2013-07-24 07:32:01 +00:00
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/*
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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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2013-09-13 03:04:10 +00:00
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#include "kernel/free_vars.h"
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#include "kernel/replace.h"
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2013-09-13 01:25:38 +00:00
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#include "kernel/metavar.h"
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2013-07-24 07:32:01 +00:00
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namespace lean {
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2013-09-13 01:25:38 +00:00
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expr instantiate_with_closed(expr const & a, unsigned n, expr const * s) {
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2013-07-24 07:32:01 +00:00
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lean_assert(std::all_of(s, s+n, closed));
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2013-09-13 01:25:38 +00:00
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auto f = [=](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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2013-07-24 07:32:01 +00:00
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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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2013-08-06 18:27:14 +00:00
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return mk_var(vidx - n);
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2013-09-13 01:25:38 +00:00
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} else {
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return m;
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2013-07-24 07:32:01 +00:00
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}
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2013-09-13 01:25:38 +00:00
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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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2013-09-17 02:21:40 +00:00
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r = add_inst(r, offset + n - i - 1, s[i]);
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return r;
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2013-09-13 01:25:38 +00:00
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} else {
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return m;
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2013-07-24 07:32:01 +00:00
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}
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};
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2013-09-13 01:25:38 +00:00
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return replace_fn<decltype(f)>(f)(a);
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2013-08-03 18:45:51 +00:00
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}
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2013-09-17 02:21:40 +00:00
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expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
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2013-09-13 01:25:38 +00:00
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auto f = [=](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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2013-09-17 02:21:40 +00:00
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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);
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2013-08-03 18:45:51 +00:00
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else
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2013-08-06 18:27:14 +00:00
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return mk_var(vidx - n);
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2013-09-13 01:25:38 +00:00
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} else {
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return m;
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2013-08-03 18:45:51 +00:00
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}
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2013-09-13 01:25:38 +00:00
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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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2013-09-17 02:21:40 +00:00
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r = add_inst(r, offset + s + n - i - 1, lift_free_vars(subst[i], offset + n - i - 1));
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return r;
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2013-09-13 01:25:38 +00:00
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} else {
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return m;
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2013-08-03 18:45:51 +00:00
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}
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};
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2013-09-13 01:25:38 +00:00
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return replace_fn<decltype(f)>(f)(a);
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2013-07-24 07:32:01 +00:00
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}
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2013-09-17 02:21:40 +00:00
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expr instantiate(expr const & e, unsigned n, expr const * s) {
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return instantiate(e, 0, n, s);
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}
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expr instantiate(expr const & e, unsigned i, expr const & s) {
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return instantiate(e, i, 1, &s);
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}
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2013-10-23 22:44:26 +00:00
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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 head_beta_reduce(expr const & t) {
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if (!is_head_beta(t)) {
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return t;
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} else {
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unsigned num = num_args(t);
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unsigned num1 = num - 1;
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expr const * f = &arg(t, 0);
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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 < num1) {
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f = &abst_body(*f);
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m++;
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}
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lean_assert(m <= num1);
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expr r = instantiate(abst_body(*f), m, &arg(t, 1));
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if (m == num1) {
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return r;
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} else {
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buffer<expr> args;
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args.push_back(r);
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m++;
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for (; m < num; m++)
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args.push_back(arg(t, m));
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return mk_app(args.size(), args.data());
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}
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}
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}
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expr beta_reduce(expr t) {
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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);
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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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2013-07-24 07:32:01 +00:00
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}
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