lean2/src/kernel/instantiate.cpp

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/*
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 <algorithm>
#include <limits>
#include "kernel/free_vars.h"
#include "kernel/replace_fn.h"
#include "kernel/metavar.h"
#include "kernel/instantiate.h"
namespace lean {
template<bool ClosedSubst>
expr instantiate_core(expr const & a, unsigned s, unsigned n, expr const * subst, optional<ro_metavar_env> const & menv) {
return replace(a, [=](expr const & m, unsigned offset) -> expr {
if (is_var(m)) {
unsigned vidx = var_idx(m);
if (vidx >= offset + s) {
if (vidx < offset + s + n) {
if (ClosedSubst)
return subst[n - (vidx - s - offset) - 1];
else
return lift_free_vars(subst[n - (vidx - s - offset) - 1], offset, menv);
} else {
return mk_var(vidx - n);
}
} else {
return m;
}
} else if (is_metavar(m)) {
expr r = m;
for (unsigned i = 0; i < n; i++) {
expr v = ClosedSubst ? subst[i] : lift_free_vars(subst[i], offset + n - i - 1, menv);
r = add_inst(r, offset + s + n - i - 1, v, menv);
}
return r;
} else {
return m;
}
});
}
expr instantiate_with_closed(expr const & a, unsigned n, expr const * s, optional<ro_metavar_env> const & menv) {
lean_assert(std::all_of(s, s+n, [&](expr const & e) { return !has_free_var(e, 0, std::numeric_limits<unsigned>::max(), menv); }));
return instantiate_core<true>(a, 0, n, s, menv);
}
expr instantiate_with_closed(expr const & e, unsigned n, expr const * s, ro_metavar_env const & menv) { return instantiate_with_closed(e, n, s, some_ro_menv(menv)); }
expr instantiate_with_closed(expr const & e, unsigned n, expr const * s) { return instantiate_with_closed(e, n, s, none_ro_menv()); }
expr instantiate_with_closed(expr const & e, std::initializer_list<expr> const & l) { return instantiate_with_closed(e, l.size(), l.begin()); }
expr instantiate_with_closed(expr const & e, expr const & s, optional<ro_metavar_env> const & menv) { return instantiate_with_closed(e, 1, &s, menv); }
expr instantiate_with_closed(expr const & e, expr const & s) { return instantiate_with_closed(e, 1, &s); }
expr instantiate_with_closed(expr const & e, expr const & s, ro_metavar_env const & menv) { return instantiate_with_closed(e, s, some_ro_menv(menv)); }
expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst, optional<ro_metavar_env> const & menv) {
return instantiate_core<false>(a, s, n, subst, menv);
}
expr instantiate(expr const & e, unsigned n, expr const * s, optional<ro_metavar_env> const & menv) { return instantiate(e, 0, n, s, menv); }
expr instantiate(expr const & e, unsigned n, expr const * s, ro_metavar_env const & menv) { return instantiate(e, n, s, some_ro_menv(menv)); }
expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, n, s, none_ro_menv()); }
expr instantiate(expr const & e, std::initializer_list<expr> const & l) { return instantiate(e, l.size(), l.begin()); }
expr instantiate(expr const & e, unsigned i, expr const & s, optional<ro_metavar_env> const & menv) { return instantiate(e, i, 1, &s, menv); }
expr instantiate(expr const & e, unsigned i, expr const & s, ro_metavar_env const & menv) { return instantiate(e, i, 1, &s, some_ro_menv(menv)); }
expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s, none_ro_menv()); }
expr instantiate(expr const & e, expr const & s, optional<ro_metavar_env> const & menv) { return instantiate(e, 1, &s, menv); }
expr instantiate(expr const & e, expr const & s, ro_metavar_env const & menv) { return instantiate(e, s, some_ro_menv(menv)); }
expr instantiate(expr const & e, expr const & s) { return instantiate(e, s, none_ro_menv()); }
bool is_head_beta(expr const & t) {
return is_app(t) && is_lambda(arg(t, 0));
}
expr apply_beta(expr f, unsigned num_args, expr const * args, optional<ro_metavar_env> const & menv) {
if (!is_lambda(f)) {
buffer<expr> new_args;
new_args.push_back(f);
new_args.append(num_args, args);
return mk_app(new_args);
} else {
unsigned m = 1;
while (is_lambda(abst_body(f)) && m < num_args) {
f = abst_body(f);
m++;
}
lean_assert(m <= num_args);
expr r = instantiate(abst_body(f), m, args, menv);
if (m == num_args) {
return r;
} else {
buffer<expr> new_args;
new_args.push_back(r);
for (; m < num_args; m++)
new_args.push_back(args[m]);
return mk_app(new_args);
}
}
}
expr apply_beta(expr f, unsigned num_args, expr const * args, ro_metavar_env const & menv) { return apply_beta(f, num_args, args, some_ro_menv(menv)); }
expr apply_beta(expr f, unsigned num_args, expr const * args) { return apply_beta(f, num_args, args, none_ro_menv()); }
expr head_beta_reduce(expr const & t, optional<ro_metavar_env> const & menv) {
if (!is_head_beta(t)) {
return t;
} else {
return apply_beta(arg(t, 0), num_args(t) - 1, &arg(t, 1), menv);
}
}
expr head_beta_reduce(expr const & t) { return head_beta_reduce(t, none_ro_menv()); }
expr head_beta_reduce(expr const & t, ro_metavar_env const & menv) { return head_beta_reduce(t, some_ro_menv(menv)); }
expr beta_reduce(expr t, optional<ro_metavar_env> const & menv) {
auto f = [=](expr const & m, unsigned) -> expr {
if (is_head_beta(m))
return head_beta_reduce(m, menv);
else
return m;
};
while (true) {
expr new_t = replace_fn<decltype(f)>(f)(t);
if (new_t == t)
return new_t;
else
t = new_t;
}
}
expr beta_reduce(expr t, ro_metavar_env const & menv) { return beta_reduce(t, some_ro_menv(menv)); }
expr beta_reduce(expr t) { return beta_reduce(t, none_ro_menv()); }
}