184 lines
6.4 KiB
C++
184 lines
6.4 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/declaration.h"
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#include "kernel/instantiate.h"
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namespace lean {
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template<bool rev>
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struct instantiate_easy_fn {
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unsigned n;
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expr const * subst;
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instantiate_easy_fn(unsigned _n, expr const * _subst):n(_n), subst(_subst) {}
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optional<expr> operator()(expr const & a, bool app) const {
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if (closed(a))
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return some_expr(a);
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if (is_var(a) && var_idx(a) < n)
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return some_expr(subst[rev ? n - var_idx(a) - 1 : var_idx(a)]);
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if (app && is_app(a))
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if (auto new_a = operator()(app_arg(a), false))
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if (auto new_f = operator()(app_fn(a), true))
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return some_expr(copy_tag(a, mk_app(*new_f, *new_a)));
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return none_expr();
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}
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};
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expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
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if (s >= get_free_var_range(a) || n == 0)
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return a;
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if (s == 0)
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if (auto r = instantiate_easy_fn<false>(n, subst)(a, true))
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return *r;
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return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
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unsigned s1 = s + offset;
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if (s1 < s)
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return some_expr(m); // overflow, vidx can't be >= max unsigned
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if (s1 >= get_free_var_range(m))
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return some_expr(m); // expression m does not contain free variables with idx >= s1
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if (is_var(m)) {
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unsigned vidx = var_idx(m);
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if (vidx >= s1) {
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unsigned h = s1 + n;
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if (h < s1 /* overflow, h is bigger than any vidx */ || vidx < h) {
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return some_expr(lift_free_vars(subst[vidx - s1], offset));
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} else {
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return some_expr(mk_var(vidx - n));
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}
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}
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}
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return none_expr();
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});
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}
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expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, 0, n, s); }
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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) { return instantiate(e, i, 1, &s); }
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expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); }
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expr instantiate_rev(expr const & a, unsigned n, expr const * subst) {
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if (closed(a))
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return a;
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if (auto r = instantiate_easy_fn<true>(n, subst)(a, true))
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return *r;
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return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
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if (offset >= get_free_var_range(m))
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return some_expr(m); // expression m does not contain free variables with idx >= offset
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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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unsigned h = offset + n;
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if (h < offset /* overflow, h is bigger than any vidx */ || vidx < h) {
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return some_expr(lift_free_vars(subst[n - (vidx - offset) - 1], offset));
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} else {
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return some_expr(mk_var(vidx - n));
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}
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}
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}
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return none_expr();
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});
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}
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bool is_head_beta(expr const & t) {
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expr const * it = &t;
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while (is_app(*it)) {
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expr const & f = app_fn(*it);
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if (is_lambda(f)) {
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return true;
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} else if (is_app(f)) {
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it = &f;
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} else {
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return false;
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}
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}
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return false;
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}
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expr apply_beta(expr f, unsigned num_args, expr const * args) {
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if (num_args == 0) {
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return f;
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} else if (!is_lambda(f)) {
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return mk_rev_app(f, num_args, args);
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} else {
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unsigned m = 1;
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while (is_lambda(binding_body(f)) && m < num_args) {
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f = binding_body(f);
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m++;
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}
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lean_assert(m <= num_args);
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return mk_rev_app(instantiate(binding_body(f), m, args + (num_args - m)), num_args - m, args);
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}
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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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buffer<expr> args;
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expr const * it = &t;
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while (true) {
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lean_assert(is_app(*it));
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expr const & f = app_fn(*it);
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args.push_back(app_arg(*it));
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if (is_lambda(f)) {
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return apply_beta(f, args.size(), args.data());
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} else {
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lean_assert(is_app(f));
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it = &f;
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}
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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) -> optional<expr> {
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if (is_head_beta(m))
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return some_expr(head_beta_reduce(m));
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else if (is_local(m) || is_metavar(m))
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return some_expr(m); // do not simplify local constants and metavariables types.
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else
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return none_expr();
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};
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while (true) {
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expr new_t = replace(t, f);
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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 instantiate_univ_params(expr const & e, level_param_names const & ps, levels const & ls) {
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if (!has_param_univ(e))
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return e;
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return replace(e, [&](expr const & e) -> optional<expr> {
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if (!has_param_univ(e))
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return some_expr(e);
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if (is_constant(e)) {
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return some_expr(update_constant(e, map_reuse(const_levels(e),
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[&](level const & l) { return instantiate(l, ps, ls); },
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[](level const & l1, level const & l2) { return is_eqp(l1, l2); })));
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} else if (is_sort(e)) {
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return some_expr(update_sort(e, instantiate(sort_level(e), ps, ls)));
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} else {
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return none_expr();
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}
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});
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}
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expr instantiate_type_univ_params(declaration const & d, levels const & ls) {
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lean_assert(length(d.get_univ_params()) == length(ls));
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return instantiate_univ_params(d.get_type(), d.get_univ_params(), ls);
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}
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expr instantiate_value_univ_params(declaration const & d, levels const & ls) {
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lean_assert(length(d.get_univ_params()) == length(ls));
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return instantiate_univ_params(d.get_value(), d.get_univ_params(), ls);
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}
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}
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