lean2/src/kernel/metavar.cpp
Leonardo de Moura 3df6149daa Add support for metavariables in the type checker.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-09-17 11:09:59 -07:00

204 lines
5.6 KiB
C++

/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include <limits>
#include "util/exception.h"
#include "kernel/metavar.h"
#include "kernel/replace.h"
#include "kernel/free_vars.h"
#include "kernel/instantiate.h"
#include "kernel/occurs.h"
#include "kernel/for_each.h"
namespace lean {
void metavar_env::inc_timestamp() {
if (m_timestamp == std::numeric_limits<unsigned>::max()) {
// This should not happen in real examples. We add it just to be safe.
throw exception("metavar_env timestamp overflow");
}
m_timestamp++;
}
metavar_env::metavar_env():m_timestamp(0) {}
expr metavar_env::mk_metavar(context const & ctx) {
inc_timestamp();
unsigned midx = m_env.size();
m_env.push_back(data(ctx));
return ::lean::mk_metavar(midx);
}
bool metavar_env::contains(unsigned midx) const {
return midx < m_env.size();
}
bool metavar_env::is_assigned(unsigned midx) const {
return m_env[midx].m_subst;
}
expr metavar_env::get_subst(unsigned midx) const {
return m_env[midx].m_subst;
}
expr metavar_env::get_type(unsigned midx, unification_problems & up) {
auto p = m_env[midx];
expr t = p->m_type;
if (t) {
return t;
} else {
t = mk_metavar();
expr s = p->m_subst;
m_env[midx] = data(s, t, p->m_ctx);
if (s)
up.add_type_of_eq(p->m_ctx, s, t);
else
up.add_type_of_eq(p->m_ctx, ::lean::mk_metavar(midx), t);
return t;
}
}
void metavar_env::assign(unsigned midx, expr const & v) {
inc_timestamp();
lean_assert(!is_assigned(midx));
auto p = m_env[midx];
m_env[midx] = data(v, p->m_type, p->m_ctx);
}
context const & metavar_env::get_context(unsigned midx) const {
return m_env[midx].m_ctx;
}
expr instantiate(expr const & s, meta_ctx const & ctx, metavar_env const & env) {
if (ctx) {
expr r = instantiate(s, tail(ctx), env);
meta_entry const & e = head(ctx);
if (e.is_lift()) {
return lift_free_vars(r, e.s(), e.n());
} else {
lean_assert(e.is_inst());
return ::lean::instantiate(r, e.s(), instantiate_metavars(e.v(), env));
}
} else {
return s;
}
}
expr metavar_env::get_subst(expr const & m) const {
expr s = get_subst(metavar_idx(m));
if (s)
return instantiate(s, metavar_ctx(m), *this);
else
return s;
}
expr metavar_env::get_type(expr const & m, unification_problems & up) {
expr s = get_type(metavar_idx(m), up);
lean_assert(is_metavar(s));
lean_assert(!metavar_ctx(s));
meta_ctx const & ctx = metavar_ctx(m);
if (ctx)
return ::lean::mk_metavar(metavar_idx(s), ctx);
else
return s;
}
void metavar_env::assign(expr const & m, expr const & t) {
lean_assert(!metavar_ctx(m));
assign(metavar_idx(m), t);
}
expr instantiate_metavars(expr const & e, metavar_env const & env) {
if (!has_metavar(e)) {
return e;
} else {
auto f = [=](expr const & m, unsigned offset) -> expr {
if (is_metavar(m) && env.contains(m)) {
expr s = env.get_subst(m);
return s ? s : m;
} else {
return m;
}
};
return replace_fn<decltype(f)>(f)(e);
}
}
meta_ctx add_lift(meta_ctx const & ctx, unsigned s, unsigned n) {
if (n == 0) {
return ctx;
} else if (ctx) {
meta_entry e = head(ctx);
// Simplification rule
// lift:(s1+n1):n2 lift:s1:n1 ---> lift:s1:n1+n2
if (e.is_lift() && s == e.s() + e.n()) {
return add_lift(tail(ctx), e.s(), e.n() + n);
}
}
return cons(mk_lift(s, n), ctx);
}
expr add_lift(expr const & m, unsigned s, unsigned n) {
return mk_metavar(metavar_idx(m), add_lift(metavar_ctx(m), s, n));
}
meta_ctx add_inst(meta_ctx const & ctx, unsigned s, expr const & v) {
if (ctx) {
meta_entry e = head(ctx);
if (e.is_lift() && e.s() <= s && s < e.s() + e.n()) {
return add_lift(tail(ctx), e.s(), e.n() - 1);
}
// Simplifications such as
// inst:4 #6 lift:5:3 --> lift:4:2
// inst:3 #7 lift:4:5 --> lift:3:4
// General rule is:
// inst:(s-1) #(s+n-2) lift:s:n --> lift:s-1:n-1
if (e.is_lift() && is_var(v) && e.s() > 0 && s == e.s() - 1 && e.s() + e.n() > 2 && var_idx(v) == e.s() + e.n() - 2) {
return add_lift(tail(ctx), e.s() - 1, e.n() - 1);
}
}
return cons(mk_inst(s, v), ctx);
}
expr add_inst(expr const & m, unsigned s, expr const & v) {
return mk_metavar(metavar_idx(m), add_inst(metavar_ctx(m), s, v));
}
bool has_context(expr const & m) {
return metavar_ctx(m);
}
expr pop_context(expr const & m) {
lean_assert(has_context(m));
return mk_metavar(metavar_idx(m), tail(metavar_ctx(m)));
}
/**
\brief Auxiliary exception used to sign that a metavariable was
found in an expression.
*/
struct found_metavar {};
bool has_metavar(expr const & e, unsigned midx, metavar_env const & menv) {
auto f = [&](expr const & m, unsigned offset) {
if (is_metavar(m)) {
unsigned midx2 = metavar_idx(m);
if (midx2 == midx)
throw found_metavar();
if (menv.contains(midx2) &&
menv.is_assigned(midx2) &&
has_metavar(menv.get_subst(midx2), midx, menv))
throw found_metavar();
}
};
try {
for_each_fn<decltype(f)> proc(f);
proc(e);
return false;
} catch (found_metavar) {
return true;
}
}
}