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feat(kernel/type_checker): add infer_type

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-04-24 17:44:43 -07:00
parent 3e122ed355
commit a55c3c617d
8 changed files with 333 additions and 40 deletions
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3
src/kernel/expr.h
View file

@ -260,9 +260,10 @@ public:
macro():m_rc(0) {} macro():m_rc(0) {}
virtual ~macro() {} virtual ~macro() {}
virtual name get_name() const = 0; virtual name get_name() const = 0;
virtual expr get_type(unsigned num_args, expr const * arg_types) const = 0; virtual expr get_type(unsigned num_args, expr const * args, expr const * arg_types) const = 0;
virtual optional<expr> expand1(unsigned num_args, expr const * args) const = 0; virtual optional<expr> expand1(unsigned num_args, expr const * args) const = 0;
virtual optional<expr> expand(unsigned num_args, expr const * args) const = 0; virtual optional<expr> expand(unsigned num_args, expr const * args) const = 0;
virtual unsigned trust_level() const = 0;
virtual int push_lua(lua_State * L) const; virtual int push_lua(lua_State * L) const;
virtual bool operator==(macro const & other) const; virtual bool operator==(macro const & other) const;
bool operator<(macro const & other) const; bool operator<(macro const & other) const;

13
src/kernel/instantiate.cpp
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@ -11,7 +11,8 @@ Author: Leonardo de Moura
#include "kernel/instantiate.h" #include "kernel/instantiate.h"
namespace lean { namespace lean {
expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) { template<typename P = default_replace_postprocessor>
expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst, P const & p = P()) {
if (s >= get_free_var_range(a) || n == 0) if (s >= get_free_var_range(a) || n == 0)
return a; return a;
return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> { return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
@ -32,7 +33,7 @@ expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
} }
} }
return none_expr(); return none_expr();
}); }, p);
} }
expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, 0, n, s); } expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, 0, n, s); }
@ -40,6 +41,14 @@ expr instantiate(expr const & e, std::initializer_list<expr> const & l) { retur
expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s); } expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s); }
expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); } expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); }
expr instantiate(expr const & e, unsigned n, expr const * s, std::function<void(expr const & old_e, expr const & new_e)> const & new_eh) {
return instantiate(e, 0, n, s, new_eh);
}
expr instantiate(expr const & e, expr const & s, std::function<void(expr const & old_e, expr const & new_e)> const & new_eh) {
return instantiate(e, 1, &s, new_eh);
}
bool is_head_beta(expr const & t) { bool is_head_beta(expr const & t) {
expr const * it = &t; expr const * it = &t;
while (is_app(*it)) { while (is_app(*it)) {

12
src/kernel/instantiate.h
View file

@ -5,6 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura Author: Leonardo de Moura
*/ */
#pragma once #pragma once
#include <functional>
#include "kernel/expr.h" #include "kernel/expr.h"
namespace lean { namespace lean {
@ -17,6 +18,17 @@ expr instantiate(expr const & e, unsigned i, expr const & s);
/** \brief Replace free variable \c 0 with \c s in \c e. */ /** \brief Replace free variable \c 0 with \c s in \c e. */
expr instantiate(expr const & e, expr const & s); expr instantiate(expr const & e, expr const & s);
/**
\brief Replace the free variables in \c e.
Whenever a new sub-expression is created in the process, the procedure \c new_eh is invoked.
*/
expr instantiate(expr const & e, unsigned n, expr const * s, std::function<void(expr const & old_e, expr const & new_e)> const & new_eh);
/**
\brief Replace free variable \c 0 with \c s in \c e.
Whenever a new sub-expression is created in the process, the procedure \c new_eh is invoked.
*/
expr instantiate(expr const & e, expr const & s, std::function<void(expr const & old_e, expr const & new_e)> const & new_eh);
expr apply_beta(expr f, unsigned num_args, expr const * args); expr apply_beta(expr f, unsigned num_args, expr const * args);
bool is_head_beta(expr const & t); bool is_head_beta(expr const & t);
expr head_beta_reduce(expr const & t); expr head_beta_reduce(expr const & t);

9
src/kernel/level.cpp
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@ -622,6 +622,15 @@ format pp(level const & l, options const & opts) {
return pp(l, get_pp_unicode(opts), get_pp_indent(opts)); return pp(l, get_pp_unicode(opts), get_pp_indent(opts));
} }
format pp(level const & lhs, level const & rhs, bool unicode, unsigned indent) {
format leq = unicode ? format("≤") : format("<=");
return group(format{pp(lhs, unicode, indent), space(), leq, line(), pp(rhs, unicode, indent)});
}
format pp(level const & lhs, level const & rhs, options const & opts) {
return pp(lhs, rhs, get_pp_unicode(opts), get_pp_indent(opts));
}
bool is_trivial(level const & lhs, level const & rhs) { bool is_trivial(level const & lhs, level const & rhs) {
check_system("level constraints"); check_system("level constraints");
if (is_zero(lhs) || lhs == rhs) { if (is_zero(lhs) || lhs == rhs) {

5
src/kernel/level.h
View file

@ -212,6 +212,11 @@ format pp(level l, bool unicode, unsigned indent);
/** \brief Pretty print the given level expression using the given configuration options. */ /** \brief Pretty print the given level expression using the given configuration options. */
format pp(level const & l, options const & opts = options()); format pp(level const & l, options const & opts = options());
/** \brief Pretty print lhs <= rhs, unicode characters are used if \c unicode is \c true. */
format pp(level const & lhs, level const & rhs, bool unicode, unsigned indent);
/** \brief Pretty print lhs <= rhs using the given configuration options. */
format pp(level const & lhs, level const & rhs, options const & opts = options());
/** \brief Auxiliary class used to manage universe constraints. */ /** \brief Auxiliary class used to manage universe constraints. */
class universe_context { class universe_context {
struct imp; struct imp;

8
src/kernel/metavar.cpp
View file

@ -216,6 +216,10 @@ std::pair<expr, justification> substitution::d_instantiate_metavars(expr const &
return mk_pair(r, fn.get_justification()); return mk_pair(r, fn.get_justification());
} }
std::pair<level, justification> substitution::instantiate_metavars(level const & l) const {
return lean::instantiate_metavars(l, const_cast<substitution&>(*this), true, false);
}
expr substitution::instantiate_metavars_wo_jst(expr const & e) const { expr substitution::instantiate_metavars_wo_jst(expr const & e) const {
return instantiate_metavars_fn(const_cast<substitution&>(*this), false, false)(e); return instantiate_metavars_fn(const_cast<substitution&>(*this), false, false)(e);
} }
@ -224,6 +228,10 @@ expr substitution::d_instantiate_metavars_wo_jst(expr const & e) {
return instantiate_metavars_fn(*this, false, true)(e); return instantiate_metavars_fn(*this, false, true)(e);
} }
level substitution::instantiate_metavars_wo_jst(level const & l) const {
return lean::instantiate_metavars(l, const_cast<substitution&>(*this), false, false).first;
}
bool substitution::occurs_expr(name const & m, expr const & e) const { bool substitution::occurs_expr(name const & m, expr const & e) const {
if (!has_metavar(e)) if (!has_metavar(e))
return false; return false;

6
src/kernel/metavar.h
View file

@ -59,6 +59,9 @@ public:
*/ */
std::pair<expr, justification> d_instantiate_metavars(expr const & e); std::pair<expr, justification> d_instantiate_metavars(expr const & e);
/** \brief Instantiate level metavariables in \c l. */
std::pair<level, justification> instantiate_metavars(level const & l) const;
/** /**
\brief Instantiate metavariables in \c e assigned in the substitution \c s, \brief Instantiate metavariables in \c e assigned in the substitution \c s,
but does not return a justification object for the new expression. but does not return a justification object for the new expression.
@ -67,6 +70,9 @@ public:
expr d_instantiate_metavars_wo_jst(expr const & e); expr d_instantiate_metavars_wo_jst(expr const & e);
/** \brief Instantiate level metavariables in \c l, but does not return justification object. */
level instantiate_metavars_wo_jst(level const & l) const;
/** \brief Return true iff the metavariable \c m occurrs (directly or indirectly) in \c e. */ /** \brief Return true iff the metavariable \c m occurrs (directly or indirectly) in \c e. */
bool occurs_expr(name const & m, expr const & e) const; bool occurs_expr(name const & m, expr const & e) const;
/** \brief Return true iff the meta universe parameter \c m occurrs (directly or indirectly) in \c e. */ /** \brief Return true iff the meta universe parameter \c m occurrs (directly or indirectly) in \c e. */

317
src/kernel/type_checker.cpp
View file

@ -12,6 +12,10 @@ Author: Leonardo de Moura
#include "kernel/instantiate.h" #include "kernel/instantiate.h"
#include "kernel/max_sharing.h" #include "kernel/max_sharing.h"
#include "kernel/free_vars.h" #include "kernel/free_vars.h"
#include "kernel/metavar.h"
#include "kernel/error_msgs.h"
#include "kernel/kernel_exception.h"
#include "kernel/abstract.h"
namespace lean { namespace lean {
/** \brief Auxiliary functional object used to implement type checker. */ /** \brief Auxiliary functional object used to implement type checker. */
@ -23,9 +27,13 @@ struct type_checker::imp {
bool m_memoize; bool m_memoize;
name_set m_extra_opaque; name_set m_extra_opaque;
max_sharing_fn m_sharing; max_sharing_fn m_sharing;
expr_map<expr> m_cache; expr_map<expr> m_infer_type_cache;
expr_map<expr> m_whnf_core_cache; expr_map<expr> m_whnf_core_cache;
expr_map<expr> m_whnf_cache; expr_map<expr> m_whnf_cache;
// The following mapping is used to store the relationship
// between temporary expressions created during type checking and the original ones.
// We need that to be able to produce error messages containing position information.
expr_map<expr> m_trace;
imp(environment const & env, name_generator const & g, constraint_handler & h, imp(environment const & env, name_generator const & g, constraint_handler & h,
optional<module_idx> mod_idx, bool memoize, name_set const & extra_opaque): optional<module_idx> mod_idx, bool memoize, name_set const & extra_opaque):
@ -42,6 +50,7 @@ struct type_checker::imp {
virtual void add_cnstr(constraint const & c) { m_imp.add_cnstr(c); } virtual void add_cnstr(constraint const & c) { m_imp.add_cnstr(c); }
}; };
bool check_memoized(expr const & e) const { return !m_memoize || m_sharing.already_processed(e); }
expr max_sharing(expr const & e) { return m_memoize ? m_sharing(e) : e; } expr max_sharing(expr const & e) { return m_memoize ? m_sharing(e) : e; }
expr instantiate(expr const & e, unsigned n, expr const * s) { return max_sharing(lean::instantiate(e, n, s)); } expr instantiate(expr const & e, unsigned n, expr const * s) { return max_sharing(lean::instantiate(e, n, s)); }
expr instantiate(expr const & e, expr const & s) { return max_sharing(lean::instantiate(e, s)); } expr instantiate(expr const & e, expr const & s) { return max_sharing(lean::instantiate(e, s)); }
@ -65,8 +74,35 @@ struct type_checker::imp {
return none_expr(); return none_expr();
} }
bool check_memoized(expr const & e) const { /** \brief Add entry <tt>new_e -> old_e</tt> in the traceability mapping */
return !m_memoize || m_sharing.already_processed(e); void add_trace(expr const & old_e, expr const & new_e) {
if (!is_eqp(old_e, new_e))
m_trace.insert(mk_pair(new_e, old_e));
}
/** \brief Return the input (sub) expression that corresponds to the (temporary) expression \c e. */
expr trace_back(expr e) const {
while (true) {
auto it = m_trace.find(e);
if (it != m_trace.end())
e = it->second;
else
return e;
}
}
/** \brief Replace free variable \c 0 with \c s in \c e, and trace new sub-expressions created in the process. */
expr instantiate_with_trace(expr const & e, expr const & s) {
return lean::instantiate(e, s, [&](expr const & old_e, expr const & new_e) { add_trace(old_e, new_e); });
}
/**
\brief Return the body of the given binder, where the free variable #0 is replaced with a fresh local constant.
It also returns the fresh local constant.
*/
std::pair<expr, expr> open_binder_body(expr const & e) {
expr local = mk_local(m_gen.next() + binder_name(e), binder_domain(e));
return mk_pair(instantiate_with_trace(binder_body(e), local), local);
} }
/** \brief Weak head normal form core procedure. It does not perform delta reduction nor normalization extensions. */ /** \brief Weak head normal form core procedure. It does not perform delta reduction nor normalization extensions. */
@ -252,9 +288,10 @@ struct type_checker::imp {
} }
/** \brief Put expression \c e in weak head normal form */ /** \brief Put expression \c e in weak head normal form */
expr whnf(expr const & e) { expr whnf(expr e) {
// check cache // check cache
if (m_memoize) { if (m_memoize) {
e = max_sharing(e);
auto it = m_whnf_cache.find(e); auto it = m_whnf_cache.find(e);
if (it != m_whnf_cache.end()) if (it != m_whnf_cache.end())
return it->second; return it->second;
@ -279,21 +316,24 @@ struct type_checker::imp {
m_chandler.add_cnstr(c); m_chandler.add_cnstr(c);
} }
/** \brief Return the current/latest justification object created by the type checker. */ /** \brief Object to simulate delayed justification creation. */
justification get_curr_justification() { class delayed_justification {
// TODO(Leo) optional<justification> m_jst;
return mk_assumption_justification(0); std::function<justification()> m_mk;
} public:
template<typename Mk> delayed_justification(Mk && mk):m_mk(mk) {}
justification get() { if (!m_jst) { m_jst = m_mk(); } return *m_jst; }
};
/** \brief Eta-expand \c s and check if it is definitionally equal to \c t. */ /** \brief Eta-expand \c s and check if it is definitionally equal to \c t. */
bool try_eta(expr const & t, expr const & s) { bool try_eta(expr const & t, expr const & s, delayed_justification & jst) {
lean_assert(is_lambda(t)); lean_assert(is_lambda(t));
lean_assert(!is_lambda(s)); lean_assert(!is_lambda(s));
expr t_s = whnf(infer_type(s)); expr t_s = whnf(infer_type(s));
if (is_pi(t_s)) { if (is_pi(t_s)) {
// new_s := lambda x : domain(t_s), s x // new_s := lambda x : domain(t_s), s x
expr new_s = mk_lambda(m_gen.next(), binder_domain(t_s), mk_app(lift_free_vars(s, 1), mk_var(0))); expr new_s = mk_lambda(m_gen.next(), binder_domain(t_s), mk_app(lift_free_vars(s, 1), mk_var(0)));
return is_def_eq(t, new_s); return is_def_eq(t, new_s, jst);
} else { } else {
return false; return false;
} }
@ -318,7 +358,7 @@ struct type_checker::imp {
and and
body(t) is convertible to body(s) body(t) is convertible to body(s)
*/ */
bool is_conv_binder(expr t, expr s, bool def_eq) { bool is_conv_binder(expr t, expr s, bool def_eq, delayed_justification & jst) {
lean_assert(t.kind() == s.kind()); lean_assert(t.kind() == s.kind());
lean_assert(is_binder(t)); lean_assert(is_binder(t));
expr_kind k = t.kind(); expr_kind k = t.kind();
@ -326,13 +366,13 @@ struct type_checker::imp {
do { do {
expr var_t_type = instantiate(binder_domain(t), subst.size(), subst.data()); expr var_t_type = instantiate(binder_domain(t), subst.size(), subst.data());
expr var_s_type = instantiate(binder_domain(s), subst.size(), subst.data()); expr var_s_type = instantiate(binder_domain(s), subst.size(), subst.data());
if (!is_def_eq(var_t_type, var_s_type)) if (!is_def_eq(var_t_type, var_s_type, jst))
return false; return false;
subst.push_back(mk_local(m_gen.next(), var_s_type)); subst.push_back(mk_local(m_gen.next() + binder_name(s), var_s_type));
t = binder_body(t); t = binder_body(t);
s = binder_body(s); s = binder_body(s);
} while (t.kind() == k && s.kind() == k); } while (t.kind() == k && s.kind() == k);
return is_conv(instantiate(t, subst.size(), subst.data()), instantiate(s, subst.size(), subst.data()), def_eq); return is_conv(instantiate(t, subst.size(), subst.data()), instantiate(s, subst.size(), subst.data()), def_eq, jst);
} }
/** /**
@ -340,30 +380,30 @@ struct type_checker::imp {
If \c def_eq is true, then it checks for definitional equality. If \c def_eq is true, then it checks for definitional equality.
*/ */
lbool quick_is_conv(expr const & t, expr const & s, bool def_eq) { lbool quick_is_conv(expr const & t, expr const & s, bool def_eq, delayed_justification & jst) {
if (t == s) if (t == s)
return l_true; // t and s are structurally equal return l_true; // t and s are structurally equal
if (is_meta(t) || is_meta(s)) { if (is_meta(t) || is_meta(s)) {
// if t or s is a metavariable (or the application of a metavariable), then add constraint // if t or s is a metavariable (or the application of a metavariable), then add constraint
if (def_eq) if (def_eq)
add_cnstr(mk_eq_cnstr(t, s, get_curr_justification())); add_cnstr(mk_eq_cnstr(t, s, jst.get()));
else else
add_cnstr(mk_conv_cnstr(t, s, get_curr_justification())); add_cnstr(mk_conv_cnstr(t, s, jst.get()));
return l_true; return l_true;
} }
if (t.kind() == s.kind()) { if (t.kind() == s.kind()) {
switch (t.kind()) { switch (t.kind()) {
case expr_kind::Lambda: case expr_kind::Lambda:
return to_lbool(is_conv_binder(t, s, true)); return to_lbool(is_conv_binder(t, s, true, jst));
case expr_kind::Pi: case expr_kind::Pi:
return to_lbool(is_conv_binder(t, s, def_eq)); return to_lbool(is_conv_binder(t, s, def_eq, jst));
case expr_kind::Sort: case expr_kind::Sort:
// t and s are Sorts // t and s are Sorts
if (is_trivial(sort_level(t), sort_level(s)) && (!def_eq || is_trivial(sort_level(s), sort_level(t)))) if (is_trivial(sort_level(t), sort_level(s)) && (!def_eq || is_trivial(sort_level(s), sort_level(t))))
return l_true; return l_true;
add_cnstr(mk_level_cnstr(sort_level(t), sort_level(s), get_curr_justification())); add_cnstr(mk_level_cnstr(sort_level(t), sort_level(s), jst.get()));
if (def_eq) if (def_eq)
add_cnstr(mk_level_cnstr(sort_level(s), sort_level(t), get_curr_justification())); add_cnstr(mk_level_cnstr(sort_level(s), sort_level(t), jst.get()));
return l_true; return l_true;
case expr_kind::Meta: case expr_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE lean_unreachable(); // LCOV_EXCL_LINE
@ -380,16 +420,16 @@ struct type_checker::imp {
\brief If def_eq is false, then return true iff t is convertible to s. \brief If def_eq is false, then return true iff t is convertible to s.
If def_eq is true, then return true iff t is definitionally equal to s. If def_eq is true, then return true iff t is definitionally equal to s.
*/ */
bool is_conv(expr const & t, expr const & s, bool def_eq) { bool is_conv(expr const & t, expr const & s, bool def_eq, delayed_justification & jst) {
check_system("is_convertible"); check_system("is_convertible");
lbool r = quick_is_conv(t, s, def_eq); lbool r = quick_is_conv(t, s, def_eq, jst);
if (r != l_undef) return r == l_true; if (r != l_undef) return r == l_true;
// apply whnf (without using delta-reduction or normalizer extensions) // apply whnf (without using delta-reduction or normalizer extensions)
expr t_n = whnf_core(t); expr t_n = whnf_core(t);
expr s_n = whnf_core(s); expr s_n = whnf_core(s);
if (!is_eqp(t_n, t) || !is_eqp(s_n, s)) { if (!is_eqp(t_n, t) || !is_eqp(s_n, s)) {
r = quick_is_conv(t_n, s_n, def_eq); r = quick_is_conv(t_n, s_n, def_eq, jst);
if (r != l_undef) return r == l_true; if (r != l_undef) return r == l_true;
} }
@ -418,7 +458,7 @@ struct type_checker::imp {
t_n = whnf_core(unfold_names(t_n, d_t->get_weight() - 1)); t_n = whnf_core(unfold_names(t_n, d_t->get_weight() - 1));
s_n = whnf_core(unfold_names(s_n, d_s->get_weight() - 1)); s_n = whnf_core(unfold_names(s_n, d_s->get_weight() - 1));
} }
r = quick_is_conv(t_n, s_n, def_eq); r = quick_is_conv(t_n, s_n, def_eq, jst);
if (r != l_undef) return r == l_true; if (r != l_undef) return r == l_true;
} }
// try normalizer extensions // try normalizer extensions
@ -430,7 +470,7 @@ struct type_checker::imp {
t_n = whnf_core(*new_t_n); t_n = whnf_core(*new_t_n);
if (new_s_n) if (new_s_n)
s_n = whnf_core(*new_s_n); s_n = whnf_core(*new_s_n);
r = quick_is_conv(t_n, s_n, def_eq); r = quick_is_conv(t_n, s_n, def_eq, jst);
if (r != l_undef) return r == l_true; if (r != l_undef) return r == l_true;
} }
@ -439,8 +479,8 @@ struct type_checker::imp {
if (m_env.eta()) { if (m_env.eta()) {
lean_assert(!is_lambda(t_n) || !is_lambda(s_n)); lean_assert(!is_lambda(t_n) || !is_lambda(s_n));
// Eta-reduction support // Eta-reduction support
if ((is_lambda(t_n) && try_eta(t_n, s_n)) || if ((is_lambda(t_n) && try_eta(t_n, s_n, jst)) ||
(is_lambda(s_n) && try_eta(s_n, t_n))) (is_lambda(s_n) && try_eta(s_n, t_n, jst)))
return true; return true;
} }
@ -449,29 +489,34 @@ struct type_checker::imp {
expr it2 = s_n; expr it2 = s_n;
bool ok = true; bool ok = true;
do { do {
if (!is_def_eq(app_arg(it1), app_arg(it2))) { if (!is_def_eq(app_arg(it1), app_arg(it2), jst)) {
ok = false; ok = false;
break; break;
} }
it1 = app_fn(it1); it1 = app_fn(it1);
it2 = app_fn(it2); it2 = app_fn(it2);
} while (is_app(it1) && is_app(it2)); } while (is_app(it1) && is_app(it2));
if (ok && is_def_eq(it1, it2)) if (ok && is_def_eq(it1, it2, jst))
return true; return true;
} }
if (m_env.proof_irrel()) { if (m_env.proof_irrel()) {
// Proof irrelevance support // Proof irrelevance support
expr t_type = infer_type(t); expr t_type = infer_type(t);
return is_proposition(t_type) && is_def_eq(t_type, infer_type(s)); return is_proposition(t_type) && is_def_eq(t_type, infer_type(s), jst);
} }
return false; return false;
} }
/** \brief Return true iff \c t is convertible to s */
bool is_conv(expr const & t, expr const & s, delayed_justification & jst) {
return is_conv(t, s, false, jst);
}
/** \brief Return true iff \c t and \c s are definitionally equal */ /** \brief Return true iff \c t and \c s are definitionally equal */
bool is_def_eq(expr const & t, expr const & s) { bool is_def_eq(expr const & t, expr const & s, delayed_justification & jst) {
return is_conv(t, s, true); return is_conv(t, s, true, jst);
} }
/** \brief Return true iff \c e is a proposition */ /** \brief Return true iff \c e is a proposition */
@ -479,9 +524,207 @@ struct type_checker::imp {
return whnf(infer_type(e)) == Bool; return whnf(infer_type(e)) == Bool;
} }
expr infer_type(expr const &) { /**
// TODO(Leo) \brief Make sure \c e "is" a sort, and return the corresponding sort.
return expr(); If \c e is not a sort, then the whnf procedure is invoked. Then, there are
two options: the normalize \c e is a sort, or it is a meta. If it is a meta,
a new constraint is created forcing it to be a sort.
\remark \c s is used to extract position (line number information) when an
error message is produced
*/
expr ensure_sort(expr e, expr const & s) {
if (is_sort(e))
return e;
e = whnf(e);
if (is_sort(e)) {
return e;
} else if (is_meta(e)) {
expr r = mk_sort(mk_meta_univ(m_gen.next()));
justification j = mk_justification(trace_back(s),
[=](formatter const & fmt, options const & o, substitution const & subst) {
return pp_type_expected(fmt, o, subst.instantiate_metavars_wo_jst(s));
});
add_cnstr(mk_eq_cnstr(e, r, j));
return r;
} else {
throw_kernel_exception(m_env, trace_back(s),
[=](formatter const & fmt, options const & o) { return pp_type_expected(fmt, o, s); });
}
} }
/** \brief Similar to \c ensure_sort, but makes sure \c e "is" a Pi. */
expr ensure_pi(expr e, expr const & s) {
if (is_pi(e))
return e;
e = whnf(e);
if (is_pi(e)) {
return e;
} else if (is_meta(e)) {
// TODO(Leo)
return e;
} else {
throw_kernel_exception(m_env, trace_back(s),
[=](formatter const & fmt, options const & o) { return pp_function_expected(fmt, o, s); });
}
}
/** \brief Create a justification for the level constraint <tt>lhs <= rhs</tt> associated with constanc \c c. */
justification mk_lvl_cnstr_jst(expr const & c, level const & lhs, level const & rhs) {
lean_assert(is_constant(c));
return mk_justification(trace_back(c),
[=](formatter const & fmt, options const & o, substitution const & subst) {
return pp_def_lvl_cnstrs_satisfied(fmt, o,
subst.instantiate_metavars_wo_jst(c),
subst.instantiate_metavars_wo_jst(lhs),
subst.instantiate_metavars_wo_jst(rhs));
});
}
/**
\brief Create a justification for a application type mismatch,
\c e is the application, \c fn_type and \c arg_type are the function and argument type.
*/
justification mk_app_mismatch_jst(expr const & e, expr const & fn_type, expr const & arg_type) {
lean_assert(is_app(e));
return mk_justification(trace_back(e),
[=](formatter const & fmt, options const & o, substitution const & subst) {
return pp_app_type_mismatch(fmt, o,
subst.instantiate_metavars_wo_jst(e),
subst.instantiate_metavars_wo_jst(binder_domain(fn_type)),
subst.instantiate_metavars_wo_jst(arg_type));
});
}
/**
\brief Create a justification for a let definition type mismatch,
\c e is the let expression, and \c val_type is the type inferred for the let value.
*/
justification mk_let_mismatch_jst(expr const & e, expr const & val_type) {
lean_assert(is_let(e));
return mk_justification(trace_back(e),
[=](formatter const & fmt, options const & o, substitution const & subst) {
return pp_def_type_mismatch(fmt, o, let_name(e),
subst.instantiate_metavars_wo_jst(let_type(e)),
subst.instantiate_metavars_wo_jst(val_type));
});
}
static constexpr char const * g_macro_error_msg = "failed to type check macro expansion";
justification mk_macro_jst(expr const & e) {
return mk_justification(trace_back(e),
[=](formatter const &, options const &, substitution const &) {
return format(g_macro_error_msg);
});
}
/**
\brief Return type of expression \c e, if \c infer_only is false, then it also check whether \c e is type correct or not.
\pre closed(e)
*/
expr infer_type_core(expr const & e, bool infer_only) {
lean_assert(closed(e));
check_system("type checker");
bool shared = false;
if (m_memoize && is_shared(e)) {
shared = true;
auto it = m_infer_type_cache.find(e);
if (it != m_infer_type_cache.end())
return it->second;
}
expr r;
switch (e.kind()) {
case expr_kind::Local: case expr_kind::Meta:
r = mlocal_type(e);
break;
case expr_kind::Var:
throw_kernel_exception(m_env, "type checker does not support free variables, replace them with local constants before invoking it");
case expr_kind::Sort:
r = mk_sort(mk_succ(sort_level(e)));
break;
case expr_kind::Constant: {
definition d = m_env.get(const_name(e));
auto const & ps = d.get_params();
auto const & ls = const_level_params(e);
auto const & cs = d.get_level_cnstrs();
if (!infer_only && !is_nil(cs)) {
// add level constraints associated with the definition
for (auto const & c : cs) {
level lhs = lean::instantiate(c.first, ps, ls);
level rhs = lean::instantiate(c.second, ps, ls);
if (!is_trivial(lhs, rhs))
add_cnstr(mk_level_cnstr(lhs, rhs, mk_lvl_cnstr_jst(e, lhs, rhs)));
}
}
r = instantiate_params(d.get_type(), ps, ls);
break;
}
case expr_kind::Macro:
r = to_macro(e).get_type(0, 0, 0);
if (!infer_only && to_macro(e).trust_level() <= m_env.trust_lvl()) {
optional<expr> m = to_macro(e).expand(0, 0);
if (!m)
throw_kernel_exception(m_env, "failed to expand macro", some_expr(e));
expr t = infer_type_core(*m, infer_only);
delayed_justification jst([=]() { return mk_macro_jst(e); });
if (!is_def_eq(r, t, jst))
throw_kernel_exception(m_env, g_macro_error_msg, some_expr(e));
}
break;
case expr_kind::Lambda: {
if (!infer_only) {
expr t = infer_type_core(binder_domain(e), infer_only);
ensure_sort(t, binder_domain(e));
}
auto b = open_binder_body(e);
r = Pi(b.second, binder_domain(e), infer_type_core(b.first, infer_only));
break;
}
case expr_kind::Pi: {
expr t1 = ensure_sort(infer_type_core(binder_domain(e), infer_only), binder_domain(e));
auto b = open_binder_body(e);
expr t2 = ensure_sort(infer_type_core(b.first, infer_only), binder_body(e));
r = mk_sort(mk_imax(sort_level(t1), sort_level(t2)));
break;
}
case expr_kind::App: {
expr f_type = ensure_pi(infer_type_core(app_fn(e), infer_only), app_fn(e));
if (!infer_only) {
expr a_type = infer_type_core(app_arg(e), infer_only);
delayed_justification jst([=]() { return mk_app_mismatch_jst(e, f_type, a_type); });
if (!is_conv(a_type, binder_domain(f_type), jst)) {
throw_kernel_exception(m_env, trace_back(e),
[=](formatter const & fmt, options const & o) { return pp_app_type_mismatch(fmt, o, e, binder_domain(f_type), a_type); });
}
}
r = instantiate(binder_body(f_type), app_arg(e));
break;
}
case expr_kind::Let:
if (!infer_only) {
ensure_sort(infer_type_core(let_type(e), infer_only), let_type(e));
expr val_type = infer_type_core(let_value(e), infer_only);
delayed_justification jst([=]() { return mk_let_mismatch_jst(e, val_type); });
if (!is_conv(val_type, let_type(e), jst)) {
throw_kernel_exception(m_env, trace_back(e),
[=](formatter const & fmt, options const & o) { return pp_def_type_mismatch(fmt, o, let_name(e), let_type(e), val_type); });
}
}
r = infer_type_core(instantiate_with_trace(let_body(e), let_value(e)), infer_only);
break;
}
if (m_memoize && shared)
m_infer_type_cache.insert(mk_pair(e, r));
return r;
}
expr infer_type(expr const & e) { return infer_type_core(e, true); }
expr check(expr const & e) { return infer_type_core(e, false); }
}; };
} }