131 lines
6.1 KiB
C++
131 lines
6.1 KiB
C++
/*
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Copyright (c) 2013 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <algorithm>
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#include <limits>
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#include "kernel/free_vars.h"
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#include "kernel/replace_fn.h"
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#include "kernel/metavar.h"
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#include "kernel/instantiate.h"
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namespace lean {
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expr instantiate_with_closed(expr const & a, unsigned n, expr const * s, optional<metavar_env> const & menv) {
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lean_assert(std::all_of(s, s+n, [&](expr const & e) { return !has_free_var(e, 0, std::numeric_limits<unsigned>::max(), menv); }));
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return replace(a, [=](expr const & m, unsigned offset) -> expr {
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if (is_var(m)) {
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unsigned vidx = var_idx(m);
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if (vidx >= offset) {
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if (vidx < offset + n)
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return s[n - (vidx - offset) - 1];
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else
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return mk_var(vidx - n);
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} else {
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return m;
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}
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} else if (is_metavar(m)) {
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expr r = m;
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for (unsigned i = 0; i < n; i++)
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r = add_inst(r, offset + n - i - 1, s[i], menv);
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return r;
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} else {
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return m;
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}
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});
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}
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expr instantiate_with_closed(expr const & e, unsigned n, expr const * s, metavar_env const & menv) { return instantiate_with_closed(e, n, s, some_menv(menv)); }
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expr instantiate_with_closed(expr const & e, unsigned n, expr const * s) { return instantiate_with_closed(e, n, s, none_menv()); }
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expr instantiate_with_closed(expr const & e, std::initializer_list<expr> const & l) { return instantiate_with_closed(e, l.size(), l.begin()); }
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expr instantiate_with_closed(expr const & e, expr const & s, optional<metavar_env> const & menv) { return instantiate_with_closed(e, 1, &s, menv); }
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expr instantiate_with_closed(expr const & e, expr const & s) { return instantiate_with_closed(e, 1, &s); }
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expr instantiate_with_closed(expr const & e, expr const & s, metavar_env const & menv) { return instantiate_with_closed(e, s, some_menv(menv)); }
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expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst, optional<metavar_env> const & menv) {
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return replace(a, [=](expr const & m, unsigned offset) -> expr {
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if (is_var(m)) {
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unsigned vidx = var_idx(m);
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if (vidx >= offset + s) {
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if (vidx < offset + s + n)
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return lift_free_vars(subst[n - (vidx - s - offset) - 1], offset, menv);
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else
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return mk_var(vidx - n);
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} else {
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return m;
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}
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} else if (is_metavar(m)) {
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expr r = m;
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for (unsigned i = 0; i < n; i++)
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r = add_inst(r, offset + s + n - i - 1, lift_free_vars(subst[i], offset + n - i - 1, menv), menv);
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return r;
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} else {
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return m;
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}
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});
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}
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expr instantiate(expr const & e, unsigned n, expr const * s, optional<metavar_env> const & menv) { return instantiate(e, 0, n, s, menv); }
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expr instantiate(expr const & e, unsigned n, expr const * s, metavar_env const & menv) { return instantiate(e, n, s, some_menv(menv)); }
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expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, n, s, none_menv()); }
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expr instantiate(expr const & e, std::initializer_list<expr> const & l) { return instantiate(e, l.size(), l.begin()); }
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expr instantiate(expr const & e, unsigned i, expr const & s, optional<metavar_env> const & menv) { return instantiate(e, i, 1, &s, menv); }
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expr instantiate(expr const & e, unsigned i, expr const & s, metavar_env const & menv) { return instantiate(e, i, 1, &s, some_menv(menv)); }
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expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s, none_menv()); }
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expr instantiate(expr const & e, expr const & s, optional<metavar_env> const & menv) { return instantiate(e, 1, &s, menv); }
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expr instantiate(expr const & e, expr const & s, metavar_env const & menv) { return instantiate(e, s, some_menv(menv)); }
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expr instantiate(expr const & e, expr const & s) { return instantiate(e, s, none_menv()); }
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bool is_head_beta(expr const & t) {
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return is_app(t) && is_lambda(arg(t, 0));
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}
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expr apply_beta(expr f, unsigned num_args, expr const * args, optional<metavar_env> const & menv) {
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lean_assert(is_lambda(f));
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unsigned m = 1;
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while (is_lambda(abst_body(f)) && m < num_args) {
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f = abst_body(f);
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m++;
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}
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lean_assert(m <= num_args);
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expr r = instantiate(abst_body(f), m, args, menv);
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if (m == num_args) {
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return r;
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} else {
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buffer<expr> new_args;
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new_args.push_back(r);
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for (; m < num_args; m++)
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new_args.push_back(args[m]);
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return mk_app(new_args);
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}
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}
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expr apply_beta(expr f, unsigned num_args, expr const * args, metavar_env const & menv) { return apply_beta(f, num_args, args, some_menv(menv)); }
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expr apply_beta(expr f, unsigned num_args, expr const * args) { return apply_beta(f, num_args, args, none_menv()); }
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expr head_beta_reduce(expr const & t, optional<metavar_env> const & menv) {
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if (!is_head_beta(t)) {
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return t;
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} else {
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return apply_beta(arg(t, 0), num_args(t) - 1, &arg(t, 1), menv);
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}
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}
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expr head_beta_reduce(expr const & t) { return head_beta_reduce(t, none_menv()); }
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expr head_beta_reduce(expr const & t, metavar_env const & menv) { return head_beta_reduce(t, some_menv(menv)); }
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expr beta_reduce(expr t, optional<metavar_env> const & menv) {
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auto f = [=](expr const & m, unsigned) -> expr {
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if (is_head_beta(m))
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return head_beta_reduce(m, menv);
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else
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return m;
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};
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while (true) {
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expr new_t = replace_fn<decltype(f)>(f)(t);
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if (new_t == t)
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return new_t;
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else
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t = new_t;
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}
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}
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expr beta_reduce(expr t, metavar_env const & menv) { return beta_reduce(t, some_menv(menv)); }
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expr beta_reduce(expr t) { return beta_reduce(t, none_menv()); }
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}
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