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feat(frontends/lean): add 'using' command

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-01-05 22:53:03 -08:00
parent 8c956280d9
commit 645e748302
4 changed files with 102 additions and 40 deletions
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19
examples/lean/even.lean
View file

@ -1,9 +1,10 @@
import macros.
import macros
using Nat
-- In this example, we prove two simple theorems about even/odd numbers.
-- First, we define the predicates even and odd.
definition even (a : Nat) := ∃ b, a = 2*b.
definition odd (a : Nat) := ∃ b, a = 2*b + 1.
definition even (a : Nat) := ∃ b, a = 2*b
definition odd (a : Nat) := ∃ b, a = 2*b + 1
-- Prove that the sum of two even numbers is even.
--
@ -34,7 +35,7 @@ theorem EvenPlusEven {a b : Nat} (H1 : even a) (H2 : even b) : even (a + b)
exists::intro (w1 + w2)
(calc a + b = 2*w1 + b : { Hw1 }
... = 2*w1 + 2*w2 : { Hw2 }
... = 2*(w1 + w2) : symm (Nat::distribute 2 w1 w2)).
... = 2*(w1 + w2) : symm (distribute 2 w1 w2))
-- In the following example, we omit the arguments for Nat::PlusAssoc, Refl and Nat::Distribute.
-- Lean can infer them automatically.
@ -53,19 +54,19 @@ theorem OddPlusOne {a : Nat} (H : odd a) : even (a + 1)
:= obtain (w : Nat) (Hw : a = 2*w + 1), from H,
exists::intro (w + 1)
(calc a + 1 = 2*w + 1 + 1 : { Hw }
... = 2*w + (1 + 1) : symm (Nat::plus::assoc _ _ _)
... = 2*w + (1 + 1) : symm (plus::assoc _ _ _)
... = 2*w + 2*1 : refl _
... = 2*(w + 1) : symm (Nat::distribute _ _ _)).
... = 2*(w + 1) : symm (distribute _ _ _))
-- The following command displays the proof object produced by Lean after
-- expanding macros, and infering implicit/missing arguments.
print environment 2.
print environment 2
-- By default, Lean does not display implicit arguments.
-- The following command will force it to display them.
set::option pp::implicit true.
set::option pp::implicit true
print environment 2.
print environment 2
-- As an exercise, prove that the sum of two odd numbers is even,
-- and other similar theorems.

57
src/frontends/lean/parser_cmds.cpp
View file

@ -51,12 +51,13 @@ static name g_scope_kwd("scope");
static name g_builtin_kwd("builtin");
static name g_namespace_kwd("namespace");
static name g_end_kwd("end");
static name g_using_kwd("using");
/** \brief Table/List with all builtin command keywords */
static list<name> g_command_keywords = {g_definition_kwd, g_variable_kwd, g_variables_kwd, g_theorem_kwd, g_axiom_kwd, g_universe_kwd, g_eval_kwd,
g_check_kwd, g_infix_kwd, g_infixl_kwd, g_infixr_kwd, g_notation_kwd,
g_set_option_kwd, g_set_opaque_kwd, g_env_kwd, g_options_kwd, g_import_kwd, g_help_kwd, g_coercion_kwd,
g_exit_kwd, g_print_kwd, g_pop_kwd, g_scope_kwd, g_alias_kwd, g_builtin_kwd,
g_namespace_kwd, g_end_kwd};
g_namespace_kwd, g_end_kwd, g_using_kwd};
// ==========================================
list<name> const & parser_imp::get_command_keywords() {
@ -618,7 +619,8 @@ void parser_imp::parse_help() {
<< " set::opaque [id] [bool] set the given definition as opaque/transparent" << endl
<< " theorem [id] : [type] := [expr] define a new theorem" << endl
<< " variable [id] : [type] declare/postulate an element of the given type" << endl
<< " universe [id] [level] declare a new universe variable that is >= the given level" << endl;
<< " universe [id] [level] declare a new universe variable that is >= the given level" << endl
<< " using [id]_1 [id]_2? create an alias for object starting with the prefix [id]_1 using the [id]_2" << endl;
#if !defined(LEAN_WINDOWS)
regular(m_io_state) << "Type Ctrl-D to exit" << endl;
#endif
@ -707,6 +709,7 @@ void parser_imp::parse_scope() {
next();
m_scope_kinds.push_back(scope_kind::Scope);
reset_env(m_env->mk_child());
m_using_decls.push();
}
void parser_imp::parse_pop() {
@ -719,6 +722,7 @@ void parser_imp::parse_pop() {
throw parser_error("main scope cannot be removed", m_last_cmd_pos);
m_scope_kinds.pop_back();
reset_env(m_env->parent());
m_using_decls.pop();
}
void parser_imp::parse_namespace() {
@ -726,6 +730,7 @@ void parser_imp::parse_namespace() {
name id = check_identifier_next("invalid namespace declaration, identifier expected");
m_scope_kinds.push_back(scope_kind::Namespace);
m_namespace_prefixes.push_back(m_namespace_prefixes.back() + id);
m_using_decls.push();
}
void parser_imp::parse_end() {
@ -754,6 +759,52 @@ void parser_imp::parse_end() {
throw parser_error("invalid end namespace command, there are no open namespaces", m_last_cmd_pos);
m_namespace_prefixes.pop_back();
}
m_using_decls.pop();
}
static name replace_prefix(name const & n, name const & prefix, name const & new_prefix) {
if (n == prefix)
return new_prefix;
name p = replace_prefix(n.get_prefix(), prefix, new_prefix);
if (n.is_string())
return name(p, n.get_string());
else
return name(p, n.get_numeral());
}
void parser_imp::parse_using() {
next();
name prefix = check_identifier_next("invalid using command, identifier expected");
name new_prefix;
if (curr_is_identifier()) {
new_prefix = curr_name();
next();
}
buffer<std::pair<name, expr>> to_add;
for (auto it = m_env->begin_objects(); it != m_env->end_objects(); ++it) {
if (it->has_type() && it->has_name() && !is_hidden_object(*it) && is_prefix_of(prefix, it->get_name())) {
auto n = replace_prefix(it->get_name(), prefix, new_prefix);
if (!n.is_anonymous())
to_add.emplace_back(n, mk_constant(it->get_name()));
}
}
for (auto p : to_add) {
auto n = p.first;
if (m_verbose) {
auto it = m_using_decls.find(n);
if (it != m_using_decls.end())
diagnostic(m_io_state) << "warning: " << n << " will shadow " << it->second << endl;
auto obj = m_env->find_object(n);
if (obj)
diagnostic(m_io_state) << "warning: " << n << " will shadow " << obj->get_name() << endl;
}
m_using_decls.insert(n, p.second);
}
if (m_verbose)
regular(m_io_state) << " Using: " << prefix;
if (new_prefix)
regular(m_io_state) << " as " << new_prefix;
regular(m_io_state) << endl;
}
/** \brief Parse a Lean command. */
@ -814,6 +865,8 @@ bool parser_imp::parse_command() {
parse_namespace();
} else if (cmd_id == g_end_kwd) {
parse_end();
} else if (cmd_id == g_using_kwd) {
parse_using();
} else if (m_cmd_macros && m_cmd_macros->find(cmd_id) != m_cmd_macros->end()) {
parse_cmd_macro(cmd_id, m_last_cmd_pos);
} else {

63
src/frontends/lean/parser_expr.cpp
View file

@ -247,40 +247,45 @@ expr parser_imp::parse_mixfixc(operator_info const & op) {
}
expr parser_imp::get_name_ref(name const & id, pos_info const & p, bool implicit_args) {
lean_assert(!m_namespace_prefixes.empty());
auto it = m_namespace_prefixes.end();
auto begin = m_namespace_prefixes.begin();
while (it != begin) {
--it;
name nid = *it + id;
optional<object> obj = m_env->find_object(nid);
if (obj) {
object_kind k = obj->kind();
if (k == object_kind::Definition || k == object_kind::Postulate || k == object_kind::Builtin) {
if (implicit_args && has_implicit_arguments(m_env, obj->get_name())) {
std::vector<bool> const & imp_args = get_implicit_arguments(m_env, obj->get_name());
buffer<expr> args;
pos_info p = pos();
expr f = (k == object_kind::Builtin) ? obj->get_value() : mk_constant(obj->get_name());
args.push_back(save(f, p));
for (unsigned i = 0; i < imp_args.size(); i++) {
if (imp_args[i]) {
args.push_back(save(mk_placeholder(), pos()));
} else {
args.push_back(parse_expr(g_app_precedence));
auto it = m_using_decls.find(id);
if (it != m_using_decls.end()) {
return it->second;
} else {
lean_assert(!m_namespace_prefixes.empty());
auto it = m_namespace_prefixes.end();
auto begin = m_namespace_prefixes.begin();
while (it != begin) {
--it;
name nid = *it + id;
optional<object> obj = m_env->find_object(nid);
if (obj) {
object_kind k = obj->kind();
if (k == object_kind::Definition || k == object_kind::Postulate || k == object_kind::Builtin) {
if (implicit_args && has_implicit_arguments(m_env, obj->get_name())) {
std::vector<bool> const & imp_args = get_implicit_arguments(m_env, obj->get_name());
buffer<expr> args;
pos_info p = pos();
expr f = (k == object_kind::Builtin) ? obj->get_value() : mk_constant(obj->get_name());
args.push_back(save(f, p));
for (unsigned i = 0; i < imp_args.size(); i++) {
if (imp_args[i]) {
args.push_back(save(mk_placeholder(), pos()));
} else {
args.push_back(parse_expr(g_app_precedence));
}
}
return mk_app(args);
} else if (k == object_kind::Builtin) {
return obj->get_value();
} else {
return mk_constant(obj->get_name());
}
return mk_app(args);
} else if (k == object_kind::Builtin) {
return obj->get_value();
} else {
return mk_constant(obj->get_name());
throw parser_error(sstream() << "invalid object reference, object '" << nid << "' is not an expression.", p);
}
} else {
throw parser_error(sstream() << "invalid object reference, object '" << nid << "' is not an expression.", p);
} else if (!m_check_identifiers) {
return mk_constant(nid);
}
} else if (!m_check_identifiers) {
return mk_constant(nid);
}
}
throw parser_error(sstream() << "unknown identifier '" << id << "'", p);

3
src/frontends/lean/parser_imp.h
View file

@ -55,6 +55,7 @@ class parser_imp {
typedef name_map<expr> builtins;
typedef expr_map<pos_info> expr_pos_info;
typedef expr_map<tactic> tactic_hints; // a mapping from placeholder to tactic
typedef scoped_map<name, expr, name_hash, name_eq> using_decls;
environment m_env;
io_state m_io_state;
scanner m_scanner;
@ -72,6 +73,7 @@ class parser_imp {
pos_info m_last_cmd_pos;
pos_info m_last_script_pos;
tactic_hints m_tactic_hints;
using_decls m_using_decls;
std::vector<name> m_namespace_prefixes;
enum class scope_kind { Scope, Namespace };
std::vector<scope_kind> m_scope_kinds;
@ -417,6 +419,7 @@ private:
void parse_builtin();
void parse_namespace();
void parse_end();
void parse_using();
bool parse_command();
/*@}*/