mercury/compiler/assertion.m

%-----------------------------------------------------------------------------%
% Copyright (C) 1999-2005 The University of Melbourne.
% This file may only be copied under the terms of the GNU General
% Public License - see the file COPYING in the Mercury distribution.
%-----------------------------------------------------------------------------%
%
% Module: assertion
%
% Main authors: petdr
%
% This module is an abstract interface to the assertion table.
% Note that this is a first design and will probably change
% substantially in the future.
%
%-----------------------------------------------------------------------------%

:- module hlds__assertion.

:- interface.

:- import_module hlds__hlds_data.
:- import_module hlds__hlds_goal.
:- import_module hlds__hlds_module.
:- import_module hlds__hlds_pred.
:- import_module parse_tree__prog_data.

:- import_module io.
:- import_module std_util.

	%
	% assertion__goal
	%
	% Get the hlds_goal which represents the assertion.
	%
:- pred assertion__goal(assert_id::in, module_info::in, hlds_goal::out) is det.

	%
	% assertion__record_preds_used_in
	%
	% Record into the pred_info of each pred used in the assertion
	% the assert_id.
	%
:- pred assertion__record_preds_used_in(hlds_goal::in, assert_id::in,
	module_info::in, module_info::out) is det.

	%
	% assertion__is_commutativity_assertion(Id, MI, Vs, CVs)
	%
	% Does the assertion represented by the assertion id, Id,
	% state the commutativity of a pred/func?
	% We extend the usual definition of commutativity to apply to
	% predicates or functions with more than two arguments as
	% follows by allowing extra arguments which must be invariant.
	% If so, this predicate returns (in CVs) the two variables which
	% can be swapped in order if it was a call to Vs.
	%
	% The assertion must be in a form similar to this
	% 	all [Is,A,B,C] ( p(Is,A,B,C) <=> p(Is,B,A,C) )
	% for the predicate to return true (note that the invariant
	% arguments, Is, can be any where providing they are in
	% identical locations on both sides of the equivalence).
	%
:- pred assertion__is_commutativity_assertion(assert_id::in, module_info::in,
	prog_vars::in, pair(prog_var)::out) is semidet.

	%
	%
	% assertion__is_associativity_assertion(Id, MI, Vs, CVs, OV)
	%
	% Does the assertion represented by the assertion id, Id,
	% state the associativity of a pred/func?
	% We extend the usual definition of associativity to apply to
	% predicates or functions with more than two arguments as
	% follows by allowing extra arguments which must be invariant.
	% If so, this predicate returns (in CVs) the two variables which
	% can be swapped in order if it was a call to Vs, and the
	% output variable, OV, related to these two variables (for the
	% case below it would be the variable in the same position as
	% AB, BC or ABC).
	%
	% The assertion must be in a form similar to this
	% 	all [Is,A,B,C,ABC]
	% 	(
	% 	  some [AB] p(Is,A,B,AB), p(Is,AB,C,ABC)
	% 	<=>
	% 	  some [BC] p(Is,B,C,BC), p(Is,A,BC,ABC)
	% 	)
	% for the predicate to return true (note that the invariant
	% arguments, Is, can be any where providing they are in
	% identical locations on both sides of the equivalence).
	%
:- pred assertion__is_associativity_assertion(assert_id::in, module_info::in,
	prog_vars::in, pair(prog_var)::out, prog_var::out) is semidet.

	%
	% assertion__is_associativity_assertion(Id, MI, PId, Vs, SPair)
	%
	% Recognise assertions in the form
	% 	all [A,B,S0,S]
	% 	(
	% 	  some [SA] p(A,S0,SA), p(B,SA,S)
	% 	<=>
	% 	  some [SB] p(B,S0,SB), p(A,SB,S)
	% 	)
	% and given the actual variables, Vs, to the call to p, return
	% the pair of variables which are state variables, SPair.
	%
:- pred assertion__is_update_assertion(assert_id::in, module_info::in,
	pred_id::in, prog_vars::in, pair(prog_var)::out) is semidet.

	%
	% assertion__is_construction_equivalence_assertion(Id, MI, C, P)
	%
	% Can a single construction unification whose functor is
	% determined by the cons_id, C, be expressed as a call
	% to the predid, P (with possibly some construction unifications
	% to initialise the arguments).
	%
	% The assertion will be in a form similar to
	% 	all [L,H,T] ( L = [H|T] <=> append([H], T, L) )
	%
:- pred assertion__is_construction_equivalence_assertion(assert_id::in,
	module_info::in, cons_id::in, pred_id::in) is semidet.

	%
	% assertion__in_interface_check
	%
	% Ensure that an assertion which is defined in an interface
	% doesn't refer to any constructors, functions and predicates
	% defined in the implementation of that module.
	%
:- pred assertion__in_interface_check(hlds_goal::in, pred_info::in,
	module_info::in, module_info::out, io::di, io::uo) is det.

	%
	% assertion__normalise_goal
	%
	% Place a hlds_goal into a standard form.  Currently all the
	% code does is replace conj([G]) with G.
	%
:- pred assertion__normalise_goal(hlds_goal::in, hlds_goal::out) is det.

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

:- implementation.

:- import_module check_hlds__type_util.
:- import_module hlds__goal_util.
:- import_module hlds__hlds_out.
:- import_module libs__globals.
:- import_module libs__options.
:- import_module mdbcomp__prim_data.
:- import_module parse_tree__error_util.
:- import_module parse_tree__prog_out.
:- import_module parse_tree__prog_util.
:- import_module parse_tree__prog_type.

:- import_module assoc_list.
:- import_module bool.
:- import_module list.
:- import_module map.
:- import_module require.
:- import_module set.
:- import_module std_util.
:- import_module string.

:- type subst == map(prog_var, prog_var).

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

assertion__is_commutativity_assertion(AssertId, Module, CallVars,
		CommutativeVars) :-
	assertion__goal(AssertId, Module, Goal),
	equivalent(Goal, P, Q),
	P = call(PredId, _, VarsP, _, _, _) - _,
	Q = call(PredId, _, VarsQ, _, _, _) - _,
	commutative_var_ordering(VarsP, VarsQ, CallVars, CommutativeVars).

	%
	% commutative_var_ordering(Ps, Qs, Vs, CommutativeVs)
	%
	% Check that the two list of variables are identical except that
	% the position of two variables has been swapped.
	% e.g [A,B,C] and [B,A,C] is true.
	% It also takes a list of variables, Vs, to a call and returns
	% the two variables in that list that can be swapped, ie [A,B].
	%
:- pred commutative_var_ordering(prog_vars::in, prog_vars::in,
	prog_vars::in, pair(prog_var)::out) is semidet.

commutative_var_ordering([P | Ps], [Q | Qs], [V | Vs], CommutativeVars) :-
	( P = Q ->
		commutative_var_ordering(Ps, Qs, Vs, CommutativeVars)
	;
		commutative_var_ordering_2(P, Q, Ps, Qs, Vs, CallVarB),
		CommutativeVars = V - CallVarB
	).

:- pred commutative_var_ordering_2(prog_var::in, prog_var::in, prog_vars::in,
		prog_vars::in, prog_vars::in, prog_var::out) is semidet.

commutative_var_ordering_2(VarP, VarQ, [P | Ps], [Q | Qs], [V | Vs],
		CallVarB) :-
	( P = Q ->
		commutative_var_ordering_2(VarP, VarQ, Ps, Qs, Vs, CallVarB)
	;
		CallVarB = V,
		P = VarQ,
		Q = VarP,
		Ps = Qs
	).

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

assertion__is_associativity_assertion(AssertId, Module, CallVars,
		AssociativeVars, OutputVar) :-
	assertion__goal(AssertId, Module, Goal - GoalInfo),
	equivalent(Goal - GoalInfo, P, Q),

	goal_info_get_nonlocals(GoalInfo, UniversiallyQuantifiedVars),

		% There may or may not be a some [] depending on whether
		% the user explicity qualified the call or not.
	(
		P = scope(_, conj(PCalls0) - _) - _PGoalInfo,
		Q = scope(_, conj(QCalls0) - _) - _QGoalInfo
	->
		PCalls = PCalls0,
		QCalls = QCalls0
	;
		P = conj(PCalls) - _PGoalInfo,
		Q = conj(QCalls) - _QGoalInfo
	),

	AssociativeVars - OutputVar =
		promise_only_solution(associative(PCalls, QCalls,
			UniversiallyQuantifiedVars, CallVars)).

	% associative(Ps, Qs, Us, R)
	%
	% If the assertion was in the form
	% 	all [Us] (some [] (Ps)) <=> (some [] (Qs))
	% try and rearrange the order of Ps and Qs so that the assertion
	% is in the standard from
	%
	% 	compose( A, B,  AB),		compose(B,  C,  BC),
	% 	compose(AB, C, ABC) 	<=>	compose(A, BC, ABC)

:- pred associative(hlds_goals::in, hlds_goals::in,
	set(prog_var)::in, prog_vars::in,
	pair(pair(prog_var), prog_var)::out) is cc_nondet.

associative(PCalls, QCalls, UniversiallyQuantifiedVars, CallVars,
		(CallVarA - CallVarB) - OutputVar) :-
	reorder(PCalls, QCalls, LHSCalls, RHSCalls),
	process_one_side(LHSCalls, UniversiallyQuantifiedVars, PredId,
		AB, PairsL, Vs),
	process_one_side(RHSCalls, UniversiallyQuantifiedVars, PredId,
		BC, PairsR, _),

		% If you read the predicate documentation, you will note
		% that for each pair of variables on the left hand side
		% there are an equivalent pair of variables on the right
		% hand side.  As the pairs of variables are not
		% symmetric, the call to list__perm will only succeed
		% once, if at all.
	assoc_list__from_corresponding_lists(PairsL, PairsR, Pairs),
	list__perm(Pairs, [(A - AB) - (B - A), (B - C) - (C - BC),
		(AB - ABC) - (BC - ABC)]),

	assoc_list__from_corresponding_lists(Vs, CallVars, AssocList),
	list__filter((pred(X-_Y::in) is semidet :- X = AB),
		AssocList, [_AB - OutputVar]),
	list__filter((pred(X-_Y::in) is semidet :- X = A),
		AssocList, [_A - CallVarA]),
	list__filter((pred(X-_Y::in) is semidet :- X = B),
		AssocList, [_B - CallVarB]).

	% reorder(Ps, Qs, Ls, Rs)
	%
	% Given both sides of the equivalence return another possible
	% ordering.

:- pred reorder(hlds_goals::in, hlds_goals::in,
	hlds_goals::out, hlds_goals::out) is multi.

reorder(PCalls, QCalls, LHSCalls, RHSCalls) :-
	list__perm(PCalls, LHSCalls),
	list__perm(QCalls, RHSCalls).
reorder(PCalls, QCalls, LHSCalls, RHSCalls) :-
	list__perm(PCalls, RHSCalls),
	list__perm(QCalls, LHSCalls).

	% process_one_side(Gs, Us, L, Ps)
	%
	% Given the list of goals, Gs, which are one side of a possible
	% associative equivalence, and the universally quantified
	% variables, Us, of the goals return L the existentially
	% quantified variable that links the two calls and Ps the list
	% of variables which are not invariants.
	%
	% ie for app(TypeInfo, X, Y, XY), app(TypeInfo, XY, Z, XYZ)
	% L <= XY and Ps <= [X - XY, Y - Z, XY - XYZ]

:- pred process_one_side(hlds_goals::in, set(prog_var)::in, pred_id::out,
	prog_var::out, assoc_list(prog_var)::out, prog_vars::out) is semidet.

process_one_side(Goals, UniversiallyQuantifiedVars, PredId,
		LinkingVar, Vars, VarsA) :-
	process_two_linked_calls(Goals, UniversiallyQuantifiedVars, PredId,
		LinkingVar, Vars0, VarsA),

		% Filter out all the invariant arguments, and then make
		% sure that their is only 3 arguments left.
	list__filter((pred(X-Y::in) is semidet :- not X = Y), Vars0, Vars),
	list__length(Vars, number_of_associative_vars).

:- func number_of_associative_vars = int.

number_of_associative_vars = 3.

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

	%
	% assertion__is_update_assertion(Id, MI, PId, Ss)
	%
	% is true iff the assertion, Id, is about a predicate, PId,
	% which takes some state as input and produces some state as
	% output and the same state is produced as input regardless of
	% the order that the state is updated.
	%
	% ie the promise should look something like this, note that A
	% and B could be vectors of variables.
	% :- promise all [A,B,SO,S]
	%	(
	%		(some [SA] (update(S0,A,SA), update(SA,B,S)))
	%	<=>
	%		(some [SB] (update(S0,B,SB), update(SB,A,S)))
	%	).
	%
assertion__is_update_assertion(AssertId, Module, _PredId, CallVars,
		StateA - StateB) :-
	assertion__goal(AssertId, Module, Goal - GoalInfo),
	equivalent(Goal - GoalInfo, P, Q),
	goal_info_get_nonlocals(GoalInfo, UniversiallyQuantifiedVars),

		% There may or may not be an explicit some [Vars] there,
		% as quantification now works correctly.
	(
		P = scope(_, conj(PCalls0) - _) - _PGoalInfo,
		Q = scope(_, conj(QCalls0) - _) - _QGoalInfo
	->
		PCalls = PCalls0,
		QCalls = QCalls0
	;
		P = conj(PCalls) - _PGoalInfo,
		Q = conj(QCalls) - _QGoalInfo
	),

	solutions(update(PCalls, QCalls, UniversiallyQuantifiedVars, CallVars),
		[StateA - StateB | _]).

	%
	% 	compose(S0, A, SA),		compose(SB, A, S),
	% 	compose(SA, B, S) 	<=>	compose(S0, B, SB)
	%
:- pred update(hlds_goals::in, hlds_goals::in, set(prog_var)::in,
	prog_vars::in, pair(prog_var)::out) is nondet.

update(PCalls, QCalls, UniversiallyQuantifiedVars, CallVars, StateA - StateB) :-
	reorder(PCalls, QCalls, LHSCalls, RHSCalls),
	process_two_linked_calls(LHSCalls, UniversiallyQuantifiedVars, PredId,
		SA, PairsL, Vs),
	process_two_linked_calls(RHSCalls, UniversiallyQuantifiedVars, PredId,
		SB, PairsR, _),

	assoc_list__from_corresponding_lists(PairsL, PairsR, Pairs0),
	list__filter((pred(X-Y::in) is semidet :- X \= Y), Pairs0, Pairs),
	list__length(Pairs) = 2,

		% If you read the predicate documentation, you will note
		% that for each pair of variables on the left hand side
		% there is an equivalent pair of variables on the right
		% hand side.  As the pairs of variables are not
		% symmetric, the call to list__perm will only succeed
		% once, if at all.
	list__perm(Pairs, [(S0 - SA) - (SB - S0), (SA - S) - (S - SB)]),

	assoc_list__from_corresponding_lists(Vs, CallVars, AssocList),
	list__filter((pred(X-_Y::in) is semidet :- X = S0),
		AssocList, [_S0 - StateA]),
	list__filter((pred(X-_Y::in) is semidet :- X = SA),
		AssocList, [_SA - StateB]).

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

	%
	% process_two_linked_calls(Gs, UQVs, PId, LV, AL, VAs)
	%
	% is true iff the list of goals, Gs, with universally quantified
	% variables, UQVs, is two calls to the same predicate, PId, with
	% one variable that links them, LV.  AL will be the assoc list
	% that is the each variable from the first call with its
	% corresponding variable in the second call, and VAs are the
	% variables of the first call.
	%
:- pred process_two_linked_calls(hlds_goals::in, set(prog_var)::in,
	pred_id::out, prog_var::out, assoc_list(prog_var)::out, prog_vars::out)
	is semidet.

process_two_linked_calls(Goals, UniversiallyQuantifiedVars, PredId,
		LinkingVar, Vars, VarsA) :-
	Goals = [call(PredId, _, VarsA, _, _, _) - _,
		call(PredId, _, VarsB, _, _, _) - _],

		% Determine the linking variable, L.
		% By definition it must be existentially quantified and
		% a member of both variable lists.
	CommonVars = list_to_set(VarsA) `intersect` list_to_set(VarsB),
	set__singleton_set(CommonVars `difference` UniversiallyQuantifiedVars,
		LinkingVar),

		% Set up mapping between the variables in the two calls.
	assoc_list__from_corresponding_lists(VarsA, VarsB, Vars).

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

assertion__is_construction_equivalence_assertion(AssertId, Module,
		ConsId, PredId) :-
	assertion__goal(AssertId, Module, Goal),
	equivalent(Goal, P, Q),
	(
		single_construction(P, ConsId)
	->
		predicate_call(Q, PredId)
	;
		single_construction(Q, ConsId),
		predicate_call(P, PredId)
	).

	%
	% One side of the equivalence must be just the single
	% unification with the correct cons_id.
	%
:- pred single_construction(hlds_goal::in, cons_id::in) is semidet.

single_construction(unify(_, UnifyRhs, _, _, _) - _,
		cons(QualifiedSymName, Arity)) :-
	UnifyRhs = functor(cons(UnqualifiedSymName, Arity), _, _),
	match_sym_name(UnqualifiedSymName, QualifiedSymName).

	%
	% The side containing the predicate call must be a single call
	% to the predicate with 0 or more construction unifications
	% which setup the arguments to the predicates.
	%
:- pred predicate_call(hlds_goal::in, pred_id::in) is semidet.

predicate_call(Goal, PredId) :-
	( Goal = conj(Goals) - _ ->
		list__member(Call, Goals),
		Call = call(PredId, _, _, _, _, _) - _,
		list__delete(Goals, Call, Unifications),
		P = (pred(G::in) is semidet :-
			not (
				G = unify(_, UnifyRhs, _, _, _) - _,
				UnifyRhs = functor(_, _, _)
			)
		),
		list__filter(P, Unifications, [])
	;
		Goal = call(PredId, _, _, _, _, _) - _
	).

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

assertion__goal(AssertId, Module, Goal) :-
	module_info_assertion_table(Module, AssertTable),
	assertion_table_lookup(AssertTable, AssertId, PredId),
	module_info_pred_info(Module, PredId, PredInfo),
	pred_info_clauses_info(PredInfo, ClausesInfo),
	clauses_info_clauses(ClausesInfo, Clauses),
	( Clauses = [clause(_ProcIds, Goal0, _Lang, _Context)] ->
		assertion__normalise_goal(Goal0, Goal)
	;
		error("assertion__goal: not an assertion")
	).

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

:- pred implies(hlds_goal::in, hlds_goal::out, hlds_goal::out) is semidet.

implies(Goal, P, Q) :-
		% Goal = (P => Q)
	Goal = not(conj(GoalList) - GI) - _,
	list__reverse(GoalList) = [NotQ | Ps],
	( Ps = [P0] ->
		P = P0
	;
		P = conj(list__reverse(Ps)) - GI
	),
	NotQ = not(Q) - _.

:- pred equivalent(hlds_goal::in, hlds_goal::out, hlds_goal::out) is semidet.

equivalent(Goal, P, Q) :-
		% Goal = P <=> Q
	Goal = conj([A, B]) - _GoalInfo,
	map__init(Subst),
	implies(A, PA, QA),
	implies(B, QB, PB),
	equal_goals(PA, PB, Subst, _),
	equal_goals(QA, QB, Subst, _),
	P = PA,
	Q = QA.

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

	%
	% equal_goals(GA, GB)
	%
	% Do these two goals represent the same hlds_goal modulo
	% renaming.
	%
:- pred equal_goals(hlds_goal::in, hlds_goal::in,
	subst::in, subst::out) is semidet.

equal_goals(conj(GoalAs) - _, conj(GoalBs) - _, !Subst) :-
	equal_goals_list(GoalAs, GoalBs, !Subst).
equal_goals(call(PredId, _, VarsA, _, _, _) - _,
		call(PredId, _, VarsB, _, _, _) - _, !Subst) :-
	equal_vars(VarsA, VarsB, !Subst).
equal_goals(generic_call(Type, VarsA, _, _) - _,
		generic_call(Type, VarsB, _, _) - _, !Subst) :-
	equal_vars(VarsA, VarsB, !Subst).
equal_goals(switch(Var, CanFail, CasesA) - _,
		switch(Var, CanFail, CasesB) - _, !Subst) :-
	equal_goals_cases(CasesA, CasesB, !Subst).
equal_goals(unify(VarA, RHSA, _, _, _) - _, unify(VarB, RHSB, _, _, _) - _,
		!Subst) :-
	equal_vars([VarA], [VarB], !Subst),
	equal_unification(RHSA, RHSB, !Subst).
equal_goals(disj(GoalAs) - _, disj(GoalBs) - _, !Subst) :-
	equal_goals_list(GoalAs, GoalBs, !Subst).
equal_goals(not(GoalA) - _, not(GoalB) - _, !Subst) :-
	equal_goals(GoalA, GoalB, !Subst).
equal_goals(scope(ReasonA, GoalA) - _, scope(ReasonB, GoalB) - _, !Subst) :-
	equal_reason(ReasonA, ReasonB, !Subst),
	equal_goals(GoalA, GoalB, !Subst).
equal_goals(if_then_else(VarsA, IfA, ThenA, ElseA) - _,
		if_then_else(VarsB, IfB, ThenB, ElseB) - _, !Subst) :-
	equal_vars(VarsA, VarsB, !Subst),
	equal_goals(IfA, IfB, !Subst),
	equal_goals(ThenA, ThenB, !Subst),
	equal_goals(ElseA, ElseB, !Subst).
equal_goals(foreign_proc(Attribs, PredId, _, ArgsA, ExtraA, _) - _,
		foreign_proc(Attribs, PredId, _, ArgsB, ExtraB, _) - _,
		!Subst) :-
	% foreign_procs with extra args are compiler generated,
	% and as such will not participate in assertions.
	ExtraA = [],
	ExtraB = [],
	VarsA = list__map(foreign_arg_var, ArgsA),
	VarsB = list__map(foreign_arg_var, ArgsB),
	equal_vars(VarsA, VarsB, !Subst).
equal_goals(par_conj(GoalAs) - _, par_conj(GoalBs) - _, !Subst) :-
	equal_goals_list(GoalAs, GoalBs, !Subst).
equal_goals(shorthand(ShorthandGoalA) - GoalInfoA,
		shorthand(ShorthandGoalB) - GoalInfoB, !Subst) :-
	equal_goals_shorthand(ShorthandGoalA - GoalInfoA,
		ShorthandGoalB - GoalInfoB, !Subst).

:- pred equal_reason(scope_reason::in, scope_reason::in, subst::in, subst::out)
	is semidet.

equal_reason(exist_quant(VarsA), exist_quant(VarsB), !Subst) :-
	equal_vars(VarsA, VarsB, !Subst).
equal_reason(barrier(Removable), barrier(Removable), !Subst).
equal_reason(commit(ForcePruning), commit(ForcePruning), !Subst).
equal_reason(from_ground_term(VarA), from_ground_term(VarB), !Subst) :-
	equal_var(VarA, VarB, !Subst).

:- pred equal_goals_shorthand(pair(shorthand_goal_expr, hlds_goal_info)::in,
	pair(shorthand_goal_expr, hlds_goal_info)::in, subst::in, subst::out)
	is semidet.

equal_goals_shorthand(bi_implication(LeftGoalA, RightGoalA) - GoalInfo,
		bi_implication(LeftGoalB, RightGoalB) - GoalInfo, !Subst) :-
	equal_goals(LeftGoalA, LeftGoalB, !Subst),
	equal_goals(RightGoalA, RightGoalB, !Subst).

:- pred equal_var(prog_var::in, prog_var::in, subst::in, subst::out)
	is semidet.

equal_var(VA, VB, !Subst) :-
	( map__search(!.Subst, VA, SubstVA) ->
		SubstVA = VB
	;
		map__insert(!.Subst, VA, VB, !:Subst)
	).

:- pred equal_vars(prog_vars::in, prog_vars::in, subst::in, subst::out)
	is semidet.

equal_vars([], [], !Subst).
equal_vars([VA | VAs], [VB | VBs], !Subst) :-
	equal_var(VA, VB, !Subst),
	equal_vars(VAs, VBs, !Subst).

:- pred equal_unification(unify_rhs::in, unify_rhs::in, subst::in, subst::out)
	is semidet.

equal_unification(var(A), var(B), !Subst) :-
	equal_vars([A], [B], !Subst).
equal_unification(functor(ConsId, E, VarsA), functor(ConsId, E, VarsB),
		!Subst) :-
	equal_vars(VarsA, VarsB, !Subst).
equal_unification(LambdaGoalA, LambdaGoalB, !Subst) :-
	LambdaGoalA = lambda_goal(Purity, PredOrFunc, EvalMethod, FixModes,
		NLVarsA, LVarsA, Modes, Det, GoalA),
	LambdaGoalB = lambda_goal(Purity, PredOrFunc, EvalMethod, FixModes,
		NLVarsB, LVarsB, Modes, Det, GoalB),
	equal_vars(NLVarsA, NLVarsB, !Subst),
	equal_vars(LVarsA, LVarsB, !Subst),
	equal_goals(GoalA, GoalB, !Subst).

:- pred equal_goals_list(hlds_goals::in, hlds_goals::in, subst::in, subst::out)
	is semidet.

equal_goals_list([], [], !Subst).
equal_goals_list([GoalA | GoalAs], [GoalB | GoalBs], !Subst) :-
	equal_goals(GoalA, GoalB, !Subst),
	equal_goals_list(GoalAs, GoalBs, !Subst).

:- pred equal_goals_cases(list(case)::in, list(case)::in,
	subst::in, subst::out) is semidet.

equal_goals_cases([], [], !Subst).
equal_goals_cases([CaseA | CaseAs], [CaseB | CaseBs], !Subst) :-
	CaseA = case(ConsId, GoalA),
	CaseB = case(ConsId, GoalB),
	equal_goals(GoalA, GoalB, !Subst),
	equal_goals_cases(CaseAs, CaseBs, !Subst).

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

assertion__record_preds_used_in(Goal, AssertId, !Module) :-
		% Explicit lambda expression needed since
		% goal_calls_pred_id has multiple modes.
	P = (pred(PredId::out) is nondet :- goal_calls_pred_id(Goal, PredId)),
	solutions(P, PredIds),
	list__foldl(update_pred_info(AssertId), PredIds, !Module).

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

	%
	% update_pred_info(Id, A, M0, M)
	%
	% Record in the pred_info pointed to by Id that that predicate
	% is used in the assertion pointed to by A.
	%
:- pred update_pred_info(assert_id::in, pred_id::in,
	module_info::in, module_info::out) is det.

update_pred_info(AssertId, PredId, !Module) :-
	module_info_pred_info(!.Module, PredId, PredInfo0),
	pred_info_get_assertions(PredInfo0, Assertions0),
	set__insert(Assertions0, AssertId, Assertions),
	pred_info_set_assertions(Assertions, PredInfo0, PredInfo),
	module_info_set_pred_info(PredId, PredInfo, !Module).

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

assertion__normalise_goal(Goal @ call(_, _, _, _, _, _) - GI, Goal - GI).
assertion__normalise_goal(Goal @ generic_call(_, _, _, _) - GI, Goal - GI).
assertion__normalise_goal(Goal @ unify(_, _, _, _, _) - GI, Goal - GI).
assertion__normalise_goal(Goal @ foreign_proc(_, _, _, _, _, _) - GI,
		Goal - GI).
assertion__normalise_goal(conj(Goals0) - GI, conj(Goals) - GI) :-
	assertion__normalise_conj(Goals0, Goals).
assertion__normalise_goal(switch(A,B,Case0s) - GI, switch(A,B,Cases)-GI) :-
	assertion__normalise_cases(Case0s, Cases).
assertion__normalise_goal(disj(Goal0s) - GI, disj(Goals) - GI) :-
	assertion__normalise_goals(Goal0s, Goals).
assertion__normalise_goal(not(Goal0) - GI, not(Goal) - GI) :-
	assertion__normalise_goal(Goal0, Goal).
assertion__normalise_goal(scope(Reason, Goal0) - GI,
		scope(Reason, Goal) - GI) :-
	assertion__normalise_goal(Goal0, Goal).
assertion__normalise_goal(if_then_else(A, If0, Then0, Else0) - GI,
		if_then_else(A, If, Then, Else) - GI) :-
	assertion__normalise_goal(If0, If),
	assertion__normalise_goal(Then0, Then),
	assertion__normalise_goal(Else0, Else).
assertion__normalise_goal(par_conj(Goal0s) - GI, par_conj(Goals) - GI) :-
	assertion__normalise_goals(Goal0s, Goals).
assertion__normalise_goal(shorthand(ShortHandGoal0) - GI0,
		shorthand(ShortHandGoal) - GI) :-
	assertion__normalise_goal_shorthand(ShortHandGoal0 - GI0,
		ShortHandGoal - GI).

	% assertion__normalise_goal_shorthand
	%
	% Place a shorthand goal into a standard form. Currently
	% all the code does is replace conj([G]) with G.
	%
:- pred assertion__normalise_goal_shorthand(
	pair(shorthand_goal_expr, hlds_goal_info)::in,
	pair(shorthand_goal_expr, hlds_goal_info)::out) is det.

assertion__normalise_goal_shorthand(bi_implication(LHS0, RHS0) - GI,
		bi_implication(LHS, RHS) - GI) :-
	assertion__normalise_goal(LHS0, LHS),
	assertion__normalise_goal(RHS0, RHS).

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

:- pred assertion__normalise_conj(hlds_goals::in, hlds_goals::out) is det.

assertion__normalise_conj([], []).
assertion__normalise_conj([Goal0 | Goal0s], Goals) :-
	goal_to_conj_list(Goal0, ConjGoals),
	assertion__normalise_conj(Goal0s, Goal1s),
	list__append(ConjGoals, Goal1s, Goals).

:- pred assertion__normalise_cases(list(case)::in, list(case)::out) is det.

assertion__normalise_cases([], []).
assertion__normalise_cases([Case0 | Case0s], [Case | Cases]) :-
	Case0 = case(ConsId, Goal0),
	assertion__normalise_goal(Goal0, Goal),
	Case = case(ConsId, Goal),
	assertion__normalise_cases(Case0s, Cases).

:- pred assertion__normalise_goals(hlds_goals::in, hlds_goals::out) is det.

assertion__normalise_goals([], []).
assertion__normalise_goals([Goal0 | Goal0s], [Goal | Goals]) :-
	assertion__normalise_goal(Goal0, Goal),
	assertion__normalise_goals(Goal0s, Goals).

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

assertion__in_interface_check(call(PredId,_,_,_,_,SymName) - GoalInfo,
		_PredInfo, !Module, !IO) :-
	module_info_pred_info(!.Module, PredId, CallPredInfo),
	pred_info_import_status(CallPredInfo, ImportStatus),
	( is_defined_in_implementation_section(ImportStatus) = yes ->
		goal_info_get_context(GoalInfo, Context),
		PredOrFunc = pred_info_is_pred_or_func(CallPredInfo),
		Arity = pred_info_orig_arity(CallPredInfo),
		write_assertion_interface_error(Context,
			call(PredOrFunc, SymName, Arity), !Module, !IO)
	;
		true
	).
assertion__in_interface_check(generic_call(_, _, _, _) - _, _,
		!Module, !IO).
assertion__in_interface_check(unify(Var, RHS, _, _, _) - GoalInfo,
		PredInfo, !Module, !IO) :-
	goal_info_get_context(GoalInfo, Context),
	assertion__in_interface_check_unify_rhs(RHS, Var, Context,
		PredInfo, !Module, !IO).
assertion__in_interface_check(foreign_proc(_, PredId, _, _, _, _) -
		GoalInfo, _PredInfo, !Module, !IO) :-
	module_info_pred_info(!.Module, PredId, PragmaPredInfo),
	pred_info_import_status(PragmaPredInfo, ImportStatus),
	( is_defined_in_implementation_section(ImportStatus) = yes ->
		goal_info_get_context(GoalInfo, Context),
		PredOrFunc = pred_info_is_pred_or_func(PragmaPredInfo),
		Name = pred_info_name(PragmaPredInfo),
		SymName = unqualified(Name),
		Arity = pred_info_orig_arity(PragmaPredInfo),
		write_assertion_interface_error(Context,
			call(PredOrFunc, SymName, Arity), !Module, !IO)
	;
		true
	).
assertion__in_interface_check(conj(Goals) - _, PredInfo, !Module, !IO) :-
	assertion__in_interface_check_list(Goals, PredInfo, !Module, !IO).
assertion__in_interface_check(switch(_, _, _) - _, _, _, _, !IO) :-
	error("assertion__in_interface_check: assertion contains switch.").
assertion__in_interface_check(disj(Goals) - _, PredInfo, !Module, !IO) :-
	assertion__in_interface_check_list(Goals, PredInfo, !Module, !IO).
assertion__in_interface_check(not(Goal) - _, PredInfo, !Module, !IO) :-
	assertion__in_interface_check(Goal, PredInfo, !Module, !IO).
assertion__in_interface_check(scope(_, Goal) - _, PredInfo, !Module, !IO) :-
	assertion__in_interface_check(Goal, PredInfo, !Module, !IO).
assertion__in_interface_check(if_then_else(_, If, Then, Else) - _,
		PredInfo, !Module, !IO) :-
	assertion__in_interface_check(If, PredInfo, !Module, !IO),
	assertion__in_interface_check(Then, PredInfo, !Module, !IO),
	assertion__in_interface_check(Else, PredInfo, !Module, !IO).
assertion__in_interface_check(par_conj(Goals) - _, PredInfo, !Module, !IO) :-
	assertion__in_interface_check_list(Goals, PredInfo, !Module, !IO).
assertion__in_interface_check(shorthand(ShorthandGoal) - _GoalInfo, PredInfo,
		!Module, !IO) :-
	assertion__in_interface_check_shorthand(ShorthandGoal,
		PredInfo, !Module, !IO).

:- pred assertion__in_interface_check_shorthand(shorthand_goal_expr::in,
	pred_info::in, module_info::in, module_info::out,
	io::di, io::uo) is det.

assertion__in_interface_check_shorthand(bi_implication(LHS, RHS), PredInfo,
		!Module, !IO) :-
	assertion__in_interface_check(LHS, PredInfo, !Module, !IO),
	assertion__in_interface_check(RHS, PredInfo, !Module, !IO).

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

:- pred assertion__in_interface_check_unify_rhs(unify_rhs::in, prog_var::in,
	prog_context::in, pred_info::in, module_info::in, module_info::out,
	io::di, io::uo) is det.

assertion__in_interface_check_unify_rhs(var(_), _, _, _, !Module, !IO).
assertion__in_interface_check_unify_rhs(functor(ConsId, _, _), Var, Context,
		PredInfo, !Module, !IO) :-
	pred_info_clauses_info(PredInfo, ClausesInfo),
	clauses_info_vartypes(ClausesInfo, VarTypes),
	map__lookup(VarTypes, Var, Type),
	( type_to_ctor_and_args(Type, TypeCtor, _) ->
		module_info_types(!.Module, Types),
		map__lookup(Types, TypeCtor, TypeDefn),
		hlds_data__get_type_defn_status(TypeDefn, TypeStatus),
		( is_defined_in_implementation_section(TypeStatus) = yes ->
			write_assertion_interface_error(Context, cons(ConsId),
				!Module, !IO)
		;
			true
		)
	;
		error("assertion__in_interface_check_unify_rhs: " ++
			"type_to_ctor_and_args failed.")
	).
assertion__in_interface_check_unify_rhs(lambda_goal(_,_,_,_,_,_,_,_,Goal),
		_Var, _Context, PredInfo, !Module, !IO) :-
	assertion__in_interface_check(Goal, PredInfo, !Module, !IO).

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

:- pred assertion__in_interface_check_list(hlds_goals::in, pred_info::in,
	module_info::in, module_info::out, io::di, io::uo)is det.

assertion__in_interface_check_list([], _, !Module, !IO).
assertion__in_interface_check_list([Goal0 | Goal0s], PredInfo, !Module, !IO) :-
	assertion__in_interface_check(Goal0, PredInfo, !Module, !IO),
	assertion__in_interface_check_list(Goal0s, PredInfo, !Module, !IO).

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

	%
	% Returns yes if the import_status indicates the item came form
	% the implementation section.
	%
:- func is_defined_in_implementation_section(import_status) = bool.

is_defined_in_implementation_section(abstract_exported) = yes.
is_defined_in_implementation_section(exported_to_submodules) = yes.
is_defined_in_implementation_section(local) = yes.
is_defined_in_implementation_section(imported(implementation)) = yes.

is_defined_in_implementation_section(imported(interface)) = no.
is_defined_in_implementation_section(imported(ancestor)) = no.
is_defined_in_implementation_section(imported(ancestor_private_interface)) = no.
is_defined_in_implementation_section(opt_imported) = no.
is_defined_in_implementation_section(abstract_imported) = no.
is_defined_in_implementation_section(pseudo_imported) = no.
is_defined_in_implementation_section(exported) = no.
is_defined_in_implementation_section(opt_exported) = yes.
is_defined_in_implementation_section(pseudo_exported) = no.

is_defined_in_implementation_section(external(Status)) =
	is_defined_in_implementation_section(Status).

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

:- type call_or_consid
	--->	call(pred_or_func, sym_name, arity)
	;	cons(cons_id).

:- pred write_assertion_interface_error(prog_context::in, call_or_consid::in,
	module_info::in, module_info::out, io::di, io::uo) is det.

write_assertion_interface_error(Context, Type, !Module, !IO) :-
	module_info_incr_errors(!Module),
	module_info_name(!.Module, ModuleName),
	ModuleStr = describe_sym_name(ModuleName),
	write_error_pieces(Context, 0,
		[words("In interface for module"), fixed(ModuleStr ++ ":")],
		!IO),

	(
		Type = call(PredOrFunc, SymName, Arity),
		IdStr = simple_call_id_to_string(PredOrFunc, SymName, Arity)
	;
		Type = cons(ConsId),
		ConsIdStr = cons_id_to_string(ConsId),
		IdStr = "constructor `" ++ ConsIdStr ++ "'"
	),

	write_error_pieces_not_first_line(Context, 0,
		[words("error: exported promise refers to"),
		words(IdStr), words("which is defined in the "),
		words("implementation section of module"),
		fixed(ModuleStr ++ ".")], !IO),

	globals__io_lookup_bool_option(verbose_errors, VerboseErrors, !IO),
	(
		VerboseErrors = yes,
		write_error_pieces_not_first_line(Context, 0,
			[words("Either move the promise into the "),
			words("implementation section or move "),
			words("the definition into the interface.")], !IO)
	;
		VerboseErrors = no
	).

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