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feat(frontends/lean): allow multiple coercions from class A to B, closes #187

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See new tests (for examples)
tests/lean/run/coe10.lean
tests/lean/run/coe11.lean
tests/lean/run/coe9.lean

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-09-14 12:01:14 -07:00
parent 1b6d4460e9
commit edcbe6fe10
14 changed files with 308 additions and 130 deletions
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63
src/frontends/lean/coercion_elaborator.cpp
View file

@ -13,21 +13,14 @@ Author: Leonardo de Moura
#include "frontends/lean/coercion_elaborator.h"
namespace lean {
struct coercion_elaborator : public choice_iterator {
coercion_info_manager & m_info;
expr m_arg;
bool m_id; // true if identity was not tried yet
list<constraints> m_choices;
list<expr> m_coercions;
coercion_elaborator(coercion_info_manager & info, expr const & arg,
list<constraints> const & choices, list<expr> const & coes):
m_info(info), m_arg(arg), m_id(true), m_choices(choices), m_coercions(coes) {
coercion_elaborator::coercion_elaborator(coercion_info_manager & info, expr const & arg,
list<constraints> const & choices, list<expr> const & coes,
bool use_id):
m_info(info), m_arg(arg), m_id(use_id), m_choices(choices), m_coercions(coes) {
lean_assert(length(m_coercions) + 1 == length(m_choices));
}
}
optional<constraints> next() {
optional<constraints> coercion_elaborator::next() {
if (!m_choices)
return optional<constraints>();
if (m_id) {
@ -41,13 +34,12 @@ struct coercion_elaborator : public choice_iterator {
auto r = head(m_choices);
m_choices = tail(m_choices);
return optional<constraints>(r);
}
};
}
constraint mk_coercion_cnstr(type_checker & tc, coercion_info_manager & infom,
expr const & m, expr const & a, expr const & a_type,
justification const & j, unsigned delay_factor, bool relax) {
auto choice_fn = [=, &tc, &infom](expr const & mvar, expr const & d_type, substitution const & s,
auto choice_fn = [=, &tc, &infom](expr const & meta, expr const & d_type, substitution const & s,
name_generator const & /* ngen */) {
expr new_a_type;
justification new_a_type_jst;
@ -65,7 +57,7 @@ constraint mk_coercion_cnstr(type_checker & tc, coercion_info_manager & infom,
delay_factor+1, relax)));
} else {
// giveup...
return lazy_list<constraints>(constraints(mk_eq_cnstr(mvar, a, justification(), relax)));
return lazy_list<constraints>(constraints(mk_eq_cnstr(meta, a, justification(), relax)));
}
}
constraint_seq cs;
@ -77,7 +69,7 @@ constraint mk_coercion_cnstr(type_checker & tc, coercion_info_manager & infom,
buffer<constraints> choices;
buffer<expr> coes;
// first alternative: no coercion
constraint_seq cs1 = cs + mk_eq_cnstr(mvar, a, justification(), relax);
constraint_seq cs1 = cs + mk_eq_cnstr(meta, a, justification(), relax);
choices.push_back(cs1.to_list());
unsigned i = alts.size();
while (i > 0) {
@ -86,26 +78,41 @@ constraint mk_coercion_cnstr(type_checker & tc, coercion_info_manager & infom,
expr coe = std::get<1>(t);
expr new_a = copy_tag(a, mk_app(coe, a));
coes.push_back(coe);
constraint_seq csi = cs + mk_eq_cnstr(mvar, new_a, new_a_type_jst, relax);
constraint_seq csi = cs + mk_eq_cnstr(meta, new_a, new_a_type_jst, relax);
choices.push_back(csi.to_list());
}
return choose(std::make_shared<coercion_elaborator>(infom, mvar,
return choose(std::make_shared<coercion_elaborator>(infom, meta,
to_list(choices.begin(), choices.end()),
to_list(coes.begin(), coes.end())));
} else {
expr new_a = a;
expr new_d_type = tc.whnf(d_type, cs);
expr const & d_cls = get_app_fn(new_d_type);
if (is_constant(d_cls)) {
if (auto c = get_coercion(tc.env(), new_a_type, const_name(d_cls))) {
new_a = copy_tag(a, mk_app(*c, a));
infom.save_coercion_info(a, new_a);
} else {
list<expr> coes = get_coercions(tc.env(), new_a_type, const_name(d_cls));
if (is_nil(coes)) {
expr new_a = a;
infom.erase_coercion_info(a);
}
}
cs += mk_eq_cnstr(mvar, new_a, new_a_type_jst, relax);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst, relax);
return lazy_list<constraints>(cs.to_list());
} else if (is_nil(tail(coes))) {
expr new_a = copy_tag(a, mk_app(head(coes), a));
infom.save_coercion_info(a, new_a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst, relax);
return lazy_list<constraints>(cs.to_list());
} else {
list<constraints> choices = map2<constraints>(coes, [&](expr const & coe) {
expr new_a = copy_tag(a, mk_app(coe, a));
constraint c = mk_eq_cnstr(meta, new_a, new_a_type_jst, relax);
return (cs + c).to_list();
});
return choose(std::make_shared<coercion_elaborator>(infom, meta, choices, coes, false));
}
} else {
expr new_a = a;
infom.erase_coercion_info(a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst, relax);
return lazy_list<constraints>(cs.to_list());
}
}
};
return mk_choice_cnstr(m, choice_fn, delay_factor, true, j, relax);

17
src/frontends/lean/coercion_elaborator.h
View file

@ -17,6 +17,19 @@ public:
virtual void save_coercion_info(expr const & e, expr const & c) = 0;
};
class coercion_elaborator : public choice_iterator {
coercion_info_manager & m_info;
expr m_arg;
bool m_id; // true if identity was not tried yet
list<constraints> m_choices;
list<expr> m_coercions;
public:
coercion_elaborator(coercion_info_manager & info, expr const & arg,
list<constraints> const & choices, list<expr> const & coes,
bool use_id = true);
optional<constraints> next();
};
/** \brief Create a metavariable, and attach choice constraint for generating
coercions of the form <tt>f a</tt>, where \c f is registered coercion,
and \c a is the input argument that has type \c a_type, but is expected
@ -34,4 +47,8 @@ public:
pair<expr, constraint> mk_coercion_elaborator(
type_checker & tc, coercion_info_manager & infom, local_context & ctx, bool relax,
expr const & a, expr const & a_type, expr const & expected_type, justification const & j);
pair<expr, constraint> coercions_to_choice(coercion_info_manager & infom, local_context & ctx,
list<expr> const & coes, expr const & a,
justification const & j, bool relax);
}

76
src/frontends/lean/elaborator.cpp
View file

@ -357,15 +357,48 @@ public:
}
if (!is_pi(f_type)) {
// try coercion to function-class
optional<expr> c = get_coercion_to_fun(env(), f_type);
if (c) {
list<expr> coes = get_coercions_to_fun(env(), f_type);
if (is_nil(coes)) {
throw_kernel_exception(env(), f, [=](formatter const & fmt) { return pp_function_expected(fmt, f); });
} else if (is_nil(tail(coes))) {
expr old_f = f;
f = mk_app(*c, f, f.get_tag());
f = mk_app(head(coes), f, f.get_tag());
f_type = infer_type(f, cs);
save_coercion_info(old_f, f);
lean_assert(is_pi(f_type));
} else {
throw_kernel_exception(env(), f, [=](formatter const & fmt) { return pp_function_expected(fmt, f); });
bool relax = m_relax_main_opaque;
justification j = mk_justification(f, [=](formatter const & fmt, substitution const & subst) {
return pp_function_expected(fmt, substitution(subst).instantiate(f));
});
auto choice_fn = [=](expr const & meta, expr const &, substitution const &, name_generator const &) {
list<constraints> choices = map2<constraints>(coes, [&](expr const & coe) {
expr new_f = copy_tag(f, ::lean::mk_app(coe, f));
constraint_seq cs;
while (true) {
expr new_f_type = m_tc[relax]->infer(new_f, cs);
if (!is_pi(new_f_type))
break;
binder_info bi = binding_info(new_f_type);
if (!bi.is_strict_implicit() && !bi.is_implicit())
break;
tag g = f.get_tag();
bool is_strict = false;
expr imp_arg = mk_placeholder_meta(some_expr(binding_domain(new_f_type)), g, is_strict, cs);
new_f = mk_app(new_f, imp_arg, g);
}
cs += mk_eq_cnstr(meta, new_f, j, relax);
return cs.to_list();
});
return choose(std::make_shared<coercion_elaborator>(*this, f, choices, coes, false));
};
f = m_full_context.mk_meta(none_expr(), f.get_tag());
cs += mk_choice_cnstr(f, choice_fn, to_delay_factor(cnstr_group::Basic), true, j, relax);
lean_assert(is_meta(f));
// let type checker add constraint
f_type = infer_type(f, cs);
lean_assert(is_pi(f_type));
f_type = m_tc[m_relax_main_opaque]->ensure_pi(f_type, f, cs);
}
} else {
erase_coercion_info(f);
@ -389,16 +422,31 @@ public:
d_type = whnf(d_type).first;
expr const & d_cls = get_app_fn(d_type);
if (is_constant(d_cls)) {
if (auto c = get_coercion(env(), a_type, const_name(d_cls))) {
expr r = mk_app(*c, a, a.get_tag());
list<expr> coes = get_coercions(env(), a_type, const_name(d_cls));
if (is_nil(coes)) {
erase_coercion_info(a);
return a;
} else if (is_nil(tail(coes))) {
expr r = mk_app(head(coes), a, a.get_tag());
save_coercion_info(a, r);
return r;
} else {
for (expr const & coe : coes) {
expr r = mk_app(coe, a, a.get_tag());
expr r_type = infer_type(r).first;
if (m_tc[m_relax_main_opaque]->is_def_eq(r_type, d_type).first) {
save_coercion_info(a, r);
return r;
}
}
erase_coercion_info(a);
}
}
return a;
}
} else {
erase_coercion_info(a);
return a;
}
}
/** \brief Given a term <tt>a : a_type</tt>, and an expected type generate a metavariable with a delayed coercion. */
pair<expr, constraint_seq> mk_delayed_coercion(expr const & a, expr const & a_type, expr const & expected_type,
@ -426,8 +474,8 @@ public:
return to_ecs(a, dcs.second);
} else {
expr new_a = apply_coercion(a, a_type, expected_type);
bool coercion_worked = false;
constraint_seq cs;
bool coercion_worked = false;
if (!is_eqp(a, new_a)) {
expr new_a_type = infer_type(new_a, cs);
coercion_worked = m_tc[relax]->is_def_eq(new_a_type, expected_type, j, cs);
@ -575,13 +623,15 @@ public:
return e;
}
}
optional<expr> c = get_coercion_to_sort(env(), t);
if (c) {
expr r = mk_app(*c, e, e.get_tag());
list<expr> coes = get_coercions_to_sort(env(), t);
if (is_nil(coes)) {
throw_kernel_exception(env(), e, [=](formatter const & fmt) { return pp_type_expected(fmt, e); });
} else {
// Remark: we ignore other coercions to sort
expr r = mk_app(head(coes), e, e.get_tag());
save_coercion_info(e, r);
return r;
}
throw_kernel_exception(env(), e, [=](formatter const & fmt) { return pp_type_expected(fmt, e); });
}
/** \brief Similar to instantiate_rev, but assumes that subst contains only local constants.

6
src/frontends/lean/info_manager.cpp
View file

@ -212,6 +212,12 @@ public:
ios.update_options(os) << m_expr << endl << "--" << endl << m_type << endl;
ios << "-- ACK" << endl;
}
virtual info_data_cell * instantiate(substitution & s) const {
expr e = s.instantiate(m_expr);
expr t = s.instantiate(m_type);
return is_eqp(e, m_expr) && is_eqp(t, m_type) ? nullptr : new coercion_info_data(get_column(), e, t);
}
};
class symbol_info_data : public info_data_cell {

113
src/library/coercion.cpp
View file

@ -71,31 +71,39 @@ struct coercion_info {
struct coercion_state {
rb_map<name, list<coercion_info>, name_quick_cmp> m_coercion_info;
// m_from and m_to contain "direct" coercions
rb_map<name, list<pair<coercion_class, expr>>, name_quick_cmp> m_from; // map user-class -> list of (class, coercion-fun)
typedef std::tuple<coercion_class, expr, expr> from_data;
rb_map<name, list<from_data>, name_quick_cmp> m_from; // map user-class -> list of (class, coercion-fun)
rb_map<coercion_class, list<name>, coercion_class_cmp_fn> m_to;
rb_map<name, pair<name, unsigned>, name_quick_cmp> m_coercions; // map coercion -> (from-class, num-args)
coercion_info get_info(name const & from, coercion_class const & to) {
template<typename F>
void for_each_info(name const & from, coercion_class const & to, F && f) {
auto it = m_coercion_info.find(from);
lean_assert(it);
for (coercion_info info : *it) {
if (info.m_to == to)
return info;
if (info.m_to == to) {
f(info);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
void update_from_to(name const & C, coercion_class const & D, expr const & f, io_state const & ios) {
}
void update_from_to(type_checker & tc, name const & C, coercion_class const & D,
expr const & f, expr const & f_type, io_state const & ios) {
auto it1 = m_from.find(C);
if (!it1) {
m_from.insert(C, to_list(mk_pair(D, f)));
m_from.insert(C, to_list(from_data(D, f, f_type)));
} else {
coercion_class D_it; expr f_it, f_type_it;
auto it = it1->begin();
auto end = it1->end();
for (; it != end; ++it)
if (it->first == D)
for (; it != end; ++it) {
std::tie(D_it, f_it, f_type_it) = *it;
if (D_it == D && tc.is_def_eq(f_type_it, f_type).first)
break;
}
if (it == end)
m_from.insert(C, cons(mk_pair(D, f), *it1));
else if (it->second != f)
m_from.insert(C, cons(from_data(D, f, f_type), *it1));
else if (std::get<1>(*it) != f)
ios.get_diagnostic_channel() << "replacing the coercion from '" << C << "' to '" << D << "'\n";
}
auto it2 = m_to.find(D);
@ -158,15 +166,23 @@ optional<coercion_class> type_to_coercion_class(expr const & t) {
}
}
typedef list<pair<name, coercion_class>> arrows;
static bool contains(arrows const & a, name const & C, coercion_class const & D) {
return std::find(a.begin(), a.end(), mk_pair(C, D)) != a.end();
typedef std::tuple<name, coercion_class, expr> arrow;
typedef list<arrow> arrows;
static bool contains(type_checker & tc, arrows const & as, name const & C, coercion_class const & D, expr const & f_type) {
name C_it; coercion_class D_it; expr f_type_it;
for (arrow const & a : as) {
std::tie(C_it, D_it, f_type_it) = a;
if (C == C_it && D == D_it && tc.is_def_eq(f_type_it, f_type).first)
return true;
}
return false;
}
static arrows insert(arrows const & a, name const & C, coercion_class const & D) {
return arrows(mk_pair(C, D), a);
static arrows insert(arrows const & a, name const & C, coercion_class const & D, expr const & f_type) {
return arrows(arrow(C, D, f_type), a);
}
struct add_coercion_fn {
type_checker m_tc;
coercion_state m_state;
arrows m_visited;
io_state const & m_ios;
@ -220,10 +236,11 @@ struct add_coercion_fn {
if (!it1)
return;
for (name const & B : *it1) {
coercion_info info = m_state.get_info(B, C_cls);
m_state.for_each_info(B, C_cls, [&](coercion_info const & info) {
// B >-> C >-> D
add_coercion_trans(B, info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args,
ls, f, f_type, num_args, cls);
});
}
}
@ -237,11 +254,12 @@ struct add_coercion_fn {
if (!it)
return;
for (auto const & p : *it) {
coercion_class E = p.first;
coercion_info info = m_state.get_info(D, E);
coercion_class E = std::get<0>(p);
m_state.for_each_info(D, E, [&](coercion_info const & info) {
// C >-> D >-> E
add_coercion_trans(C, ls, f, f_type, num_args,
info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args, info.m_to);
});
}
}
@ -253,7 +271,9 @@ struct add_coercion_fn {
m_state.m_coercion_info.insert(C, infos);
} else {
list<coercion_info> infos = *it;
infos = filter(infos, [&](coercion_info const & info) { return info.m_to != cls; });
infos = filter(infos, [&](coercion_info const & info) {
return info.m_to != cls || !m_tc.is_def_eq(info.m_fun_type, f_type).first;
});
infos = cons(coercion_info(f, f_type, ls, num_args, cls), infos);
m_state.m_coercion_info.insert(C, infos);
}
@ -263,23 +283,23 @@ struct add_coercion_fn {
void add_coercion(name const & C, expr const & f, expr const & f_type,
level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
if (contains(m_visited, C, cls))
if (contains(m_tc, m_visited, C, cls, f_type))
return;
if (cls.kind() == coercion_class_kind::User && cls.get_name() == C)
return;
m_visited = insert(m_visited, C, cls);
m_visited = insert(m_visited, C, cls, f_type);
add_coercion_core(C, f, f_type, ls, num_args, cls);
add_coercion_trans_to(C, f, f_type, ls, num_args, cls);
add_coercion_trans_from(C, f, f_type, ls, num_args, cls);
}
add_coercion_fn(coercion_state const & s, io_state const & ios):
m_state(s), m_ios(ios) {}
add_coercion_fn(environment const & env, coercion_state const & s, io_state const & ios):
m_tc(env), m_state(s), m_ios(ios) {}
coercion_state operator()(name const & C, expr const & f, expr const & f_type,
level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
add_coercion(C, f, f_type, ls, num_args, cls);
m_state.update_from_to(C, cls, f, m_ios);
m_state.update_from_to(m_tc, C, cls, f, f_type, m_ios);
return m_state;
}
};
@ -305,7 +325,7 @@ coercion_state add_coercion(environment const & env, io_state const & ios, coerc
throw exception(sstream() << "invalid coercion, '" << f << "' cannot be used as a coercion from '" << C << "'");
else if (cls->kind() == coercion_class_kind::User && cls->get_name() == C)
throw exception(sstream() << "invalid coercion, '" << f << "' is a coercion from '" << C << "' to itself");
return add_coercion_fn(st, ios)(C, fn, d.get_type(), d.get_univ_params(), num, *cls);
return add_coercion_fn(env, st, ios)(C, fn, d.get_type(), d.get_univ_params(), num, *cls);
}
t = binding_body(t);
num++;
@ -414,34 +434,35 @@ bool has_coercions_from(environment const & env, expr const & C) {
length(head(cs).m_level_params) == length(const_levels(C_fn));
}
optional<expr> get_coercion(environment const & env, expr const & C, coercion_class const & D) {
list<expr> get_coercions(environment const & env, expr const & C, coercion_class const & D) {
buffer<expr> args;
expr const & C_fn = get_app_rev_args(C, args);
if (!is_constant(C_fn))
return none_expr();
return list<expr>();
coercion_state const & ext = coercion_ext::get_state(env);
auto it = ext.m_coercion_info.find(const_name(C_fn));
if (!it)
return none_expr();
return list<expr>();
buffer<expr> r;
for (coercion_info const & info : *it) {
if (info.m_to == D && info.m_num_args == args.size() && length(info.m_level_params) == length(const_levels(C_fn))) {
expr f = instantiate_univ_params(info.m_fun, info.m_level_params, const_levels(C_fn));
return some_expr(apply_beta(f, args.size(), args.data()));
r.push_back(apply_beta(f, args.size(), args.data()));
}
}
return none_expr();
return to_list(r.begin(), r.end());
}
optional<expr> get_coercion(environment const & env, expr const & C, name const & D) {
return get_coercion(env, C, coercion_class::mk_user(D));
list<expr> get_coercions(environment const & env, expr const & C, name const & D) {
return get_coercions(env, C, coercion_class::mk_user(D));
}
optional<expr> get_coercion_to_sort(environment const & env, expr const & C) {
return get_coercion(env, C, coercion_class::mk_sort());
list<expr> get_coercions_to_sort(environment const & env, expr const & C) {
return get_coercions(env, C, coercion_class::mk_sort());
}
optional<expr> get_coercion_to_fun(environment const & env, expr const & C) {
return get_coercion(env, C, coercion_class::mk_fun());
list<expr> get_coercions_to_fun(environment const & env, expr const & C) {
return get_coercions(env, C, coercion_class::mk_fun());
}
bool get_user_coercions(environment const & env, expr const & C, buffer<std::tuple<name, expr, expr>> & result) {
@ -535,16 +556,16 @@ static int has_coercions_from(lua_State * L) {
return push_boolean(L, has_coercions_from(to_environment(L, 1), to_name_ext(L, 2)));
}
static int get_coercion(lua_State * L) {
return push_optional_expr(L, get_coercion(to_environment(L, 1), to_expr(L, 2), to_name_ext(L, 3)));
static int get_coercions(lua_State * L) {
return push_list_expr(L, get_coercions(to_environment(L, 1), to_expr(L, 2), to_name_ext(L, 3)));
}
static int get_coercion_to_sort(lua_State * L) {
return push_optional_expr(L, get_coercion_to_sort(to_environment(L, 1), to_expr(L, 2)));
static int get_coercions_to_sort(lua_State * L) {
return push_list_expr(L, get_coercions_to_sort(to_environment(L, 1), to_expr(L, 2)));
}
static int get_coercion_to_fun(lua_State * L) {
return push_optional_expr(L, get_coercion_to_fun(to_environment(L, 1), to_expr(L, 2)));
static int get_coercions_to_fun(lua_State * L) {
return push_list_expr(L, get_coercions_to_fun(to_environment(L, 1), to_expr(L, 2)));
}
static int get_user_coercions(lua_State * L) {
@ -595,9 +616,9 @@ void open_coercion(lua_State * L) {
SET_GLOBAL_FUN(add_coercion, "add_coercion");
SET_GLOBAL_FUN(is_coercion, "is_coercion");
SET_GLOBAL_FUN(has_coercions_from, "has_coercions_from");
SET_GLOBAL_FUN(get_coercion, "get_coercion");
SET_GLOBAL_FUN(get_coercion_to_sort, "get_coercion_to_sort");
SET_GLOBAL_FUN(get_coercion_to_fun, "get_coercion_to_fun");
SET_GLOBAL_FUN(get_coercions, "get_coercions");
SET_GLOBAL_FUN(get_coercions_to_sort, "get_coercions_to_sort");
SET_GLOBAL_FUN(get_coercions_to_fun, "get_coercions_to_fun");
SET_GLOBAL_FUN(get_user_coercions, "get_user_coercions");
SET_GLOBAL_FUN(for_each_coercion_user, "for_each_coercion_user");
SET_GLOBAL_FUN(for_each_coercion_sort, "for_each_coercion_sort");

6
src/library/coercion.h
View file

@ -53,9 +53,9 @@ bool has_coercions_to(environment const & env, name const & D);
The coercion is a unary function that takes a term of type (C_name.{l1 lk} t_1 ... t_n) and returns
and element of type (D.{L_1 L_o} s_1 ... s_m)
*/
optional<expr> get_coercion(environment const & env, expr const & C, name const & D);
optional<expr> get_coercion_to_sort(environment const & env, expr const & C);
optional<expr> get_coercion_to_fun(environment const & env, expr const & C);
list<expr> get_coercions(environment const & env, expr const & C, name const & D);
list<expr> get_coercions_to_sort(environment const & env, expr const & C);
list<expr> get_coercions_to_fun(environment const & env, expr const & C);
/**
\brief Return all user coercions C >-> D for the type C of the form (C_name.{l1 ... lk} t_1 ... t_n)
The result is a pair (user-class D, coercion, coercion type), and is stored in the result buffer \c result.

17
tests/lean/run/coe10.lean Normal file
View file

@ -0,0 +1,17 @@
import data.nat
open nat
inductive fn2 (A B C : Type) :=
mk : (A → C) → (B → C) → fn2 A B C
definition to_ac [coercion] {A B C : Type} (f : fn2 A B C) : A → C :=
fn2.rec (λ f g, f) f
definition to_bc [coercion] {A B C : Type} (f : fn2 A B C) : B → C :=
fn2.rec (λ f g, g) f
variable f : fn2 Prop nat nat
variable a : Prop
variable n : nat
check f a
check f n

25
tests/lean/run/coe11.lean Normal file
View file

@ -0,0 +1,25 @@
import data.category
open category
inductive my_functor {obC obD : Type} (C : category obC) (D : category obD) : Type :=
mk : Π (obF : obC → obD) (morF : Π{A B : obC}, mor A B → mor (obF A) (obF B)),
(Π {A : obC}, morF (ID A) = ID (obF A)) →
(Π {A B C : obC} {f : mor A B} {g : mor B C}, morF (g ∘ f) = morF g ∘ morF f) →
my_functor C D
definition my_object [coercion] {obC obD : Type} {C : category obC} {D : category obD} (F : my_functor C D) : obC → obD :=
my_functor.rec (λ obF morF Hid Hcomp, obF) F
definition my_morphism [coercion] {obC obD : Type} {C : category obC} {D : category obD} (F : my_functor C D) :
Π{A B : obC}, mor A B → mor (my_object F A) (my_object F B) :=
my_functor.rec (λ obF morF Hid Hcomp, morF) F
variables obC obD : Type
variables a b : obC
variable C : category obC
instance C
variable D : category obD
variable F : my_functor C D
variable m : mor a b
check F a
check F m

27
tests/lean/run/coe9.lean Normal file
View file

@ -0,0 +1,27 @@
import data.nat
open nat
variable list.{l} : Type.{l} → Type.{l}
variable vector.{l} : Type.{l} → nat → Type.{l}
variable matrix.{l} : Type.{l} → nat → nat → Type.{l}
variable length : Pi {A : Type}, list A → nat
variable list_to_vec {A : Type} (l : list A) : vector A (length l)
variable to_row {A : Type} {n : nat} : vector A n → matrix A 1 n
variable to_col {A : Type} {n : nat} : vector A n → matrix A n 1
variable to_list {A : Type} {n : nat} : vector A n → list A
coercion to_row
coercion to_col
coercion list_to_vec
coercion to_list
variable f {A : Type} {n : nat} (M : matrix A n 1) : nat
variable g {A : Type} {n : nat} (M : matrix A 1 n) : nat
variable v : vector nat 10
variable l : list nat
check f v
check g v
check f l
check g l

28
tests/lua/coe1.lua
View file

@ -32,33 +32,41 @@ env = add_coercion(env, "lst2vec")
assert(is_coercion(env, Const("lst2vec", {l})))
assert(has_coercions_from(env, "lst"))
local lst_nat = lst_1(nat)
print(get_coercion(env, lst_nat, "vec"))
function display_coercions(coes)
if not coes:is_nil() then
print(coes:head())
display_coercions(coes:tail())
end
end
display_coercions(get_coercions(env, lst_nat, "vec"))
env = add_coercion(env, "vec2mat")
print(get_coercion(env, lst_nat, "mat"))
assert(env:type_check(get_coercion(env, lst_nat, "mat")))
display_coercions(get_coercions(env, lst_nat, "mat"))
assert(env:type_check(get_coercions(env, lst_nat, "mat"):head()))
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
env = add_coercion(env, "nat2lst")
print("---------")
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
print(get_coercion(env, nat, "mat"))
assert(env:type_check(get_coercion(env, nat, "mat")))
print(get_coercions(env, nat, "mat"):head())
assert(env:type_check(get_coercions(env, nat, "mat"):head()))
env = add_coercion(env, "mat2dlst")
print("---------")
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
print(get_coercion(env, lst_nat, "dlst"))
assert(env:type_check(get_coercion(env, lst_nat, "dlst")))
print(get_coercions(env, lst_nat, "dlst"):head())
assert(env:type_check(get_coercions(env, lst_nat, "dlst"):head()))
env:export("coe1_mod.olean")
local env2 = import_modules("coe1_mod")
print(get_coercion(env2, lst_nat, "dlst"))
assert(env2:type_check(get_coercion(env2, lst_nat, "dlst")))
print(get_coercions(env2, lst_nat, "dlst"):head())
assert(env2:type_check(get_coercions(env2, lst_nat, "dlst"):head()))
assert(is_coercion(env2, "vec2mat"))
assert(is_coercion(env2, "lst2vec"))
env2 = add_decl(env2, mk_var_decl("lst2vec2", {l}, Pi(A, ll, vec_l(A, len_l(A, ll)))))
print("======")
env2 = add_coercion(env2, "lst2vec2")
print("======")
print(get_coercion(env2, lst_nat, "dlst"))
print(get_coercions(env2, lst_nat, "dlst"):head())
print("---------")
for_each_coercion_user(env2, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
env2 = add_coercion(env2, "vec2lst")

6
tests/lua/coe2.lua
View file

@ -13,9 +13,9 @@ env = add_decl(env, mk_var_decl("real", Type))
local nat = Const("nat")
local real = Const("real")
env = add_decl(env, mk_var_decl("f1", Const("functor", {1, 1})(nat, real)))
print(get_coercion_to_fun(env, Const("functor", {1, 1})(nat, real)))
print(get_coercions_to_fun(env, Const("functor", {1, 1})(nat, real)):head())
env = add_decl(env, mk_var_decl("sfunctor", {l1}, mk_arrow(mk_sort(l1), mk_sort(l1))))
env = add_decl(env, mk_var_decl("sf2f", {l1}, Pi(A, mk_arrow(Const("sfunctor", {l1})(A), Const("functor", {l1, l1})(A, A)))))
env = add_coercion(env, "sf2f")
print(get_coercion_to_fun(env, Const("sfunctor", {1})(nat)))
assert(env:type_check(get_coercion_to_fun(env, Const("sfunctor", {1})(nat))))
print(get_coercions_to_fun(env, Const("sfunctor", {1})(nat)):head())
assert(env:type_check(get_coercions_to_fun(env, Const("sfunctor", {1})(nat)):head()))

4
tests/lua/coe3.lua
View file

@ -9,5 +9,5 @@ env = add_coercion(env, "carrier")
env = add_decl(env, mk_var_decl("abg2g", {l}, mk_arrow(ab_group, group)))
env = add_coercion(env, "abg2g")
for_each_coercion_sort(env, function(C, f) print(tostring(C) .. " >-> sort : " .. tostring(f)) end)
print(get_coercion_to_sort(env, Const("abelian_group", {1})))
assert(env:type_check(get_coercion_to_sort(env, Const("abelian_group", {1}))))
print(get_coercions_to_sort(env, Const("abelian_group", {1})):head())
assert(env:type_check(get_coercions_to_sort(env, Const("abelian_group", {1})):head()))

4
tests/lua/coe5.lua
View file

@ -22,8 +22,8 @@ env = add_coercion(env, "ar2ag")
for_each_coercion_sort(env, function(C, f) print(tostring(C) .. " >-> sort : " .. tostring(f)) end)
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
print(get_coercion_to_sort(env, Const("abelian_ring", {1})))
assert(env:type_check(get_coercion_to_sort(env, Const("abelian_ring", {1}))))
print(get_coercions_to_sort(env, Const("abelian_ring", {1})):head())
assert(env:type_check(get_coercions_to_sort(env, Const("abelian_ring", {1})):head()))
print("Coercions (abelian ring): ")
cs = get_user_coercions(env, ab_ring)
for i = 1, #cs do

6
tests/lua/scope.lua
View file

@ -31,10 +31,10 @@ env = add_decl(env, mk_var_decl("nat2lst", mk_arrow(nat, lst_1(nat))))
env = add_coercion(env, "lst2vec")
env = push_scope(env, "tst")
local lst_nat = lst_1(nat)
print(get_coercion(env, lst_nat, "vec"))
print(get_coercions(env, lst_nat, "vec"):head())
env = add_coercion(env, "vec2mat")
print(get_coercion(env, lst_nat, "mat"))
assert(env:type_check(get_coercion(env, lst_nat, "mat")))
print(get_coercions(env, lst_nat, "mat"):head())
assert(env:type_check(get_coercions(env, lst_nat, "mat"):head()))
function get_num_coercions(env)
local r = 0
for_each_coercion_user(env, function(C, D, f) r = r + 1 end)