text: /*
  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 <vector>
  #include "kernel/free_vars.h"
  #include "kernel/replace_fn.h"
  #include "kernel/declaration.h"
  #include "kernel/instantiate.h"
  #include "kernel/instantiate_univ_cache.h"
  
  #ifndef LEAN_INST_UNIV_CACHE_SIZE
  #define LEAN_INST_UNIV_CACHE_SIZE 1023
  #endif
  
  namespace lean {
  template<bool rev>
  struct instantiate_easy_fn {
      unsigned n;
      expr const * subst;
      instantiate_easy_fn(unsigned _n, expr const * _subst):n(_n), subst(_subst) {}
      optional<expr> operator()(expr const & a, bool app) const {
          if (closed(a))
              return some_expr(a);
          if (is_var(a) && var_idx(a) < n)
              return some_expr(subst[rev ? n - var_idx(a) - 1 : var_idx(a)]);
          if (app && is_app(a))
          if (auto new_a = operator()(app_arg(a), false))
          if (auto new_f = operator()(app_fn(a), true))
              return some_expr(mk_app(*new_f, *new_a, a.get_tag()));
          return none_expr();
      }
  };
  
  expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
      if (s >= get_free_var_range(a) || n == 0)
          return a;
      if (s == 0)
          if (auto r = instantiate_easy_fn<false>(n, subst)(a, true))
              return *r;
      return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
              unsigned s1 = s + offset;
              if (s1 < s)
                  return some_expr(m); // overflow, vidx can't be >= max unsigned
              if (s1 >= get_free_var_range(m))
                  return some_expr(m); // expression m does not contain free variables with idx >= s1
              if (is_var(m)) {
                  unsigned vidx = var_idx(m);
                  if (vidx >= s1) {
                      unsigned h = s1 + n;
                      if (h < s1 /* overflow, h is bigger than any vidx */ || vidx < h) {
                          return some_expr(lift_free_vars(subst[vidx - s1], offset));
                      } else {
                          return some_expr(mk_var(vidx - n));
                      }
                  }
              }
              return none_expr();
          });
  }
  
  expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, 0, n, s); }
  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) { return instantiate(e, i, 1, &s); }
  expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); }
  
  expr instantiate_rev(expr const & a, unsigned n, expr const * subst) {
      if (closed(a))
          return a;
      if (auto r = instantiate_easy_fn<true>(n, subst)(a, true))
          return *r;
      return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
              if (offset >= get_free_var_range(m))
                  return some_expr(m); // expression m does not contain free variables with idx >= offset
              if (is_var(m)) {
                  unsigned vidx = var_idx(m);
                  if (vidx >= offset) {
                      unsigned h = offset + n;
                      if (h < offset /* overflow, h is bigger than any vidx */ || vidx < h) {
                          return some_expr(lift_free_vars(subst[n - (vidx - offset) - 1], offset));
                      } else {
                          return some_expr(mk_var(vidx - n));
                      }
                  }
              }
              return none_expr();
          });
  }
  
  bool is_head_beta(expr const & t) {
      return is_app(t) && is_lambda(get_app_fn(t));
  }
  
  expr apply_beta(expr f, unsigned num_args, expr const * args) {
      if (num_args == 0) {
          return f;
      } else if (!is_lambda(f)) {
          return mk_rev_app(f, num_args, args);
      } else {
          unsigned m = 1;
          while (is_lambda(binding_body(f)) && m < num_args) {
              f = binding_body(f);
              m++;
          }
          lean_assert(m <= num_args);
          return mk_rev_app(instantiate(binding_body(f), m, args + (num_args - m)), num_args - m, args);
      }
  }
  
  expr head_beta_reduce(expr const & t) {
      if (!is_head_beta(t)) {
          return t;
      } else {
          buffer<expr> args;
          expr const & f = get_app_rev_args(t, args);
          lean_assert(is_lambda(f));
          return head_beta_reduce(apply_beta(f, args.size(), args.data()));
      }
  }
  
  expr instantiate_univ_params(expr const & e, level_param_names const & ps, levels const & ls) {
      if (!has_param_univ(e))
          return e;
      return replace(e, [&](expr const & e) -> optional<expr> {
              if (!has_param_univ(e))
                  return some_expr(e);
              if (is_constant(e)) {
                  return some_expr(update_constant(e, map_reuse(const_levels(e),
                                                                [&](level const & l) { return instantiate(l, ps, ls); },
                                                                [](level const & l1, level const & l2) { return is_eqp(l1, l2); })));
              } else if (is_sort(e)) {
                  return some_expr(update_sort(e, instantiate(sort_level(e), ps, ls)));
              } else {
                  return none_expr();
              }
          });
  }
  
  MK_THREAD_LOCAL_GET(instantiate_univ_cache, get_type_univ_cache, LEAN_INST_UNIV_CACHE_SIZE);
  MK_THREAD_LOCAL_GET(instantiate_univ_cache, get_value_univ_cache, LEAN_INST_UNIV_CACHE_SIZE);
  
  expr instantiate_type_univ_params(declaration const & d, levels const & ls) {
      lean_assert(d.get_num_univ_params() == length(ls));
      if (is_nil(ls) || !has_param_univ(d.get_type()))
          return d.get_type();
      instantiate_univ_cache & cache = get_type_univ_cache();
      if (auto r = cache.is_cached(d, ls))
          return *r;
      expr r = instantiate_univ_params(d.get_type(), d.get_univ_params(), ls);
      cache.save(d, ls, r);
      return r;
  }
  
  expr instantiate_value_univ_params(declaration const & d, levels const & ls) {
      lean_assert(d.get_num_univ_params() == length(ls));
      if (is_nil(ls) || !has_param_univ(d.get_value()))
          return d.get_value();
      instantiate_univ_cache & cache = get_value_univ_cache();
      if (auto r = cache.is_cached(d, ls))
          return *r;
      expr r = instantiate_univ_params(d.get_value(), d.get_univ_params(), ls);
      cache.save(d, ls, r);
      return r;
  }
  
  void clear_instantiate_cache() {
      get_type_univ_cache().clear();
      get_value_univ_cache().clear();
  }
  }
  