr(( a(6)-->b,c ), 
   (a(6,_606,_607):-b(_606,_612),c(_612,_607))).

gr(( a(7)-->b;c ), 
   (a(7,_606,_607):-b(_606,_607);c(_606,_607))).

gr(( a(8)-->b->c ), 
   (a(8,_606,_607):-b(_606,_615)->c(_615,_607))).

gr(( a(9)-->b1,b2->c;d ), 
   (a(9,_612,_613):-b1(_612,_624),b2(_624,_629)->c(_629,_613);d(_612,_613))).

gr(( a(10)-->b->c1,c2;d ), 
   (a(10,_612,_613):-b(_612,_624)->c1(_624,_629),c2(_629,_613);d(_612,_613))).

gr(( a(11)-->b->c;d1,d2 ), 
   (a(11,_612,_613):-b(_612,_624)->c(_624,_613);d1(_612,_634),d2(_634,_613))).

gr(( a(12)-->b,!,c,d ), 
   (a(12,_612,_613):-b(_612,_618),!,c(_618,_623),d(_623,_613))).

gr(( a(13)-->b,!,c;d ), 
   (a(13,_612,_613):-b(_612,_621),!,c(_621,_613);d(_612,_613))).

gr(( a(14)-->[abc,xyz] ), 
   (a(14,_607,_608):-'C'(_607,abc,_612),'C'(_612,xyz,_608))).

gr(( a(16)-->[_567] ), 
   (a(16,_605,_606):-'C'(_605,_567,_606))).

gr(( a(17)-->[[],{},3,3.2,a(b)] ), 
   (a(17,_619,_620):-'C'(_619,[],_642),'C'(_642,{},_635),'C'(_635,3,_628),'C'(_628,3.2,_624),'C'(_624,a(b),_620))).

gr(( a(18)-->_571 ), 
   (a(18,_603,_604):-phrase(_571,_603,_604))).

gr(( a(19)-->{c,d} ), 
   (a(19,_608,_609):-(c,d),_609=_608)).

gr(( a(20)-->{c,d} ), 
   (a(20,_608,_609):-(c,d),_609=_608)).

gr(( a(21),[t]-->b,c ), 
   (a(21,_614,_615):-(b(_614,_620),c(_620,_625)),'C'(_615,t,_625))).

gr(( a(22),[t]-->b,[t] ), 
   (a(22,_616,_617):-(b(_616,_622),'C'(_622,t,_628)),'C'(_617,t,_628))).

gr(( a(23),[t]-->b,[s,t] ), 
   (a(23,_618,_619):-(b(_618,_624),'C'(_624,s,_628),'C'(_628,t,_630)),'C'(_619,t,_630))).

gr(( a(24),[t]-->b,[s],[t] ), 
   (a(24,_621,_622):-(b(_621,_627),'C'(_627,s,_633),'C'(_633,t,_639)),'C'(_622,t,_639))).

gr(( a(28)--> \+b,c ), 
   (a(28,_608,_609):-(b(_608,_619)->fail;_617=_608),c(_617,_609))).

gr(( a(29)-->true,c ), 
   (a(29,_606,_607):-true(_606,_612),c(_612,_607))).

gr(( a(30)-->false,c ), 
   (a(30,_606,_607):-false(_606,_612),c(_612,_607))).

gr(( a(31)-->b,\+c,d ), 
   (a(31,_611,_612):-b(_611,_617),(c(_617,_627)->fail;_625=_617),d(_625,_612))).

gr(( a(32,_574)-->call(_574),c ), 
   (a(32,_574,_610,_611):-call(_574,_610,_617),c(_617,_611))).

gr(( '['-->b,c ), 
   ('['(_603,_604):-b(_603,_609),c(_609,_604))).

gr(( = -->b,c ), 
   (_603=_604:-b(_603,_609),c(_609,_604))).

gr(( c(_570)-->b(_570) ), 
   (c(_570,_605,_606):-b(_570,_605,_606))).

grp(( 'C'(_581,_582,_583) ), 
   ([built_in])).

grp(( term_expansion(_581,_582) ), 
   ([])).

grp(( expand_term(_581,_582) ), 
   ([built_in])).

grp(( phrase(_581,_582) ), 
   ([(meta_predicate phrase(:,?)),built_in])).

grp(( phrase(_581,_582,_583) ), 
   ([(meta_predicate phrase(:,?,?)),built_in])).


:- dynamic a/3.

a(1,_668,_669):-b(_668,_669).

a(2,_668,_669):-'C'(_668,b,_669).

a(3,_668,_669):-_669=_668.

a(4,_668,_669):-'C'(_668,98,_669).

a(5,_668,_669):-b,_669=_668.

a(6,_668,_669):-b(_668,_696),c(_696,_669).

a(7,_668,_669):-b(_668,_669);c(_668,_669).

a(8,_668,_669):-b(_668,_696)->c(_696,_669).

a(9,_668,_669):-b1(_668,_702),b2(_702,_699)->c(_699,_669);d(_668,_669).

a(10,_668,_669):-b(_668,_705)->c1(_705,_699),c2(_699,_669);d(_668,_669).

a(11,_668,_669):-b(_668,_705)->c(_705,_669);d1(_668,_696),d2(_696,_669).

a(12,_668,_669):-b(_668,_705),!,c(_705,_696),d(_696,_669).

a(13,_668,_669):-b(_668,_702),!,c(_702,_669);d(_668,_669).

a(14,_668,_669):-'C'(_668,abc,_698),'C'(_698,xyz,_669).

a(16,_668,_669):-'C'(_668,_693,_669).

a(17,_668,_669):-'C'(_668,[],_725),'C'(_725,{},_718),'C'(_718,3,_711),'C'(_711,3.2,_704),'C'(_704,a(b),_669).

a(18,_668,_669):-phrase(user:_693,_668,_669).

a(19,_668,_669):-(c,d),_669=_668.

a(20,_668,_669):-(c,d),_669=_668.

a(21,_668,_669):-(b(_668,_700),c(_700,_697)),'C'(_669,t,_697).

a(22,_668,_669):-(b(_668,_701),'C'(_701,t,_698)),'C'(_669,t,_698).

a(23,_668,_669):-(b(_668,_708),'C'(_708,s,_702),'C'(_702,t,_698)),'C'(_669,t,_698).

a(24,_668,_669):-(b(_668,_708),'C'(_708,s,_702),'C'(_702,t,_698)),'C'(_669,t,_698).

a(28,_668,_669):-(b(_668,_699)->fail;_695=_668),c(_695,_669).

a(29,_668,_669):-true(_668,_696),c(_696,_669).

a(30,_668,_669):-false(_668,_696),c(_696,_669).

a(31,_668,_669):-b(_668,_711),(c(_711,_699)->fail;_695=_711),d(_695,_669).


/* A3.3 Report produced by checking GRIND (r382c1) 
  Checking Grammar Rules in system SICStus 3.8 (sparc-solaris-5.5.1)
  using system SICStus 3.8 (sparc-solaris-5.5.1)

(1) - Does expand_term/3 work as expected?
  ok - expanding a(1)-->b
  ok - expanding a(2)-->[b]
  ok - expanding a(3)-->[]
  ok - expanding a(4)-->[98]
  ok - expanding a(5)-->{b}
  ok - expanding a(6)-->b,c
  ok - expanding a(7)-->b;c
  ok - expanding a(8)-->b->c
  ok - expanding a(9)-->b1,b2->c;d
  ok - expanding a(10)-->b->c1,c2;d
  ok - expanding a(11)-->b->c;d1,d2
  ok - expanding a(12)-->b,!,c,d
  ok - expanding a(13)-->b,!,c;d
  ok - expanding a(14)-->[abc,xyz]
  ok - expanding a(16)-->[_886]
  ok - expanding a(17)-->[[],{},3,3.2,a(b)]
  ok - expanding a(18)-->_890
  ok - expanding a(19)-->{c,d}
  ok - expanding a(20)-->{c,d}
  ok - expanding a(21),[t]-->b,c
  ok - expanding a(22),[t]-->b,[t]
  ok - expanding a(23),[t]-->b,[s,t]
  ok - expanding a(24),[t]-->b,[s],[t]
  ok - expanding a(28)--> \+b,c
  ok - expanding a(29)-->true,c
  ok - expanding a(30)-->false,c
  ok - expanding a(31)-->b,\+c,d
  ok - expanding a(32,_900)-->call(_900),c
  ok - expanding [-->b,c
  ok - expanding = -->b,c
  ok - expanding c(_889)-->b(_889)
 not tested - expanding a(15)-->[abc|xyz]
 not tested - expanding a(25),[t],[t2]-->b,c
 not tested - expanding a(26),b-->c
 not tested - expanding [b],a(27)-->c

(2a) - The following procedures exist in the system
 C/3 - [built_in]
 term_expansion/2 - []
 expand_term/2 - [built_in]
 phrase/2 - [(meta_predicate phrase(:,?)),built_in]
 phrase/3 - [(meta_predicate phrase(:,?,?)),built_in]

(2b) - The following procedures do not exist in the system

(3) - Are grammar rule clauses consistent with expand_term/3?

  ok - a(1)
  ok - a(2)
  ok - a(3)
  ok - a(4)
  ok - a(5)
  ok - a(6)
  ok - a(7)
  ok - a(8)
  ok - a(9)
  ok - a(10)
  ok - a(11)
  ok - a(12)
  ok - a(13)
  ok - a(14)
  ok - a(16)
  ok - a(17)
  ok - a(18)
  ok - a(19)
  ok - a(20)
  ok - a(28)
  ok - a(29)
  ok - a(30)
  ok - a(31)
*/

***************************************************************************************************
A.4 Problem cases
Note that
?- expand_term((a --> [X]), X).
results in an infinite term in SICStus 2.1 #9: Wed Sep 20 15:29:20 BST 1995.
X = (a(_B,_A):-'C'(_B,(a(_B,_A):-'C'(_B,(a(_B,_A):-'C'(_B,(a(_B,_A):- ...
but 
% capulin% sicstus
% SICStus 3.8 (sparc-solaris-5.5.1): Mon Nov 22 10:54:50 MET 1999
% Licensed to npl.co.uk
% | ?- expand_term((a --> [X]), X).
% 
% X = a(_A,_B):-'C'(_A,(a(_A,_B):-'C'(_A,(a(_A,_B):-'C'(_A,(a(_A,_B)
%  :-'C'(_A,(a(...):-'C'(...)),_B)),_B)),_B)),_B) ? ;

no

Annex B - A logical expansion of grammar rules
These tables present a logical view for the expansion of grammar rules.
B.1 Expand a grammar rule
 ‘-->‘(‘,’(Head, Terminal_list), Body)	‘:-’(head(Head, S0, S2), ‘,’(body(Body, S0, S1), terminals(Terminal_list, S1, S2))	
‘-->‘(Head, Body)	‘:-’(head(Head, S0, S2), body(Body, S0, S2))	
B.2 Expand a terminal list
terminals([], S0, S1)		
terminals(‘.’(T, []), S0, S1)	T_t = ‘C’(S0, T, S1)	
terminals(‘.’(T1, T2), S0, S2)	T_t1 = ‘C’(S0, T1, S1)	
	T_t2 = ‘C’(S1, T2, S2)	
	T_t = ‘,’(T_t1, T_t2)	
B.3 Expand a head
head(Head, S0, S2)	Head =.. Univ_head,	
	append(Univ_head, [S0, S2], Univ_H),	
	H =.. Univ_H	
B.4 Expand a body
body(‘;’(‘->‘(If, Then), Else), S0, S2)	B_if = body(If, S0, S1),	
	B_then = body(Then, S1, S2),	
	B_else = body(Else, S1, S2),	
	B = ‘;’(‘->‘(B_if, B_then), B_else)	
body(‘->‘(If, Then), S0, S2)	B_if = body(If, S0, S1),	
	B_then = body(Then, S1, S2),	
	B = ‘->‘(B_if, B_then)	
body(‘;‘(Either, Or), S0, S1)	B_either = body(Either, S0, S1),	
	B_or = body(Or, S0, S1),	
	B = ‘;‘(B_either, B_or)	
body(‘,’(First, Second), S0, S1)	B_first = body(First, S0, S1),	
	B_second = body(Second, S1, S2),	
	B = ‘,’(B_first, B_second)	
body(!, S0, S2)	B = ‘,’(!, S0 = S2)	
body(‘{}’(Goal), S0, S2)	B = ‘,’(Goal, S0 = S2)	
body([], S0, S2)		
body(‘.’(T, []), S0, S1)	B = terminals(‘.’(T, []), S0, S1)	
body(‘.’(T1, T2), S0, S2)	B = terminals(‘.’(T1, T2), S0, S2)	
body(Body, S0, S2)	Body =.. Univ_body,	
	append(Univ_body, [S0, S2], Univ_B),	
	B =.. Univ_B