optional<expr> mk_class_instance(environment const & env, io_state const & ios, local_context const & ctx,
name const & prefix, expr const & type, bool relax_opaque, bool use_local_instances,
unifier_config const & cfg) {
auto C = std::make_shared<class_instance_context>(env, ios, prefix, relax_opaque, use_local_instances);
if (!is_ext_class(C->tc(), type))
return none_expr();
expr meta = ctx.mk_meta(C->m_ngen, some_expr(type), type.get_tag());
unsigned depth = 0;
constraint c = mk_class_instance_cnstr(C, ctx, meta, depth);
unifier_config new_cfg(cfg);
new_cfg.m_discard = true;
new_cfg.m_use_exceptions = true;
new_cfg.m_pattern = true;
new_cfg.m_kind = C->m_conservative ? unifier_kind::VeryConservative : unifier_kind::Liberal;
try {
auto seq = unify(env, 1, &c, C->m_ngen.mk_child(), substitution(), new_cfg);
while (true) {
auto p = seq.pull();
lean_assert(p);
substitution s = p->first.first;
expr r = s.instantiate_all(meta);
if (!has_expr_metavar_relaxed(r))
return some_expr(r);
seq = p->second;
}
} catch (exception &) {
return none_expr();
}
}
expr collect(expr const & e) {
return replace(e, [&](expr const & e, unsigned) {
if (is_metavar(e)) {
name const & id = mlocal_name(e);
if (auto r = m_meta_to_param.find(id)) {
return some_expr(*r);
} else {
expr type = m_ctx.infer(e);
expr x = m_ctx.push_local("_x", type);
m_meta_to_param.insert(id, x);
m_meta_to_param_inv.insert(mlocal_name(x), e);
m_params.push_back(x);
return some_expr(x);
}
} else if (is_local(e)) {
name const & id = mlocal_name(e);
if (!m_found_local.contains(id)) {
m_found_local.insert(id);
m_params.push_back(e);
}
} else if (is_sort(e)) {
return some_expr(update_sort(e, collect(sort_level(e))));
} else if (is_constant(e)) {
return some_expr(update_constant(e, collect(const_levels(e))));
}
return none_expr();
});
}
static optional<pair<expr, expr>> mk_op(environment const & env, old_local_context & ctx, type_checker_ptr & tc,
name const & op, unsigned nunivs, unsigned nargs, std::initializer_list<expr> const & explicit_args,
constraint_seq & cs, tag g) {
levels lvls;
for (unsigned i = 0; i < nunivs; i++)
lvls = levels(mk_meta_univ(mk_fresh_name()), lvls);
expr c = mk_constant(op, lvls);
expr op_type = instantiate_type_univ_params(env.get(op), lvls);
buffer<expr> args;
for (unsigned i = 0; i < nargs; i++) {
if (!is_pi(op_type))
return optional<pair<expr, expr>>();
expr arg = ctx.mk_meta(some_expr(binding_domain(op_type)), g);
args.push_back(arg);
op_type = instantiate(binding_body(op_type), arg);
}
expr r = mk_app(c, args, g);
for (expr const & explicit_arg : explicit_args) {
if (!is_pi(op_type))
return optional<pair<expr, expr>>();
r = mk_app(r, explicit_arg);
expr type = tc->infer(explicit_arg, cs);
justification j = mk_app_justification(r, op_type, explicit_arg, type);
if (!tc->is_def_eq(binding_domain(op_type), type, j, cs))
return optional<pair<expr, expr>>();
op_type = instantiate(binding_body(op_type), explicit_arg);
}
return some(mk_pair(r, op_type));
}
static int mk_expr_placeholder(lua_State * L) {
int nargs = lua_gettop(L);
if (nargs == 0)
return push_expr(L, mk_expr_placeholder());
else
return push_expr(L, mk_expr_placeholder(some_expr(to_expr(L, 1))));
}
optional<expr> expand_core(expr const & e) {
lean_assert(!is_lambda(e));
expr t = ctx().whnf(ctx().infer(e));
if (!is_pi(t))
return none_expr();
expr r = mk_lambda(name("x"), binding_domain(t), mk_app(e, mk_var(0)));
return some_expr(visit(r));
}
action mk_exprs_action(name const & sep, expr const & rec, optional<expr> const & ini,
optional<name> const & terminator, bool right, unsigned rbp) {
if (get_free_var_range(rec) > 2)
throw exception("invalid notation, the expression used to combine a sequence of expressions "
"must not contain free variables with de Bruijn indices greater than 1");
expr new_rec = annotate_macro_subterms(rec);
optional<expr> new_ini = ini ? some_expr(annotate_macro_subterms(*ini)) : none_expr();
return action(new exprs_action_cell(sep, new_rec, new_ini, terminator, right, rbp));
}
optional<expr> defeq_canonizer::find_defeq(name const & h, expr const & e) {
list<expr> const * lst = m_state.m_M.find(h);
if (!lst) return none_expr();
for (expr const & e1 : *lst) {
if (locals_subset(e1, e) && m_ctx.is_def_eq(e1, e))
return some_expr(e1);
}
return none_expr();
}
/** \brief Given \c a, an expression that is the denotation of an expression, if \c a is a variable,
then use the actions in the transitions \c ts to expand \c a. The idea is to produce a head symbol
we can use to decide whether the notation should be considered during pretty printing.
\see get_head_index
*/
static expr expand_pp_pattern(unsigned num, transition const * ts, expr const & a) {
lean_assert(is_simple(num, ts));
if (!is_var(a))
return a;
return replace(a, [&](expr const & e) {
if (is_var(e)) {
unsigned vidx = var_idx(e);
unsigned i = num;
unsigned offset = 0;
while (i > 0) {
--i;
action const & act = ts[i].get_action();
switch (act.kind()) {
case action_kind::Binder: case action_kind::Binders: case action_kind::Skip:
break;
case action_kind::Ext: case action_kind::LuaExt:
lean_unreachable();
case action_kind::Expr:
if (vidx == 0) return none_expr();
offset++;
vidx--;
break;
case action_kind::Exprs:
if (vidx == 0)
return some_expr(lift_free_vars(act.get_rec(), offset));
offset++;
vidx--;
break;
case action_kind::ScopedExpr:
if (vidx == 0)
return some_expr(lift_free_vars(act.get_rec(), offset));
offset++;
vidx--;
break;
}
}
return none_expr();
} else {
return none_expr();
}
});
}
static int mk_exprs_action(lua_State * L) {
int nargs = lua_gettop(L);
unsigned rbp = nargs <= 5 ? 0 : lua_tonumber(L, 6);
optional<name> terminator;
if (nargs >= 4) terminator = to_optional_name(L, 4);
return push_notation_action(L, mk_exprs_action(to_name_ext(L, 1),
to_expr(L, 2),
lua_isnil(L, 3) ? none_expr() : some_expr(to_expr(L, 3)),
terminator,
lua_toboolean(L, 5),
rbp));
}
virtual optional<expr> expand(expr const & m, extension_context & ctx) const {
environment const & env = ctx.env();
check_num_args(env, m);
expr l = whnf(macro_arg(m, 0), ctx);
expr not_l = whnf(mk_app(*g_not, l), ctx);
expr H1 = macro_arg(m, 1);
expr H2 = macro_arg(m, 2);
expr C1 = infer_type(H1, ctx, true);
expr C2 = infer_type(H2, ctx, true);
expr R = mk_resolvent(env, ctx, m, l, not_l, C1, C2);
return some_expr(mk_or_elim_tree1(l, not_l, C1, H1, C2, H2, R, ctx));
}
action replace(action const & a, std::function<expr(expr const &)> const & f) {
switch (a.kind()) {
case action_kind::Skip: case action_kind::Binder: case action_kind::Binders:
case action_kind::Ext: case action_kind::LuaExt: case action_kind::Expr:
return a;
case action_kind::Exprs:
return mk_exprs_action(a.get_sep(), f(a.get_rec()), a.get_initial() ? some_expr(f(*a.get_initial())) : none_expr(), a.get_terminator(),
a.is_fold_right(), a.rbp());
case action_kind::ScopedExpr:
return mk_scoped_expr_action(f(a.get_rec()), a.rbp(), a.use_lambda_abstraction());
}
lean_unreachable(); // LCOV_EXCL_LINE
}
optional<constraints> try_instance(expr const & inst, expr const & inst_type) {
type_checker & tc = m_C->tc();
name_generator & ngen = m_C->m_ngen;
tag g = inst.get_tag();
try {
flet<local_context> scope(m_ctx, m_ctx);
buffer<expr> locals;
expr meta_type = m_meta_type;
while (true) {
meta_type = tc.whnf(meta_type).first;
if (!is_pi(meta_type))
break;
expr local = mk_local(ngen.next(), binding_name(meta_type),
binding_domain(meta_type), binding_info(meta_type));
m_ctx.add_local(local);
locals.push_back(local);
meta_type = instantiate(binding_body(meta_type), local);
}
expr type = inst_type;
expr r = inst;
buffer<constraint> cs;
while (true) {
type = tc.whnf(type).first;
if (!is_pi(type))
break;
expr arg;
if (binding_info(type).is_inst_implicit()) {
pair<expr, constraint> ac = mk_class_instance_elaborator(m_C, m_ctx, some_expr(binding_domain(type)),
g, m_depth+1);
arg = ac.first;
cs.push_back(ac.second);
} else {
arg = m_ctx.mk_meta(m_C->m_ngen, some_expr(binding_domain(type)), g);
}
r = mk_app(r, arg, g);
type = instantiate(binding_body(type), arg);
}
r = Fun(locals, r);
trace(meta_type, r);
bool relax = m_C->m_relax;
constraint c = mk_eq_cnstr(m_meta, r, m_jst, relax);
return optional<constraints>(mk_constraints(c, cs));
} catch (exception &) {
return optional<constraints>();
}
}
virtual optional<expr> expand(expr const & m, abstract_type_context & ctx) const {
check_macro(m);
expr const & s = macro_arg(m, 0);
expr new_s = ctx.whnf(s);
buffer<expr> c_args;
expr const & c = get_app_args(new_s, c_args);
if (is_constant(c) && const_name(c) == m_constructor_name && m_idx < c_args.size()) {
return some_expr(c_args[m_idx]);
} else {
// expand into recursor
expr s_type = ctx.whnf(ctx.infer(s));
buffer<expr> args;
expr const & I = get_app_args(s_type, args);
if (!is_constant(I) || length(m_ps) != length(const_levels(I)))
return none_expr();
expr r = instantiate_univ_params(m_val, m_ps, const_levels(I));
args.push_back(new_s);
return some(instantiate_rev(r, args.size(), args.data()));
}
}
virtual optional<expr> expand(expr const & m, extension_context &) const {
check_macro(m);
return some_expr(macro_arg(m, 1));
}
optional<expr> is_neg(expr const & e) {
if (!is_const_app(e, get_has_neg_neg_name(), 3))
return none_expr();
return some_expr(app_arg(e));
}
optional<expr> is_bit1(expr const & e) {
if (!is_const_app(e, get_bit1_name(), 4))
return none_expr();
return some_expr(app_arg(e));
}
optional<expr> depends_on(unsigned sz, expr const * es, expr const & h) {
for (unsigned i = 0; i < sz; i++)
if (depends_on(es[i], h))
return some_expr(es[i]);
return none_expr();
}
declaration update_declaration(declaration const & d, level_param_names const & ps, expr const & type) {
return update_declaration(d, optional<level_param_names>(ps), some_expr(type), none_expr());
}
virtual optional<expr> expand(expr const & m, abstract_type_context &) const {
check_macro(m);
return some_expr(macro_arg(m, 1));
}
optional<expr> expand_string_macro(expr const & e) {
if (!is_string_macro(e)) return none_expr();
return some_expr(from_string_core(to_string_macro(e).get_value()));
}
optional<expr> placeholder_type(expr const & e) {
if (is_local(e) && is_placeholder(e))
return some_expr(mlocal_type(e));
else
return none_expr();
}
optional<expr> apply(optional<expr> const & a) {
if (a)
return some_expr(apply(*a));
else
return a;
}
static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s,
expr const & _e, buffer<constraint> & cs,
add_meta_kind add_meta, subgoals_action_kind subgoals_action,
optional<unifier_kind> const & uk = optional<unifier_kind>()) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
bool class_inst = get_apply_class_instance(ios.get_options());
name_generator ngen = s.get_ngen();
std::shared_ptr<type_checker> tc(mk_type_checker(env, ngen.mk_child()));
goal g = head(gs);
goals tail_gs = tail(gs);
expr t = g.get_type();
expr e = _e;
auto e_t_cs = tc->infer(e);
e_t_cs.second.linearize(cs);
expr e_t = e_t_cs.first;
buffer<expr> metas;
local_context ctx;
bool initialized_ctx = false;
unifier_config cfg(ios.get_options());
if (uk)
cfg.m_kind = *uk;
if (add_meta != DoNotAdd) {
unsigned num_e_t = get_expect_num_args(*tc, e_t);
if (add_meta == AddDiff) {
unsigned num_t = get_expect_num_args(*tc, t);
if (num_t <= num_e_t)
num_e_t -= num_t;
else
num_e_t = 0;
} else {
lean_assert(add_meta == AddAll);
}
for (unsigned i = 0; i < num_e_t; i++) {
auto e_t_cs = tc->whnf(e_t);
e_t_cs.second.linearize(cs);
e_t = e_t_cs.first;
expr meta;
if (class_inst && binding_info(e_t).is_inst_implicit()) {
if (!initialized_ctx) {
ctx = g.to_local_context();
initialized_ctx = true;
}
bool use_local_insts = true;
bool is_strict = false;
auto mc = mk_class_instance_elaborator(
env, ios, ctx, ngen.next(), optional<name>(),
use_local_insts, is_strict,
some_expr(head_beta_reduce(binding_domain(e_t))), e.get_tag(), cfg, nullptr);
meta = mc.first;
cs.push_back(mc.second);
} else {
meta = g.mk_meta(ngen.next(), head_beta_reduce(binding_domain(e_t)));
}
e = mk_app(e, meta);
e_t = instantiate(binding_body(e_t), meta);
metas.push_back(meta);
}
}
metavar_closure cls(t);
cls.mk_constraints(s.get_subst(), justification());
pair<bool, constraint_seq> dcs = tc->is_def_eq(t, e_t);
if (!dcs.first) {
throw_tactic_exception_if_enabled(s, [=](formatter const & fmt) {
format r = format("invalid 'apply' tactic, failed to unify");
r += pp_indent_expr(fmt, t);
r += compose(line(), format("with"));
r += pp_indent_expr(fmt, e_t);
return r;
});
return proof_state_seq();
}
dcs.second.linearize(cs);
unify_result_seq rseq = unify(env, cs.size(), cs.data(), ngen.mk_child(), s.get_subst(), cfg);
list<expr> meta_lst = to_list(metas.begin(), metas.end());
return map2<proof_state>(rseq, [=](pair<substitution, constraints> const & p) -> proof_state {
substitution const & subst = p.first;
constraints const & postponed = p.second;
name_generator new_ngen(ngen);
substitution new_subst = subst;
expr new_e = new_subst.instantiate_all(e);
assign(new_subst, g, new_e);
goals new_gs = tail_gs;
if (subgoals_action != IgnoreSubgoals) {
buffer<expr> metas;
for (auto m : meta_lst) {
if (!new_subst.is_assigned(get_app_fn(m)))
metas.push_back(m);
}
if (subgoals_action == AddRevSubgoals) {
for (unsigned i = 0; i < metas.size(); i++)
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
} else {
lean_assert(subgoals_action == AddSubgoals || subgoals_action == AddAllSubgoals);
if (subgoals_action == AddSubgoals)
remove_redundant_metas(metas);
unsigned i = metas.size();
while (i > 0) {
--i;
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
}
}
}
return proof_state(s, new_gs, new_subst, new_ngen, postponed);
});
}
virtual optional<expr> expand(expr const &, abstract_type_context &) const {
return some_expr(from_string_core(m_value));
}
declaration update_declaration_value(declaration const & d, expr const & value) {
return update_declaration(d, optional<level_param_names>(), none_expr(), some_expr(value));
}
optional<expr> substitution::get_expr(name const & m) const {
auto it = m_expr_subst.find(m);
return it ? some_expr(*it) : none_expr();
}
/** \brief Create a "choice" constraint that postpones the resolution of a calc proof step.
By delaying it, we can perform quick fixes such as:
- adding symmetry
- adding !
- adding subst
*/
constraint mk_calc_proof_cnstr(environment const & env, options const & opts,
old_local_context const & _ctx, expr const & m, expr const & _e,
constraint_seq const & cs, unifier_config const & cfg,
info_manager * im, update_type_info_fn const & fn) {
justification j = mk_failed_to_synthesize_jst(env, m);
auto choice_fn = [=](expr const & meta, expr const & _meta_type, substitution const & _s) {
old_local_context ctx = _ctx;
expr e = _e;
substitution s = _s;
expr meta_type = _meta_type;
type_checker_ptr tc = mk_type_checker(env);
constraint_seq new_cs = cs;
expr e_type = tc->infer(e, new_cs);
e_type = s.instantiate(e_type);
tag g = e.get_tag();
bool calc_assistant = get_elaborator_calc_assistant(opts);
if (calc_assistant) {
// add '!' is needed
while (is_norm_pi(*tc, e_type, new_cs)) {
binder_info bi = binding_info(e_type);
if (!bi.is_implicit() && !bi.is_inst_implicit()) {
if (!has_free_var(binding_body(e_type), 0)) {
// if the rest of the type does not reference argument,
// then we also stop consuming arguments
break;
}
}
expr imp_arg = ctx.mk_meta(some_expr(binding_domain(e_type)), g);
e = mk_app(e, imp_arg, g);
e_type = instantiate(binding_body(e_type), imp_arg);
}
if (im)
fn(e);
}
e_type = head_beta_reduce(e_type);
expr const & meta_type_fn = get_app_fn(meta_type);
expr const & e_type_fn = get_app_fn(e_type);
if (is_constant(meta_type_fn) && (!is_constant(e_type_fn) || const_name(e_type_fn) != const_name(meta_type_fn))) {
// try to make sure meta_type and e_type have the same head symbol
if (!try_normalize_to_head(env, const_name(meta_type_fn), e_type, new_cs) &&
is_constant(e_type_fn)) {
try_normalize_to_head(env, const_name(e_type_fn), meta_type, new_cs);
}
}
auto try_alternative = [&](expr const & e, expr const & e_type, constraint_seq fcs, bool conservative) {
justification new_j = mk_type_mismatch_jst(e, e_type, meta_type);
if (!tc->is_def_eq(e_type, meta_type, new_j, fcs))
throw unifier_exception(new_j, s);
buffer<constraint> cs_buffer;
fcs.linearize(cs_buffer);
metavar_closure cls(meta);
cls.add(meta_type);
cls.mk_constraints(s, j, cs_buffer);
unifier_config new_cfg(cfg);
new_cfg.m_discard = false;
new_cfg.m_kind = conservative ? unifier_kind::Conservative : unifier_kind::Liberal;
unify_result_seq seq = unify(env, cs_buffer.size(), cs_buffer.data(), substitution(), new_cfg);
auto p = seq.pull();
lean_assert(p);
substitution new_s = p->first.first;
constraints postponed = map(p->first.second,
[&](constraint const & c) {
// we erase internal justifications
return update_justification(c, j);
});
expr new_e = new_s.instantiate(e);
if (conservative && has_expr_metavar_relaxed(new_s.instantiate_all(e)))
throw_elaborator_exception("solution contains metavariables", e);
if (im)
im->instantiate(new_s);
constraints r = cls.mk_constraints(new_s, j);
buffer<expr> locals;
expr mvar = get_app_args(meta, locals);
expr val = Fun(locals, new_e);
r = cons(mk_eq_cnstr(mvar, val, j), r);
return append(r, postponed);
};
if (!get_elaborator_calc_assistant(opts)) {
bool conservative = false;
return try_alternative(e, e_type, new_cs, conservative);
} else {
// TODO(Leo): after we have the simplifier and rewriter tactic, we should revise
// this code. It is "abusing" the higher-order unifier.
{
// Try the following possible intrepretations using a "conservative" unification procedure.
// That is, we only unfold definitions marked as reducible.
// Assume pr is the proof provided.
// 1. pr
bool conservative = true;
try { return try_alternative(e, e_type, new_cs, conservative); } catch (exception & ex) {}
// 2. eq.symm pr
constraint_seq symm_cs = new_cs;
auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
if (symm) {
try { return try_alternative(symm->first, symm->second, symm_cs, conservative); } catch (exception &) {}
}
// 3. subst pr (eq.refl lhs)
constraint_seq subst_cs = new_cs;
if (auto subst = apply_subst(env, ctx, tc, e, e_type, meta_type, subst_cs, g)) {
try { return try_alternative(subst->first, subst->second, subst_cs, conservative); } catch (exception&) {}
}
// 4. subst (eq.symm pr) (eq.refl lhs)
if (symm) {
constraint_seq subst_cs = symm_cs;
if (auto subst = apply_subst(env, ctx, tc, symm->first, symm->second,
meta_type, subst_cs, g)) {
try { return try_alternative(subst->first, subst->second, subst_cs, conservative); }
catch (exception&) {}
}
}
}
{
// Try the following possible insterpretations using the default unification procedure.
// 1. pr
bool conservative = false;
std::unique_ptr<throwable> saved_ex;
try {
return try_alternative(e, e_type, new_cs, conservative);
} catch (exception & ex) {
saved_ex.reset(ex.clone());
}
// 2. eq.symm pr
constraint_seq symm_cs = new_cs;
auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
if (symm) {
try { return try_alternative(symm->first, symm->second, symm_cs, conservative); }
catch (exception &) {}
}
// We use the exception for the first alternative as the error message
saved_ex->rethrow();
lean_unreachable();
}
}
};
bool owner = false;
return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Epilogue), owner, j);
}
