template_cpp.cc

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/*
 * Copyright 2020 Cerebras Systems. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 *    1. Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 *
 *    2. Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
 *       disclaimer in the documentation and/or other materials provided
 *       with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY CEREBRAS SYSTEMS ''AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CEREBRAS SYSTEMS OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
 * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The views and conclusions contained in the software and documentation
 * are those of the authors and should not be interpreted as
 * representing official policies, either expressed or implied, of
 * Cerebras Systems.
 */
 
#include <ctype.h>
 
#include <algorithm>
#include <iostream>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
 
#include "template_cpp.h"
#include "isl_config.h"
 
/* The textual representation of this tuple kind.
 *
 * By default, the textual representation is just the name.
 */
std::string TupleKind::to_string() const
{
  return name;
}
 
/* Return the parameters of this tuple kind.
 *
 * By default, there are no parameters.
 */
std::vector<std::string> TupleKind::params() const
{
  return { };
}
 
/* Apply the substitution "subs" to this tuple kind and return the result.
 * "self" is a shared pointer to this.
 *
 * If the name of this tuple kind appears in the substitution,
 * then return the corresponding tuple kind pointer.
 * Otherwise, return "self".
 */
TupleKindPtr TupleKind::apply(const Substitution &subs,
  const TupleKindPtr &self) const
{
  if (subs.count(name) != 0)
    return subs.at(name);
  return self;
}
 
/* Apply the substitution "subs" to "tuple" and return the result.
 */
static TupleKindPtr apply(const TupleKindPtr tuple, const Substitution &subs)
{
  return tuple->apply(subs, tuple);
}
 
/* Return the left child of this tuple kind.
 *
 * Since this is not a pair, there is no left child.
 */
TupleKindPtr TupleKind::left() const
{
  return TupleKindPtr();
}
 
/* Return the right child of this tuple kind.
 *
 * Since this is not a pair, there is no right child.
 */
TupleKindPtr TupleKind::right() const
{
  return TupleKindPtr();
}
 
/* Helper class used to construct a pointer to a tuple kind
 * that refers to a non-template type.
 */
struct Fixed {
};
 
/* Construct a pointer to a tuple kind that refers to a non-template type.
 *
 * Use an empty string as name.  Since this is a non-template type,
 * the kind name will never appear in the generated code.
 */
TupleKindPtr::TupleKindPtr(Fixed) : Base(std::make_shared<TupleKind>(""))
{
}
 
/* Tuple pointers for non-template types.
 */
static TupleKindPtr Ctx{Fixed()};
static TupleKindPtr Integer{Fixed()};
static TupleKindPtr Str{Fixed()};
static TupleKindPtr Res{Fixed()};
 
/* Special tuple pointers.
 * Anonymous appears in the generated code but cannot be unified
 * with anything else since it is a predefined template argument.
 * Leaf can only be unified with something that is not a pair and
 * does not appear in the generated code.
 */
static TupleKindPtr Anonymous("Anonymous");
static TupleKindPtr Leaf("Leaf");
 
/* Placeholder tuple pointers that refer to (part of) the domain or range.
 */
static TupleKindPtr Domain("Domain");
static TupleKindPtr Domain2("Domain2");
static TupleKindPtr Domain3("Domain3");
static TupleKindPtr Range("Range");
static TupleKindPtr Range2("Range2");
static TupleKindPtr Range3("Range3");
 
/* A representation of a proper tuple kind that is used as a template
 * parameter or a template argument.
 */
struct ProperTupleKind : public TupleKind {
  ProperTupleKind(const std::string &name) : TupleKind(name) {}
 
  virtual std::vector<std::string> params() const override;
};
 
/* Return the parameters of this tuple kind.
 *
 * Return the name of this tuple kind, unless it is the special Anonymous
 * predefined template argument.
 */
std::vector<std::string> ProperTupleKind::params() const
{
  if (Anonymous.get() == this)
    return { };
  return { name };
}
 
/* Construct a pointer to a tuple kind that refers
 * to a proper tuple kind with the given name.
 */
TupleKindPtr::TupleKindPtr(const std::string &name) :
  Base(std::make_shared<ProperTupleKind>(name))
{
}
 
/* A tuple kind that represents an anonymous pair of nested tuple kinds.
 */
struct Pair : public TupleKind {
  Pair(const TupleKindPtr &tuple1, const TupleKindPtr &tuple2) :
    TupleKind(""), tuple1(tuple1), tuple2(tuple2) {}
 
  virtual std::string to_string() const override;
  virtual std::vector<std::string> params() const override;
  virtual TupleKindPtr apply(const Substitution &match,
    const TupleKindPtr &self) const override;
  virtual TupleKindPtr left() const override;
  virtual TupleKindPtr right() const override;
 
  const TupleKindPtr tuple1;
  const TupleKindPtr tuple2;
};
 
/* The textual representation of this tuple kind.
 *
 * The textual representation of a pair is of the form "pair<tuple1, tuple2>".
 */
std::string Pair::to_string() const
{
  return std::string("pair<") + tuple1->to_string() + ", " +
          tuple2->to_string() + ">";
}
 
/* Add the elements of "vec2" that do not already appear in "vec1"
 * at the end of "vec1".
 *
 * The two vectors are assumed not to have any repeated elements.
 * The updated vector will then also not have repeated elements.
 */
static void combine(std::vector<std::string> &vec1,
  const std::vector<std::string> &vec2)
{
  for (const auto &s : vec2)
    if (std::find(vec1.begin(), vec1.end(), s) == vec1.end())
      vec1.emplace_back(s);
}
 
/* Return the parameters of this tuple kind.
 *
 * Combine the parameters of the two nested tuple kinds.
 */
std::vector<std::string> Pair::params() const
{
  auto names1 = tuple1->params();
  auto names2 = tuple2->params();
 
  combine(names1, names2);
 
  return names1;
}
 
/* Apply the substitution "subs" to this tuple kind and return the result.
 * "self" is a shared pointer to this.
 *
 * Construct a new tuple kind consisting of the result of applying
 * the substitution to the two nested tuple kinds.
 */
TupleKindPtr Pair::apply(const Substitution &subs, const TupleKindPtr &self)
  const
{
  return TupleKindPtr(::apply(tuple1, subs), ::apply(tuple2, subs));
}
 
/* Return the left child of this tuple kind.
 */
TupleKindPtr Pair::left() const
{
  return tuple1;
}
 
/* Return the right child of this tuple kind.
 */
TupleKindPtr Pair::right() const
{
  return tuple2;
}
 
/* Construct a pointer to a tuple kind that refers
 * to the given pair of nested tuple kinds.
 */
TupleKindPtr::TupleKindPtr(const TupleKindPtr &left, const TupleKindPtr &right)
  : Base(std::make_shared<Pair>(left, right))
{
}
 
/* Is this a kind of object representing an anonymous function?
 */
bool Kind::is_anon() const
{
  return size() != 0 && back() == Anonymous;
}
 
/* Is this a kind of object with a single tuple?
 */
bool Kind::is_set() const
{
  return size() == 1;
}
 
/* Is this a kind of object with a single, anonymous tuple?
 */
bool Kind::is_anon_set() const
{
  return is_set() && is_anon();
}
 
/* Return the parameters of this kind.
 *
 * Collect the parameters of the tuple kinds in the sequence.
 */
std::vector<std::string> Kind::params() const
{
  std::vector<std::string> params;
 
  for (const auto &tuple : *this)
    combine(params, tuple->params());
 
  return params;
}
 
/* Apply the substitution "subs" to this kind and return the result.
 *
 * Apply the substitution to each of the tuple kinds in the sequence.
 */
Kind Kind::apply(const Substitution &subs) const
{
  Kind applied;
 
  for (const auto &tuple : *this)
    applied.emplace_back(::apply(tuple, subs));
 
  return applied;
}
 
/* A signature of a method in terms of kinds,
 * consisting of a return kind and a sequence of argument kinds.
 */
struct Signature {
  Kind ret;
  std::vector<Kind> args;
 
  std::vector<std::string> params() const;
  Signature apply(const Substitution &match) const;
};
 
/* Return the parameters of this signature.
 *
 * Collect the parameters of the argument kinds and the return kind.
 */
std::vector<std::string> Signature::params() const
{
  std::vector<std::string> params;
 
  for (const auto &arg : args)
    combine(params, arg.params());
  combine(params, ret.params());
 
  return params;
}
 
/* Apply the substitution "subs" to this kind and return the result.
 *
 * Apply the substitution to the argument kinds and the return kind.
 */
Signature Signature::apply(const Substitution &subs) const
{
  std::vector<Kind> applied_args;
 
  for (const auto &arg : args)
    applied_args.emplace_back(arg.apply(subs));
 
  return { ret.apply(subs), applied_args };
}
 
/* Return a renaming substitution that renames the elements of "params"
 * using names starting with "prefix".
 */
static Substitution param_renamer(const std::vector<std::string> &params,
  const std::string &prefix)
{
  Substitution renamer;
  int n = 0;
 
  for (const auto &name : params) {
    auto suffix = std::to_string(++n);
    auto arg_name = prefix + suffix;
    auto arg = TupleKindPtr(arg_name);
 
    if (name == Leaf->name)
      generator::die("Leaf cannot be renamed");
 
    renamer.emplace(name, arg);
  }
 
  return renamer;
}
 
/* Does the vector "v" contain the element "el"?
 */
static bool contains(const std::vector<std::string> &v, const std::string &el)
{
   return find(v.begin(), v.end(), el) != v.end();
 }
 
 
/* Return the shared elements of "v1" and "v2", preserving the order
 * of those elements in "v1".
 */
static std::vector<std::string> intersect(const std::vector<std::string> &v1,
  const std::vector<std::string> &v2)
{
  std::vector<std::string> intersection;
 
  for (const auto &el : v1)
    if (contains(v2, el))
      intersection.push_back(el);
 
  return intersection;
}
 
/* Return a renaming substitution that renames
 * any parameters that appears in both "sig" and "kind".
 */
static Substitution shared_param_renamer(const Signature &sig, const Kind &kind)
{
  return param_renamer(intersect(sig.params(), kind.params()), "Arg");
}
 
/* Signatures for unary operations.
 * Functions have at least one tuple.
 */
static Signature un_params = { { }, { { } } };
static Signature un_set = { { Domain }, { { Domain } } };
static Signature un_map = { { Domain, Range }, { { Domain, Range } } };
static std::vector<Signature> un_op = { un_params, un_set, un_map };
static std::vector<Signature> fn_un_op = { un_set, un_map };
 
/* Signatures for binary operations, with the second argument
 * possibly referring to part of the first argument.
 * Functions have at least one tuple.
 */
static Signature bin_params = { { }, { { }, { } } };
static Signature bin_set = { { Domain }, { { Domain }, { Domain } } };
static Signature bin_map =
  { { Domain, Range }, { { Domain, Range }, { Domain, Range } } };
static std::vector<Signature> bin_op = { bin_params, bin_set, bin_map };
static std::vector<Signature> fn_bin_op = { bin_set, bin_map };
static Signature bin_set_params = { { Domain }, { { Domain }, { } } };
static Signature bin_map_params =
  { { Domain, Range }, { { Domain, Range }, { } } };
static Signature bin_map_domain =
  { { Domain, Range }, { { Domain, Range }, { Domain } } };
static Signature bin_map_range =
  { { Domain, Range }, { { Domain, Range }, { Range } } };
static Signature bin_map_domain_wrapped_domain =
  { { { Domain, Domain2 }, Range },
    { { { Domain, Domain2 }, Range }, { Domain } } };
static Signature bin_map_range_wrapped_domain =
  { { Domain, { Range, Range2 } },
    { { Domain, { Range, Range2 } }, { Range } } };
 
/* Signatures for binary operations, where the second argument
 * is an identifier (with an anonymous tuple).
 */
static Signature bin_params_anon = { { }, { { }, { Anonymous } } };
static Signature bin_set_anon = { { Domain }, { { Domain }, { Anonymous } } };
static Signature bin_map_anon =
  { { Domain, Range }, { { Domain, Range }, { Anonymous } } };
static std::vector<Signature> bin_op_anon =
  { bin_params_anon, bin_set_anon, bin_map_anon };
 
/* Signatures for ternary operations, where the last two arguments are integers.
 */
static Signature ter_params_int_int =
  { { }, { { }, { Integer }, { Integer } } };
static Signature ter_set_int_int =
  { { Domain }, { { Domain }, { Integer }, { Integer } } };
static Signature ter_map_int_int =
  { { Domain, Range }, { { Domain, Range }, { Integer }, { Integer } } };
static std::vector<Signature> ter_int_int =
  { ter_params_int_int, ter_set_int_int, ter_map_int_int };
 
/* Signatures for ternary operations.
 * Functions have at least one tuple.
 */
static Signature ter_set =
  { { Domain }, { { Domain }, { Domain }, { Domain } } };
static Signature ter_map =
  { { Domain, Range },
    { { Domain, Range }, { Domain, Range }, { Domain, Range } } };
static std::vector<Signature> fn_ter_op = { ter_set, ter_map };
 
/* Signatures for naming a leaf tuple using an identifier (with an anonymous
 * tuple).
 */
static Signature update_set = { { Domain2 }, { { Leaf }, { Anonymous } } };
static Signature update_domain =
  { { Domain2, Range }, { { Leaf, Range }, { Anonymous } } };
static Signature update_range =
  { { Domain, Range2 }, { { Domain, Leaf }, { Anonymous } } };
 
/* Signatures for the functions "min" and "max", which can be either
 * unary or binary operations.
 */
static std::vector<Signature> min_max = { un_set, bin_set, un_map, bin_map };
 
/* Signatures for adding an unnamed tuple to an object with zero or one tuple.
 */
static Signature to_set = { { Domain }, { { }, { Integer } } };
static Signature add_range = { { Domain, Range }, { { Domain }, { Integer } } };
/* Signatures for adding a named tuple to an object with zero or one tuple.
 */
static Signature to_set_named =
  { { Domain }, { { }, { Anonymous }, { Integer } } };
static Signature add_range_named =
  { { Domain, Range }, { { Domain }, { Anonymous }, { Integer } } };
 
/* Signatures for methods applying a map to a set, a function or
 * part of a map.
 */
static Signature set_forward = { { Range }, { { Domain }, { Domain, Range } } };
static Signature domain_forward =
  { { Domain2, Range }, { { Domain, Range }, { Domain, Domain2 } } };
static Signature range_forward =
  { { Domain, Range2 }, { { Domain, Range }, { Range, Range2 } } };
 
/* Signatures for methods plugging in a function into a set, a function or
 * part of a map.
 */
static Signature set_backward =
  { { Domain2 }, { { Domain }, { Domain2, Domain } } };
static Signature domain_backward =
  { { Domain2, Range }, { { Domain, Range }, { Domain2, Domain } } };
static Signature range_backward =
  { { Domain, Range2 }, { { Domain, Range }, { Range2, Range } } };
static Signature domain_wrapped_domain_backward =
  { { { Domain3, Domain2 }, Range },
    { { { Domain, Domain2 }, Range }, { Domain3, Domain } } };
 
/* Signatures for methods binding a set, a function,
 * or (part of) a map to parameters or an object of the same kind.
 */
static Signature bind_set = { { }, { { Domain }, { Domain } } };
static Signature bind_domain = { { Range }, { { Domain, Range }, { Domain } } };
static Signature bind_range = { { Domain }, { { Domain, Range }, { Range } } };
static Signature bind_domain_wrapped_domain =
  { { Range2, Range }, { { { Domain2, Range2 }, Range }, { Domain2 } } };
 
/* Signatures for functions that take a callback accepting
 * objects of the same kind (but a different type).
 *
 * The return and argument kinds of the callback appear
 * at the position of the callback.
 */
static Signature each_params = { { Res }, { { }, { Res }, { } } };
static Signature each_set = { { Res }, { { Domain }, { Res }, { Domain } } };
static Signature each_map =
  { { Res }, { { Domain, Range }, { Res }, { Domain, Range } } };
static std::vector<Signature> each = { each_params, each_set, each_map };
 
/* Signatures for isl_*_list_foreach_scc.
 *
 * The first callback takes two elements with the same tuple kinds.
 * The second callback takes a list with the same tuple kinds.
 */
static Signature each_scc_params =
  { { Res }, { { }, { Res }, { }, { }, { Res }, { } } };
static Signature each_scc_set =
  { { Res }, { { Domain },
         { Res }, { Domain }, { Domain },
         { Res }, { Domain } } };
static Signature each_scc_map =
  { { Res }, { { Domain, Range },
         { Res }, { Domain, Range }, { Domain, Range },
         { Res }, { Domain, Range } } };
static std::vector<Signature> each_scc =
  { each_scc_params, each_scc_set, each_scc_map };
 
/* Signature for creating a map from a range,
 * where the domain is given by an extra argument.
 */
static Signature map_from_range_and_domain =
  { { Domain, Range }, { { Range }, { Domain } } };
 
 
/* Signatures for creating a set from a parameter set or
 * a map from a domain,
 * where the domain/range is given by an extra argument.
 */
static Signature set_from_params = { { Domain }, { { }, { Domain } } };
static Signature map_from_domain_and_range =
  { { Domain, Range }, { { Domain }, { Range } } };
static std::vector<Signature> from_domain =
  { set_from_params, map_from_domain_and_range };
 
/* Signatures for creating an anonymous set from a parameter set
 * or a map from a domain, where the range is anonymous.
 */
static Signature anonymous_set_from_params = { { Anonymous }, { { } } };
static Signature anonymous_map_from_domain =
  { { Domain, Anonymous }, { { Domain } } };
static std::vector<Signature> anonymous_from_domain =
  { anonymous_set_from_params, anonymous_map_from_domain };
 
/* Signatures for creating an anonymous function from a domain,
 * where the second argument is an identifier (with an anonymous tuple).
 */
static Signature anonymous_set_from_params_bin_anon =
  { { Anonymous }, { { }, { Anonymous } } };
static Signature anonymous_map_from_domain_bin_anon =
  { { Domain, Anonymous }, { { Domain }, { Anonymous } } };
static std::vector<Signature> anonymous_from_domain_bin_anon = {
    anonymous_set_from_params_bin_anon,
    anonymous_map_from_domain_bin_anon
  };
 
/* Signature for creating a map from a domain,
 * where the range tuple is equal to the domain tuple.
 */
static Signature set_to_map = { { Domain, Domain }, { { Domain } } };
 
/* Signatures for obtaining the range or the domain of a map.
 * In case of a transformation, the domain and range are the same.
 */
static Signature domain = { { Domain }, { { Domain, Range } } };
static Signature range = { { Range }, { { Domain, Range } } };
static Signature transformation_domain = { { Domain }, { { Domain, Domain } } };
 
/* Signatures for obtaining the parameter domain of a set or map.
 */
static Signature set_params = { { }, { { Domain } } };
static Signature map_params = { { }, { { Domain, Range } } };
 
/* Signatures for obtaining the domain of a function.
 */
static std::vector<Signature> fn_domain = { domain, set_params };
 
/* Signatures for interchanging (wrapped) domain and range.
 */
static Signature set_reverse =
  { { { Range, Domain } }, { { { Domain, Range } } } };
static Signature map_reverse = { { Range, Domain }, { { Domain, Range } } };
static Signature map_domain_reverse =
  { { { Domain2, Domain }, Range }, { { { Domain, Domain2 }, Range } } };
static Signature map_range_reverse =
  { { Domain, { Range2, Range } }, { { Domain, { Range, Range2 } } } };
 
/* Signatures for constructing products.
 */
static Signature set_product =
  { { { Domain, Range } }, { { Domain }, { Range } } };
static Signature map_product =
  { { { Domain, Domain2 }, { Range, Range2 } },
    { { Domain, Range }, { Domain2, Range2 } } };
static Signature domain_product =
  { { { Domain, Domain2 }, Range },
    { { Domain, Range }, { Domain2, Range } } };
static Signature range_product =
  { { Domain, { Range, Range2 } },
    { { Domain, Range }, { Domain, Range2 } } };
 
/* Signatures for obtaining factors from a product.
 */
static Signature domain_factor_domain =
  { { Domain, Range }, { { { Domain, Domain2 }, Range } } };
static Signature domain_factor_range =
  { { Domain2, Range }, { { { Domain, Domain2 }, Range } } };
static Signature range_factor_domain =
  { { Domain, Range }, { { Domain, { Range, Range2 } } } };
static Signature range_factor_range =
  { { Domain, Range2 }, { { Domain, { Range, Range2 } } } };
 
/* Signatures for (un)currying.
 */
static Signature curry =
  { { Domain, { Range, Range2 } },
    { { { Domain, Range }, Range2 } } };
static Signature uncurry =
  { { { Domain, Range }, Range2 },
    { { Domain, { Range, Range2 } } } };
 
/* Signatures for (un)wrapping.
 */
static Signature wrap = { { { Domain, Range } }, { { Domain, Range } } };
static Signature unwrap = { { Domain, Range }, { { { Domain, Range } } } };
 
/* Signatures for constructing objects that map to the domain or range
 * of a map.
 */
static Signature domain_map =
  { { { Domain, Range }, Domain }, { { Domain, Range } } };
static Signature range_map =
  { { { Domain, Range }, Range }, { { Domain, Range } } };
 
/* Signature for applying a comparison between the domain and the range
 * of a map.
 */
static Signature map_cmp =
  { { Domain, Domain }, { { Domain, Domain }, { Domain, Range } } };
 
/* Signature for creating a set corresponding to the domains
 * of two functions.
 */
static Signature set_join =
  { { Domain }, { { Domain, Range }, { Domain, Range } } };
 
/* Signatures for flattening the domain or range of a map,
 * replacing it with either an anonymous tuple or a tuple with a given name.
 */
static Signature anonymize_nested_domain =
  { { Anonymous, Range2 }, { { { Domain, Range }, Range2 } } };
static Signature anonymize_nested_range =
  { { Domain, Anonymous }, { { Domain, { Range, Range2 } } } };
static Signature replace_nested_domain =
  { { Domain2, Range2 },
    { { { Domain, Range }, Range2 }, { Anonymous} } };
static Signature replace_nested_range =
  { { Domain, Range3 }, { { Domain, { Range, Range2 } }, { Anonymous} } };
static std::vector<Signature> flatten_domain =
  { anonymize_nested_domain, replace_nested_domain };
static std::vector<Signature> flatten_range =
  { anonymize_nested_range, replace_nested_range };
 
/* Signatures for "set_at" methods.
 */
static Signature set_at_set =
  { { Domain }, { { Domain }, { Integer }, { Anonymous } } };
static Signature set_at_map =
  { { Domain, Range },
    { { Domain, Range }, { Integer }, { Domain, Anonymous } } };
static std::vector<Signature> set_at = { set_at_set, set_at_map };
 
/* Signatures for "list" methods, extracting a list
 * from a multi-expression.
 */
static Signature to_list_set = { { Anonymous }, { { Domain } } };
static Signature to_list_map = { { Domain, Anonymous }, { { Domain, Range } } };
 
/* Signatures for functions constructing an object from only an isl::ctx.
 */
static Signature ctx_params = { { }, { { Ctx } } };
static Signature ctx_set = { { Domain }, { { Ctx } } };
static Signature ctx_map = { { Domain, Range }, { { Ctx } } };
 
/* Helper structure for sorting the keys of static_methods and
 * special_member_methods such that the larger keys appear first.
 * In particular, a key should appear before any key that appears
 * as a substring in the key.
 * Note that this sorting is currently only important
 * for special_member_methods.
 */
struct larger_infix {
  bool operator()(const std::string &x, const std::string &y) const {
    if (x.length() > y. length())
      return true;
    return x < y;
  }
};
 
/* A map from part of a type name to a sequence of signatures.
 */
typedef std::map<std::string, std::vector<Signature>, larger_infix> infix_map;
 
/* A map from a method name to a map from part of a type name
 * to a sequence of signatures.
 */
typedef std::map<std::string, infix_map> infix_map_map;
 
/* Signatures for static methods.
 *
 * The "unit" static method is only available in a 0-tuple space.
 *
 * The "empty" static method creates union objects with the relevant
 * number of tuples.
 *
 * The "universe" static methods create objects from the corresponding spaces.
 */
static const infix_map_map static_methods {
  { "unit",
    { { "space",      { ctx_params } } }
  },
  { "empty",
    {
      { "union_set",    { ctx_params, ctx_set } },
      { "union_map",    { ctx_map } },
      { "union_pw_multi_aff", { ctx_set, ctx_map } },
    }
  },
  { "universe",
    {
      { "set",      { un_params, un_set } },
      { "map",      { un_map } },
    }
  },
};
 
/* Signatures for unary operations that either take something in a set space
 * and return something in the same space or take something in a map space
 * and return something in the range of that space.
 */
static std::vector<Signature> range_op = { un_set, range };
 
/* Signatures for binary operations where the second argument
 * is a (multi-)value.
 */
static std::vector<Signature> bin_val = { bin_set, bin_map_range };
 
/* The (default) signatures for methods with a given name.
 * Some of these are overridden by special_member_methods.
 */
static const std::unordered_map<std::string, std::vector<Signature>>
member_methods {
  { "add",    bin_op },
  { "add_constant", bin_val },
  { "add_named_tuple",  { to_set_named, add_range_named } },
  { "add_param",    bin_op_anon },
  { "add_unnamed_tuple",  { to_set, add_range } },
  { "apply",    { set_forward, range_forward } },
  { "apply_domain", { domain_forward } },
  { "apply_range",  { range_forward } },
  { "as",     un_op },
  { "as_map",   { un_map } },
  { "as_union_map", { un_map } },
  { "as_set",   { un_set } },
  { "bind",   { bind_set, bind_range } },
  { "bind_domain",  { bind_domain } },
  { "bind_range",   { bind_range } },
  { "bind_domain_wrapped_domain",
        { bind_domain_wrapped_domain } },
  { "ceil",   fn_un_op },
  { "coalesce",   un_op },
  { "cond",   fn_ter_op },
  { "constant",   range_op },
  { "curry",    { curry } },
  { "deltas",   { transformation_domain } },
  { "detect_equalities",  un_op },
  { "domain",   fn_domain },
  { "domain_factor_domain",
        { domain_factor_domain } },
  { "domain_factor_range",
        { domain_factor_range } },
  { "domain_map",   { domain_map } },
  { "domain_product", { domain_product } },
  { "domain_reverse", { map_domain_reverse } },
  { "drop",   ter_int_int },
  { "drop_all_params",  un_op },
  { "drop_unused_params", un_op },
  { "eq_at",    { map_cmp } },
  { "every",    each },
  { "extract",    bin_op },
  { "flatten_domain", flatten_domain },
  { "flatten_range",  flatten_range },
  { "floor",    fn_un_op },
  { "foreach",    each },
  { "foreach_scc",  each_scc },
  { "ge_set",   { set_join } },
  { "gt_set",   { set_join } },
  { "gist",   bin_op },
  { "gist_domain",  { bin_map_domain } },
  { "gist_params",  { bin_set_params, bin_map_params } },
  { "identity",   { un_map, set_to_map } },
  { "identity_on_domain", { set_to_map } },
  { "indicator_function", anonymous_from_domain },
  { "insert_domain",  { map_from_range_and_domain } },
  { "intersect",    bin_op },
  { "intersect_params", { bin_set_params, bin_map_params } },
  { "intersect_domain", { bin_map_domain } },
  { "intersect_domain_wrapped_domain",
        { bin_map_domain_wrapped_domain } },
  { "intersect_range",  { bin_map_range } },
  { "intersect_range_wrapped_domain",
        { bin_map_range_wrapped_domain } },
  { "lattice_tile", { un_set } },
  { "le_set",   { set_join } },
  { "lt_set",   { set_join } },
  { "lex_le_at",    { map_cmp } },
  { "lex_lt_at",    { map_cmp } },
  { "lex_ge_at",    { map_cmp } },
  { "lex_gt_at",    { map_cmp } },
  { "lexmin",   fn_un_op },
  { "lexmax",   fn_un_op },
  { "list",   { to_list_set, to_list_map } },
  { "lower_bound",  fn_bin_op },
  { "map_from_set", { set_to_map } },
  { "max",    min_max },
  { "max_val",    range_op },
  { "max_multi_val",  range_op },
  { "min",    min_max },
  { "min_val",    range_op },
  { "min_multi_val",  range_op },
  { "mod",    bin_val },
  { "on_domain",    from_domain },
  { "neg",    fn_un_op },
  { "offset",   fn_un_op },
  { "param_on_domain",  anonymous_from_domain_bin_anon },
  { "params",   { set_params, map_params } },
  { "plain_multi_val_if_fixed",
        { un_set } },
  { "preimage",   { set_backward } },
  { "preimage_domain",  { domain_backward } },
  { "preimage_domain_wrapped_domain",
        { domain_wrapped_domain_backward } },
  { "preimage_range", { range_backward } },
  { "product",    { set_product, map_product } },
  { "project_out_param",  bin_op_anon },
  { "project_out_all_params",
        un_op },
  { "pullback",   { domain_backward, bind_domain } },
  { "range",    { range } },
  { "range_factor_domain",
        { range_factor_domain } },
  { "range_factor_range", { range_factor_range } },
  { "range_lattice_tile", { un_map } },
  { "range_map",    { range_map } },
  { "range_product",  { range_product } },
  { "range_reverse",  { map_range_reverse } },
  { "range_simple_fixed_box_hull",
        { un_map } },
  { "reverse",    { map_reverse } },
  { "scale",    bin_val },
  { "scale_down",   bin_val },
  { "set_at",   set_at },
  { "set_domain_tuple", { update_domain } },
  { "set_range_tuple",  { update_set, update_range } },
  { "simple_fixed_box_hull",
        { un_set } },
  { "sub",    fn_bin_op },
  { "subtract",   bin_op },
  { "subtract_domain",  { bin_map_domain } },
  { "subtract_range", { bin_map_range } },
  { "translation",  { set_to_map } },
  { "to",     un_op },
  { "unbind_params",  { set_from_params } },
  { "unbind_params_insert_domain",
        { map_from_range_and_domain } },
  { "uncurry",    { uncurry } },
  { "union_add",    fn_bin_op },
  { "unite",    bin_op },
  { "universe",   un_op },
  { "unwrap",   { unwrap } },
  { "upper_bound",  fn_bin_op },
  { "wrap",   { wrap } },
  { "wrapped_reverse",  { set_reverse } },
  { "zero",   fn_un_op },
  { "zero_on_domain", { anonymous_map_from_domain } },
};
 
/* Signatures for constructors of multi-expressions
 * from a space and a list, with a special case for multi-union-expressions.
 */
static Signature from_list_set = { { Domain }, { { Domain }, { Anonymous } } };
static Signature from_list_map =
  { { Domain, Range }, { { Domain, Range }, { Domain, Anonymous } } };
static Signature from_list_map_union =
  { { Domain, Range }, { { Range }, { Domain, Anonymous } } };
 
/* Signatures for methods of types containing a given substring
 * that override the default signatures, where larger substrings
 * appear first.
 *
 * In particular, "gist" is usually a regular binary operation,
 * but for any type derived from "aff", the argument refers
 * to the domain of the function.
 *
 * When constructing a multi-expression from a space and a list,
 * the kind of the space is usually the same as that of
 * the constructed multi-expression.  However, if the constructed object
 * is a multi-union-expression, then the space is the fixed range space
 * of the multi-union-expression, so it always has a single tuple.
 * This happens in particular for constructing objects
 * of type "multi_union_pw_aff".
 * See also the "space" method below.
 *
 * The "size" method can usually simply be inherited from
 * the corresponding plain C++ type, but for a "fixed_box",
 * the size lives in the space of the box or its range.
 *
 * The "space" method is usually a regular unary operation
 * that returns the single space of the elements in the object,
 * with the same number of tuples.
 * However, a "union" object may contain elements from many spaces and
 * therefore its space only refers to the symbolic constants and
 * has zero tuples, except if it is also a "multi_union" object,
 * in which case it has a fixed range space and the space of the object
 * has a single tuple.
 * Note that since "space' is also the name of a template class,
 * the default space method is handled by print_type_named_member_method.
 */
static const infix_map_map special_member_methods {
  { "gist",
    { { "aff",    { bin_set_params, bin_map_domain } } }
  },
  { "multi_union_pw_aff",
    { { "space",    { from_list_set, from_list_map_union } } }
  },
  { "size",
    { { "fixed_box",  range_op } },
  },
  { "space",
    {
      { "multi_union",  range_op },
      { "union",    { un_params, set_params, map_params } },
    }
  },
};
 
/* Generic kinds for objects with zero, one or two tuples,
 * the last of which may be anonymous.
 */
static Kind params{};
static Kind set_type{ Domain };
static Kind set_anon{ Anonymous };
static Kind map_type{ Domain, Range };
static Kind map_anon{ Domain, Anonymous };
 
/* The initial sequence of specialization kinds for base types.
 * The specialization kinds for other types are derived
 * from the corresponding base types.
 *
 * In particular, this sequence specifies how many tuples
 * a given type can have and whether it is anonymous.
 *
 * "space" can have any number of tuples.
 * "set" and "point" can have zero or one tuple.
 * "map" can only have two tuples.
 * "aff" can have one or two tuples, the last of which is anonymous.
 * "fixed_box" can represent a (proper) set) or a map.
 * "val" and "id" are treated as anonymous sets so that
 * they can form the basis of "multi_val" and "multi_id".
 */
static const std::unordered_map<std::string, std::vector<Kind>> base_kinds {
  { "space",  { params, set_type, map_type } },
  { "set",  { params, set_type } },
  { "point",  { params, set_type } },
  { "map",  { map_type } },
  { "aff",  { set_anon, map_anon } },
  { "fixed_box",  { set_type, map_type } },
  { "val",  { set_anon } },
  { "id",   { set_anon } },
};
 
/* Prefixes introduced by type constructors.
 */
static const std::unordered_set<std::string> type_prefixes {
  "basic",
  "multi",
  "pw",
  "union",
};
 
/* If "type" has a "_list" suffix, then return "type" with this suffix removed.
 * Otherwise, simply return "type".
 */
static std::string drop_list(const std::string &type)
{
  size_t pos = type.rfind('_');
 
  if (pos == std::string::npos)
    return type;
  if (type.substr(pos + 1) == "list")
    return type.substr(0, pos);
  return type;
}
 
/* Given the name of a plain C++ type, return the base type
 * from which it was derived using type constructors.
 *
 * In particular, drop any "list" suffix and
 * drop any prefixes from type_prefixes, stopping
 * as soon as a base type is found for which kinds have been registered
 * in base_kinds.
 */
static std::string base_type(const std::string &type)
{
  auto base = type;
  size_t pos;
 
  base = drop_list(base);
  while (base_kinds.count(base) == 0 &&
      (pos = base.find('_')) != std::string::npos &&
      type_prefixes.count(base.substr(0, pos)) != 0) {
    base = base.substr(pos + 1);
  }
 
  return base;
}
 
/* A mapping from anonymous kinds to named kinds.
 */
static std::map<Kind, Kind> anon_to_named {
  { set_anon, set_type },
  { map_anon, map_type },
};
 
/* Given a sequence of anonymous kinds, replace them
 * by the corresponding named kinds.
 */
static std::vector<Kind> add_name(const std::vector<Kind> &tuples)
{
  std::vector<Kind> named;
 
  for (const auto &tuple : tuples)
    named.emplace_back(anon_to_named.at(tuple));
 
  return named;
}
 
/* Look up the (initial) specializations of the class called "name".
 * If no specializations have been defined, then return an empty vector.
 *
 * Start from the initial specializations of the corresponding base type.
 * If this template class is a multi-expression, then it was derived
 * from an anonymous function type.  Replace the final Anonymous
 * tuple kind by a placeholder in this case.
 */
static std::vector<Kind> lookup_class_tuples(const std::string &name)
{
  std::string base = base_type(name);
 
  if (base_kinds.count(base) == 0)
    return { };
  if (name.find("multi_") != std::string::npos)
    return add_name(base_kinds.at(base));
  return base_kinds.at(base);
}
 
/* Add a template class called "name", of which the methods are described
 * by "clazz" and the initial specializations by "class_tuples".
 */
void template_cpp_generator::add_template_class(const isl_class &clazz,
  const std::string &name, const std::vector<Kind> &class_tuples)
{
  auto isl_namespace = cpp_type_printer().isl_namespace();
  auto super = isl_namespace + name;
 
  template_classes.emplace(name,
    template_class{name, super, clazz, class_tuples});
}
 
/* Construct a templated C++ bindings generator from
 * the exported types and functions and the set of all declared functions.
 *
 * On top of the initialization of the shared parts
 * of C++ bindings generators, add a template class
 * for each plain C++ class for which template kinds
 * have been defined.
 * In particular, determine the base type from which the plain C++ class
 * was derived using type constructors and check if any template kinds
 * have been registered for this base type.
 */
template_cpp_generator::template_cpp_generator(clang::SourceManager &SM,
  std::set<clang::RecordDecl *> &exported_types,
  std::set<clang::FunctionDecl *> exported_functions,
  std::set<clang::FunctionDecl *> functions) :
    cpp_generator(SM, exported_types, exported_functions,
      functions)
{
  for (const auto &kvp : classes) {
    const auto &clazz = kvp.second;
    std::string name = type2cpp(clazz);
    const auto &class_tuples = lookup_class_tuples(name);
 
    if (class_tuples.empty())
      continue;
    add_template_class(clazz, name, class_tuples);
  }
}
 
/* Call "fn" on each template class.
 */
void template_cpp_generator::foreach_template_class(
  const std::function<void(const template_class &)> &fn) const
{
  for (const auto &kvp : template_classes)
    fn(kvp.second);
}
 
/* Print forward declarations for all template classes to "os".
 *
 * For template classes that represent an anonymous function
 * that can also have a domain tuple, provide an <name>_on alias
 * that adds the fixed Anonymous tuple kind.
 */
void template_cpp_generator::print_forward_declarations(std::ostream &os)
{
  foreach_template_class([&os] (const template_class &template_class) {
    auto name = template_class.class_name;
 
    os << "\n";
    os << "template <typename...>\n";
    os << "struct " << name << ";\n";
 
    if (!template_class.is_anon())
      return;
    if (template_class.is_anon_set())
      return;
 
    os << "\n";
    os << "template <typename...Ts>\n";
    os << "using " << name << "_on = "
       << name << "<Ts..., Anonymous>;\n";
  });
}
 
/* Print friend declarations for all template classes to "os".
 */
void template_cpp_generator::print_friends(std::ostream &os)
{
  foreach_template_class([&os] (const template_class &template_class) {
    os << "  template <typename...>\n";
    os << "  friend struct " << template_class.class_name << ";\n";
  });
}
 
/* Print a template parameter or argument.
 * In case of a std::string, it's a template parameter
 * that needs to be declared.
 */
static void print_template_arg(std::ostream &os, const std::string &arg)
{
  os << "typename " << arg;
}
 
/* Print a template parameter or argument.
 * In case of a TupleKindPtr, it's a template argument.
 */
static void print_template_arg(std::ostream &os, const TupleKindPtr &kind)
{
  os << kind->to_string();
}
 
/* Print a sequence of template parameters (std::string) or
 * arguments (TupleKindPtr) "args", without the enclosing angle brackets.
 */
template <typename List>
static void print_pure_template_args(std::ostream &os, const List &args)
{
  for (size_t i = 0; i < args.size(); ++i) {
    if (i != 0)
      os << ", ";
    print_template_arg(os, args[i]);
  }
}
 
/* Print a sequence of template parameters (std::string) or
 * arguments (TupleKindPtr) "args".
 */
template <typename List>
static void print_template_args(std::ostream &os, const List &args)
{
  os << "<";
  print_pure_template_args(os, args);
  os << ">";
}
 
/* Print a declaration of the template parameters "params".
 */
static void print_template(std::ostream &os,
  const std::vector<std::string> &params)
{
  os << "template ";
  print_template_args(os, params);
  os << "\n";
}
 
/* Print a declaration of the template parameters "params",
 * if there are any.
 */
static void print_non_empty_template(std::ostream &os,
  const std::vector<std::string> &params)
{
  if (params.size() > 0)
    print_template(os, params);
}
 
/* Print a bare template type, i.e., without namespace,
 * consisting of the type "type" and the kind "kind" to "os".
 *
 * In particular, print "type" followed by the template arguments
 * as specified by "kind".
 */
static void print_bare_template_type(std::ostream &os, const std::string &type,
  const Kind &kind)
{
  os << type;
  print_template_args(os, kind);
}
 
/* A specific instance of "template_class", with tuple kinds given by "kind".
 */
struct specialization {
  struct template_class &template_class;
  Kind kind;
 
  const std::string &base_name() const;
  const std::string &class_name() const;
};
 
/* The name of the plain C++ interface class
 * from which this template class (instance) derives.
 */
const std::string &specialization::base_name() const
{
  return template_class.super_name;
}
 
/* The name of the template class.
 */
const std::string &specialization::class_name() const
{
  return template_class.class_name;
}
 
/* Helper class for printing the specializations of template classes
 * that is used to print both the class declarations and the class definitions.
 *
 * "os" is the stream onto which the classes should be printed.
 * "generator" is the templated C++ interface generator printing the classes.
 */
struct specialization_printer {
  specialization_printer(std::ostream &os,
      template_cpp_generator &generator) :
    os(os), generator(generator) {}
 
  virtual void print_class(const specialization &instance) const = 0;
  void print_classes() const;
 
  std::ostream &os;
  template_cpp_generator &generator;
};
 
/* Print all specializations of all template classes.
 *
 * Each class has a predefined set of initial specializations,
 * but while such a specialization is being printed,
 * the need for other specializations may arise and
 * these are added at the end of the list of specializations.
 * That is, class_tuples.size() may change during the execution
 * of the loop.
 *
 * For each specialization of a template class, call
 * the print_class virtual method.
 */
void specialization_printer::print_classes() const
{
  for (auto &kvp : generator.template_classes) {
    auto &template_class = kvp.second;
    const auto &class_tuples = template_class.class_tuples;
 
    for (size_t i = 0; i < class_tuples.size(); ++i)
      print_class({ template_class, class_tuples[i] });
  }
}
 
/* A helper class for printing method declarations and definitions
 * of a template class specialization.
 *
 * "instance" is the template class specialization for which methods
 * are printed.
 * "generator" is the templated C++ interface generator printing the classes.
 */
struct template_cpp_generator::class_printer :
    public cpp_generator::class_printer {
  class_printer(const specialization &instance,
      const specialization_printer &instance_printer,
      bool is_declaration);
 
  void print_return_type(const Method &method, const Kind &kind)
    const;
  void print_method_template_arguments(const Signature &sig);
  void print_method_header(const Method &method, const Signature &sig);
  bool print_special_method(const Method &method,
    const infix_map_map &special_methods);
  void print_static_method(const Method &method);
  void print_constructor(const Method &method);
  bool is_return_kind(const Method &method, const Kind &return_kind);
  void add_specialization(const Kind &kind);
  bool print_matching_method(const Method &method, const Signature &sig,
    const Kind &match_arg);
  bool print_matching_method(const Method &method, const Signature &sig);
  void print_matching_method(const Method &method,
    const std::vector<Signature> &signatures);
  void print_at_method(const Method &method);
  bool print_special_member_method(const Method &method);
  bool print_type_named_member_method(const Method &method);
  bool print_member_method_with_name(const Method &method,
    const std::string &name);
  void print_member_method(const Method &method);
  void print_any_method(const Method &method);
  virtual void print_method(const Method &method) override;
  virtual void print_method(const ConversionMethod &method) override;
  virtual void print_method_sig(const Method &method,
    const Signature &sig, bool deleted) = 0;
  virtual bool want_descendent_overloads(const function_set &methods)
    override;
  void print_all_methods();
 
  const specialization &instance;
  template_cpp_generator &generator;
};
 
/* Construct a class_printer from the template class specialization
 * for which methods are printed and
 * the printer of the template class.
 *
 * The template class printer is only used to obtain the output stream and
 * the templated C++ interface generator printing the classes.
 */
template_cpp_generator::class_printer::class_printer(
    const specialization &instance,
    const specialization_printer &instance_printer,
    bool is_declaration) :
  cpp_generator::class_printer(instance_printer.os,
    instance.template_class.clazz, instance_printer.generator,
    is_declaration),
  instance(instance), generator(instance_printer.generator)
{
}
 
/* An abstract template type printer, where the way of obtaining
 * the argument kind is specified by the subclasses.
 */
struct template_cpp_type_printer : public cpp_type_printer {
  template_cpp_type_printer() {}
 
  std::string base(const std::string &type, const Kind &kind) const;
  virtual Kind kind(int arg) const = 0;
  virtual std::string qualified(int arg, const std::string &cpp_type)
    const override;
};
 
/* Print a template type consisting of the type "type" and the kind "kind",
 * including the "typed::" namespace specifier.
 */
std::string template_cpp_type_printer::base(const std::string &type,
  const Kind &kind) const
{
  std::ostringstream ss;
 
  ss << "typed::";
  print_bare_template_type(ss, type, kind);
  return ss.str();
}
 
/* Return the qualified form of the given C++ isl type name appearing
 * in argument position "arg" (-1 for return type).
 *
 * isl::ctx is not templated, so if "cpp_type" is "ctx",
 * then print a non-templated version.
 * Otherwise, look up the kind of the argument and print
 * the corresponding template type.
 */
std::string template_cpp_type_printer::qualified(int arg,
  const std::string &cpp_type) const
{
  if (cpp_type == "ctx")
    return cpp_type_printer::qualified(arg, cpp_type);
 
  return base(cpp_type, kind(arg));
}
 
/* A template type printer for printing types with a fixed kind.
 *
 * "fixed_kind" is the fixed kind.
 */
struct template_cpp_kind_type_printer : public template_cpp_type_printer {
  template_cpp_kind_type_printer(const Kind &kind) :
    template_cpp_type_printer(), fixed_kind(kind) {}
 
  virtual Kind kind(int arg) const override;
 
  const Kind &fixed_kind;
};
 
/* Return the kind of the argument at position "arg",
 * where position -1 refers to the return type.
 *
 * Always use the fixed kind.
 */
Kind template_cpp_kind_type_printer::kind(int arg) const
{
  return fixed_kind;
}
 
/* A template type printer for printing a method with a given signature.
 *
 * "sig" is the signature of the method being printed.
 */
struct template_cpp_arg_type_printer : public template_cpp_type_printer {
  template_cpp_arg_type_printer(const Signature &sig) :
    template_cpp_type_printer(), sig(sig) {}
 
  virtual Kind kind(int arg) const override;
 
  const Signature &sig;
};
 
/* Return the kind of the argument at position "arg",
 * where position -1 refers to the return type.
 *
 * Look up the kind in the signature.
 */
Kind template_cpp_arg_type_printer::kind(int arg) const
{
  int n_args = sig.args.size();
 
  if (arg < 0)
    return sig.ret;
  if (arg >= n_args)
    generator::die("argument out of bounds");
  return sig.args[arg];
}
 
/* A template type printer for printing a method with a given signature
 * as part of a template class specialization of a given kind.
 *
 * "class_kind" is the template class specialization kind.
 */
struct template_method_type_printer : public template_cpp_arg_type_printer {
  template_method_type_printer(const Signature &sig,
      const Kind &class_kind) :
    template_cpp_arg_type_printer(sig),
    class_kind(class_kind) {}
 
  virtual std::string class_type(const std::string &cpp_name)
    const override;
 
  const Kind &class_kind;
};
 
/* Print the class type "cpp_name".
 *
 * Print the templated version using the template class specialization kind.
 */
std::string template_method_type_printer::class_type(
  const std::string &cpp_name) const
{
  return base(cpp_name, class_kind);
}
 
/* Print the templated return type of "method" of the kind "return_kind".
 *
 * Construct a type printer with "return_kind" as fixed kind and
 * use it to print the return type.
 */
void template_cpp_generator::class_printer::print_return_type(
  const Method &method, const Kind &return_kind) const
{
  template_cpp_kind_type_printer printer(return_kind);
 
  os << printer.return_type(method);
}
 
/* Remove the initial "n" elements from "v".
 */
template <typename T>
static void drop_initial(std::vector<T> &v, size_t n)
{
  v.erase(v.begin(), v.begin() + n);
}
 
/* If a method with signature "sig" requires additional template parameters
 * compared to those of the class, then print a declaration for them.
 * If this->declarations is set, then this will be part of a method declaration,
 * requiring extra indentation.
 *
 * Construct the sequence of all required template parameters
 * with those of the template class appearing first.
 * If this sequence has any parameters not induced by the template class itself,
 * then print a declaration for these extra parameters.
 */
void template_cpp_generator::class_printer::print_method_template_arguments(
  const Signature &sig)
{
  std::vector<std::string> class_params, method_params;
 
  class_params = instance.kind.params();
  method_params = class_params;
  combine(method_params, sig.params());
 
  if (class_params.size() == method_params.size())
    return;
 
  drop_initial(method_params, class_params.size());
 
  if (declarations)
    os << "  ";
  print_template(os, method_params);
}
 
/* Print the header for "method" with signature "sig".
 *
 * First print any additional template parameters that may be required and
 * then print a regular method header, using a template type printer.
 */
void template_cpp_generator::class_printer::print_method_header(
  const Method &method, const Signature &sig)
{
  template_method_type_printer type_printer(sig, instance.kind);
 
  print_method_template_arguments(sig);
  cpp_generator::class_printer::print_method_header(method,
              type_printer);
}
 
/* Given a group of methods with the same name,
 * should extra methods be added that take as arguments
 * those types that can be converted to the original argument type
 * through a unary constructor?
 *
 * Since type deduction does not consider implicit conversions,
 * these extra methods should always be printed.
 */
bool template_cpp_generator::class_printer::want_descendent_overloads(
  const function_set &methods)
{
  return true;
}
 
/* Print all constructors and methods that forward
 * to the corresponding methods in the plain C++ interface class.
 */
void template_cpp_generator::class_printer::print_all_methods()
{
  print_constructors();
  print_methods();
}
 
/* A helper class for printing method declarations
 * of a template class specialization.
 */
struct template_cpp_generator::method_decl_printer :
    public template_cpp_generator::class_printer {
  method_decl_printer(const specialization &instance,
      const struct specialization_printer &instance_printer) :
    class_printer(instance, instance_printer, true) {}
 
  virtual void print_method_sig(const Method &method,
    const Signature &sig, bool deleted) override;
  virtual void print_get_method(FunctionDecl *fd) override;
};
 
/* Print a declaration of the method "method" with signature "sig".
 * Mark is "delete" if "deleted" is set.
 */
void template_cpp_generator::method_decl_printer::print_method_sig(
  const Method &method, const Signature &sig, bool deleted)
{
  print_method_header(method, sig);
  if (deleted)
    os << " = delete";
  os << ";\n";
}
 
/* Return the total number of arguments in the signature for "method",
 * taking into account any possible callback arguments.
 *
 * In particular, if the method has a callback argument,
 * then the return kind of the callback appears at the position
 * of the callback and the kinds of the arguments (except
 * the user pointer argument) appear in the following positions.
 * The user pointer argument that follows the callback argument
 * is also removed.
 */
static int total_params(const Method &method)
{
  int n = method.num_params();
 
  for (const auto &callback : method.callbacks) {
    auto callback_type = callback->getType();
    auto proto = generator::extract_prototype(callback_type);
 
    n += proto->getNumArgs() - 1;
    n -= 1;
  }
 
  return n;
}
 
/* Return a signature for "method" that matches "instance".
 */
static Signature instance_sig(const Method &method,
  const specialization &instance)
{
  std::vector<Kind> args(total_params(method));
 
  args[0] = instance.kind;
  return { instance.kind, args };
}
 
/* Print a declaration for the "get" method "fd",
 * using a name that includes the "get_" prefix.
 *
 * These methods are only included in the plain interface.
 * Explicitly delete them from the templated interface.
 */
void template_cpp_generator::method_decl_printer::print_get_method(
  FunctionDecl *fd)
{
  Method method(clazz, fd, clazz.base_method_name(fd));
 
  print_method_sig(method, instance_sig(method, instance), true);
}
 
/* A helper class for printing method definitions
 * of a template class specialization.
 */
struct template_cpp_generator::method_impl_printer :
    public template_cpp_generator::class_printer {
  method_impl_printer(const specialization &instance,
      const struct specialization_printer &instance_printer) :
    class_printer(instance, instance_printer, false) {}
 
  void print_callback_method_body(const Method &method,
    const Signature &sig);
  void print_method_body(const Method &method, const Signature &sig);
  void print_constructor_body(const Method &method, const Signature &sig);
  virtual void print_method_sig(const Method &method,
    const Signature &sig, bool deleted) override;
  virtual void print_get_method(FunctionDecl *fd) override;
};
 
/* Print a definition of the constructor "method" with signature "sig".
 *
 * Simply pass all arguments to the constructor of the corresponding
 * plain type.
 */
void template_cpp_generator::method_impl_printer::print_constructor_body(
  const Method &method, const Signature &sig)
{
  const auto &base_name = instance.base_name();
 
  os << "  : " << base_name;
  method.print_cpp_arg_list(os, [&] (int i, int arg) {
    os << method.fd->getParamDecl(i)->getName().str();
  });
  os << "\n";
 
  os << "{\n";
  os << "}\n";
}
 
/* Print the arguments of the callback function "callback" to "os",
 * calling "print_arg" with the type and the name of the arguments,
 * where the type is obtained from "type_printer" with argument positions
 * shifted by "shift".
 * None of the arguments should be skipped.
 */
static void print_callback_args(std::ostream &os,
  const FunctionProtoType *callback, const cpp_type_printer &type_printer,
  int shift,
  const std::function<void(const std::string &type,
    const std::string &name)> &print_arg)
{
  auto n_arg = callback->getNumArgs() - 1;
 
  Method::print_arg_list(os, 0, n_arg, [&] (int i) {
    auto type = callback->getArgType(i);
    auto name = "arg" + std::to_string(i);
    auto cpptype = type_printer.param(shift + i, type);
 
    print_arg(cpptype, name);
 
    return false;
  });
}
 
/* Print a lambda corresponding to "callback"
 * with signature "sig" and argument positions shifted by "shift".
 *
 * The lambda takes arguments with plain isl types and
 * calls the callback of "method" with templated arguments.
 */
static void print_callback_lambda(std::ostream &os, ParmVarDecl *callback,
  const Signature &sig, int shift)
{
  auto callback_type = callback->getType();
  auto callback_name = callback->getName().str();
  auto proto = generator::extract_prototype(callback_type);
 
  os << "  auto lambda_" << callback_name << " = [&] ";
  print_callback_args(os, proto, cpp_type_printer(), shift,
    [&] (const std::string &type, const std::string &name) {
      os << type << " " << name;
    });
  os << " {\n";
 
  os << "    return " << callback_name;
  print_callback_args(os, proto, template_cpp_arg_type_printer(sig),
    shift,
    [&] (const std::string &type, const std::string &name) {
      os << type << "(" << name << ")";
    });
  os << ";\n";
 
  os << "  };\n";
}
 
/* Print lambdas for passing to the plain method corresponding to "method"
 * with signature "sig".
 *
 * The method is assumed to have only callbacks as argument,
 * which means the arguments of the first callback are shifted by 2
 * with respect to the arguments of the signature
 * (one for the position of the callback argument plus
 * one for the return kind of the callback).
 * The arguments of a subsequent callback are shifted by
 * the number of arguments of the previous callback minus one
 * for the user pointer plus one for the return kind.
 */
static void print_callback_lambdas(std::ostream &os, const Method &method,
  const Signature &sig)
{
  int shift;
 
  if (method.num_params() != 1 + 2 * method.callbacks.size())
    generator::die("callbacks are assumed to be only arguments");
 
  shift = 2;
  for (const auto &callback : method.callbacks) {
    print_callback_lambda(os, callback, sig, shift);
    shift += generator::prototype_n_args(callback->getType());
  }
}
 
/* Print a definition of the member method "method", which is known
 * to have a callback argument, with signature "sig".
 *
 * First print lambdas for passing to the corresponding plain method and
 * calling the callback of "method" with templated arguments.
 * Then call the plain method, replacing the original callbacks
 * by the lambdas.
 *
 * The return value is assumed to be isl_bool or isl_stat
 * so that no conversion to a template type is required.
 */
void template_cpp_generator::method_impl_printer::print_callback_method_body(
  const Method &method, const Signature &sig)
{
  const auto &base_name = instance.base_name();
  auto return_type = method.fd->getReturnType();
 
  if (!is_isl_bool(return_type) && !is_isl_stat(return_type))
    die("only isl_bool and isl_stat return types are supported");
 
  os << "{\n";
 
  print_callback_lambdas(os, method, sig);
 
  os << "  return ";
  os << base_name << "::" << method.name;
  method.print_cpp_arg_list(os, [&] (int i, int arg) {
    auto param = method.fd->getParamDecl(i);
 
    if (generator::is_callback(param->getType()))
      os << "lambda_";
    os << param->getName().str();
  });
  os << ";\n";
 
  os << "}\n";
}
 
/* Print a definition of the member or static method "method"
 * with signature "sig".
 *
 * The body calls the corresponding method of the base class
 * in the plain interface and
 * then casts the result to the templated result type.
 */
void template_cpp_generator::method_impl_printer::print_method_body(
  const Method &method, const Signature &sig)
{
  const auto &base_name = instance.base_name();
 
  os << "{\n";
  os << "  auto res = ";
  os << base_name << "::" << method.name;
  method.print_cpp_arg_list(os, [&] (int i, int arg) {
    os << method.fd->getParamDecl(i)->getName().str();
  });
  os << ";\n";
 
  os << "  return ";
  print_return_type(method, sig.ret);
  os << "(res);\n";
  os << "}\n";
}
 
/* Print a definition of the method "method" with signature "sig",
 * if "deleted" is not set.
 *
 * If "deleted" is set, then the corresponding declaration
 * is marked "delete" and no definition needs to be printed.
 *
 * Otherwise print the method header, preceded by the template parameters,
 * if needed.
 * The body depends on whether the method is a constructor or
 * takes any callbacks.
 */
void template_cpp_generator::method_impl_printer::print_method_sig(
  const Method &method, const Signature &sig, bool deleted)
{
  if (deleted)
    return;
 
  os << "\n";
  print_non_empty_template(os, instance.kind.params());
  print_method_header(method, sig);
  os << "\n";
  if (method.kind == Method::Kind::constructor)
    print_constructor_body(method, sig);
  else if (method.callbacks.size() != 0)
    print_callback_method_body(method, sig);
  else
    print_method_body(method, sig);
}
 
/* Print a definition for the "get" method "fd" in class "clazz",
 * using a name that includes the "get_" prefix, to "os".
 *
 * The declarations of these methods are explicitly delete'd
 * so no definition needs to be printed.
 */
void template_cpp_generator::method_impl_printer::print_get_method(
  FunctionDecl *fd)
{
}
 
/* Print a declaration or definition of the static method "method",
 * if it has a signature specified by static_methods.
 */
void template_cpp_generator::class_printer::print_static_method(
  const Method &method)
{
  print_special_method(method, static_methods);
}
 
/* Signatures for constructors from a string.
 */
static Signature params_from_str = { { }, { { Ctx }, { Str } } };
static Signature set_from_str = { { Domain }, { { Ctx }, { Str } } };
static Signature map_from_str = { { Domain, Range }, { { Ctx }, { Str } } };
static std::vector<Signature> from_str =
  { params_from_str, set_from_str, map_from_str };
 
/* Signature for a constructor from an integer.
 */
static Signature int_from_si = { { Anonymous }, { { Ctx }, { Integer } } };
 
/* Signatures for constructors of lists from the initial number
 * of elements.
 */
static Signature alloc_params = { { }, { { Ctx }, { Integer } } };
static Signature alloc_set = { { Domain }, { { Ctx }, { Integer } } };
static Signature alloc_map = { { Domain, Range }, { { Ctx }, { Integer } } };
 
/* Signatures for constructors and methods named after some other class.
 *
 * Two forms of constructors are handled
 * - conversion from another object
 * - construction of a multi-expression from a space and a list
 *
 * Methods named after some other class also come in two forms
 * - extraction of information such as the space or a list
 * - construction of a multi-expression from a space and a list
 *
 * In both cases, the first form is a unary operation and
 * the second has an extra argument with a kind that is equal
 * to that of the first argument, except that the final tuple is anonymous.
 */
static std::vector<Signature> constructor_sig = {
  un_params,
  un_set,
  un_map,
  from_list_set,
  from_list_map,
};
 
/* Signatures for constructors derived from methods
 * with the given names that override the default signatures.
 */
static const std::unordered_map<std::string, std::vector<Signature>>
special_constructors {
  { "alloc",    { alloc_params, alloc_set, alloc_map } },
  { "int_from_si",  { int_from_si } },
  { "read_from_str",  from_str },
};
 
/* Print a declaration or definition of the constructor "method".
 */
void template_cpp_generator::class_printer::print_constructor(
  const Method &method)
{
  if (special_constructors.count(method.name) != 0) {
    const auto &sigs = special_constructors.at(method.name);
    return print_matching_method(method, sigs);
  }
  print_matching_method(method, constructor_sig);
}
 
/* Does this template class represent an anonymous function?
 *
 * If any specialization represents an anonymous function,
 * then every specialization does, so simply check
 * the first specialization.
 */
bool template_class::is_anon() const
{
  return class_tuples[0].is_anon();
}
 
/* Does this template class represent an anonymous value?
 *
 * That is, is there only a single specialization that moreover
 * has a single, anonymous tuple?
 */
bool template_class::is_anon_set() const
{
  return class_tuples.size() == 1 && class_tuples[0].is_anon_set();
}
 
/* Update the substitution "sub" to map "general" to "specific"
 * if "specific" is a special case of "general" consistent with "sub",
 * given that "general" is not a pair and can be assigned "specific".
 * Return true if successful.
 * Otherwise, return false.
 *
 * Check whether "general" is already assigned something in "sub".
 * If so, it must be assigned "specific".
 * Otherwise, there is a conflict.
 */
static bool update_sub_base(Substitution &sub, const TupleKindPtr &general,
  const TupleKindPtr &specific)
{
  auto name = general->name;
 
  if (sub.count(name) != 0 && sub.at(name) != specific)
    return false;
  sub.emplace(name, specific);
  return true;
}
 
/* Update the substitution "sub" to map "general" to "specific"
 * if "specific" is a special case of "general" consistent with "sub".
 * Return true if successful.
 * Otherwise, return false.
 *
 * If "general" is a pair and "specific" is not,
 * then "specific" cannot be a special case.
 * If both are pairs, then update the substitution based
 * on both sides.
 * If "general" is Anonymous, then "specific" must be Anonymous as well.
 * If "general" is Leaf, then "specific" cannot be a pair.
 *
 * Otherwise, assign "specific" to "general", if possible.
 */
static bool update_sub(Substitution &sub, const TupleKindPtr &general,
  const TupleKindPtr &specific)
{
  if (general->left() && !specific->left())
    return false;
  if (general->left())
    return update_sub(sub, general->left(), specific->left()) &&
        update_sub(sub, general->right(), specific->right());
  if (general == Anonymous && specific != Anonymous)
    return false;
  if (general == Leaf && specific->left())
    return false;
 
  return update_sub_base(sub, general, specific);
}
 
/* Check if "specific" is a special case of "general" and,
 * if so, return true along with a substitution
 * that maps "general" to "specific".
 * Otherwise return false.
 *
 * This can only happen if the number of tuple kinds is the same.
 * If so, start with an empty substitution and update it
 * for each pair of tuple kinds, checking that each update succeeds.
 */
static std::pair<bool, Substitution> specializer(const Kind &general,
  const Kind &specific)
{
  Substitution specializer;
 
  if (general.size() != specific.size())
    return { false, Substitution() };
 
  for (size_t i = 0; i < general.size(); ++i) {
    auto general_tuple = general[i];
 
    if (!update_sub(specializer, general[i], specific[i]))
      return { false, Substitution() };
  }
 
  return { true, specializer };
}
 
/* Is "kind1" equivalent to "kind2"?
 * That is, is each a special case of the other?
 */
static bool equivalent(const Kind &kind1, const Kind &kind2)
{
  return specializer(kind1, kind2).first &&
         specializer(kind2, kind1).first;
}
 
/* Add the specialization "kind" to the sequence of specializations,
 * provided there is no equivalent specialization already in there.
 */
void template_class::add_specialization(const Kind &kind)
{
  for (const auto &special : class_tuples)
    if (equivalent(special, kind))
      return;
  class_tuples.emplace_back(kind);
}
 
/* A type printer that prints the plain interface type,
 * without namespace.
 */
struct plain_cpp_type_printer : public cpp_type_printer {
  plain_cpp_type_printer() {}
 
  virtual std::string qualified(int arg, const std::string &cpp_type)
    const override;
};
 
/* Return the qualified form of the given C++ isl type name appearing
 * in argument position "arg" (-1 for return type).
 *
 * For printing the plain type without namespace, no modifications
 * are required.
 */
std::string plain_cpp_type_printer::qualified(int arg,
  const std::string &cpp_type) const
{
  return cpp_type;
}
 
/* Return a string representation of the plain type "type".
 *
 * For the plain printer, the argument position is irrelevant,
 * so simply pass in -1.
 */
static std::string plain_type(QualType type)
{
  return plain_cpp_type_printer().param(-1, type);
}
 
/* Return a string representation of the plain return type of "method".
 */
static std::string plain_return_type(const Method &method)
{
  return plain_type(method.fd->getReturnType());
}
 
/* Return that part of the signature "sig" that should match
 * the template class specialization for the given method.
 *
 * In particular, if the method is a regular member method,
 * then the instance should match the first argument.
 * Otherwise, it should match the return kind.
 */
static const Kind &matching_kind(const Method &method, const Signature &sig)
{
  if (method.kind == Method::Kind::member_method)
    return sig.args[0];
  else
    return sig.ret;
}
 
/* Is it possible for "template_class" to have the given kind?
 *
 * If the template class represents an anonymous function,
 * then so must the given kind.
 * There should also be specialization with the same number of tuple kinds.
 */
static bool has_kind(const template_class &template_class, const Kind &kind)
{
  if (template_class.is_anon() && !kind.is_anon())
    return false;
  for (const auto &class_tuple : template_class.class_tuples)
    if (class_tuple.size() == kind.size())
      return true;
  return false;
}
 
/* Is "return_kind" a possible kind for the return type of "method"?
 *
 * If the return type is not a template class,
 * then "return_kind" should not have any template parameters.
 * Otherwise, "return_kind" should be a valid kind for the template class.
 */
bool template_cpp_generator::class_printer::is_return_kind(
  const Method &method, const Kind &return_kind)
{
  const auto &template_classes = generator.template_classes;
  auto return_type = plain_return_type(method);
 
  if (template_classes.count(return_type) == 0)
    return return_kind.params().size() == 0;
  return has_kind(template_classes.at(return_type), return_kind);
}
 
/* Is "kind" a placeholder that can be assigned something else
 * in a substitution?
 *
 * Anonymous can only be mapped to itself.  This is taken care of
 * by assign().
 * Leaf can only be assigned a placeholder, but there is no need
 * to handle this specifically since Leaf can still be assigned
 * to the placeholder.
 */
static bool assignable(const TupleKindPtr &kind)
{
  return kind != Anonymous && kind != Leaf;
}
 
/* Return a substitution that maps "kind1" to "kind2", if possible.
 * Otherwise return an empty substitution.
 *
 * Check if "kind1" can be assigned anything or
 * if "kind1" and "kind2" are identical.
 * The latter case handles mapping Anonymous to itself.
 */
static Substitution assign(const TupleKindPtr &kind1, const TupleKindPtr &kind2)
{
  Substitution res;
 
  if (assignable(kind1) || kind1 == kind2)
    res.emplace(kind1->name, kind2);
  return res;
}
 
/* Return a substitution that first applies "first" and then "second".
 *
 * The result consists of "second" and of "second" applied to "first".
 */
static Substitution compose(const Substitution &first,
  const Substitution &second)
{
  Substitution res = second;
 
  for (const auto &kvp : first)
    res.emplace(kvp.first, apply(kvp.second, second));
 
  return res;
}
 
static Substitution compute_unifier(const TupleKindPtr &kind1,
  const TupleKindPtr &kind2);
 
/* Try and extend "unifier" with a unifier for "kind1" and "kind2".
 * Return the resulting unifier if successful.
 * Otherwise, return an empty substitution.
 *
 * First apply "unifier" to "kind1" and "kind2".
 * Then compute a unifier for the resulting tuple kinds and
 * combine it with "unifier".
 */
static Substitution combine_unifiers(const TupleKindPtr &kind1,
  const TupleKindPtr &kind2, const Substitution &unifier)
{
  auto k1 = apply(kind1, unifier);
  auto k2 = apply(kind2, unifier);
  auto u = compute_unifier(k1, k2);
  if (u.size() == 0)
    return Substitution();
  return compose(unifier, u);
}
 
/* Try and compute a unifier of "kind1" and "kind2",
 * i.e., a substitution that produces the same result when
 * applied to both "kind1" and "kind2",
 * for the case where both "kind1" and "kind2" are pairs.
 * Return this unifier if it was found.
 * Return an empty substitution if no unifier can be found.
 *
 * First compute a unifier for the left parts of the pairs and,
 * if successful, combine it with a unifier for the right parts.
 */
static Substitution compute_pair_unifier(const TupleKindPtr &kind1,
  const TupleKindPtr &kind2)
{
  auto unifier_left = compute_unifier(kind1->left(), kind2->left());
  if (unifier_left.size() == 0)
    return Substitution();
  return combine_unifiers(kind1->right(), kind2->right(), unifier_left);
}
 
/* Try and compute a unifier of "kind1" and "kind2",
 * i.e., a substitution that produces the same result when
 * applied to both "kind1" and "kind2".
 * Return this unifier if it was found.
 * Return an empty substitution if no unifier can be found.
 *
 * If one of the tuple kinds is a pair then assign it
 * to the other tuple kind, if possible.
 * If neither is a pair, then try and assign one to the other.
 * Otherwise, let compute_pair_unifier compute a unifier.
 *
 * Note that an assignment is added to the unifier even
 * if "kind1" and "kind2" are identical.
 * This ensures that a successful substitution is never empty.
 */
static Substitution compute_unifier(const TupleKindPtr &kind1,
  const TupleKindPtr &kind2)
{
  if (kind1->left() && !kind2->left())
    return assign(kind2, kind1);
  if (!kind1->left() && kind2->left())
    return assign(kind1, kind2);
  if (!kind1->left() && !kind2->left()) {
    if (assignable(kind1))
      return assign(kind1, kind2);
    else
      return assign(kind2, kind1);
  }
 
  return compute_pair_unifier(kind1, kind2);
}
 
/* Try and compute a unifier of "kind1" and "kind2",
 * i.e., a substitution that produces the same result when
 * applied to both "kind1" and "kind2".
 * Return this unifier if it was found.
 * Return an empty substitution if no unifier can be found.
 *
 * Start with an empty substitution and compute a unifier for
 * each pair of tuple kinds, combining the results.
 * If no combined unifier can be found or
 * if the numbers of tuple kinds are different, then return
 * an empty substitution.
 * This assumes that the number of tuples is greater than zero,
 * as otherwise an empty substitution would be returned as well.
 */
static Substitution compute_unifier(const Kind &kind1, const Kind &kind2)
{
  Substitution unifier;
 
  if (kind1.size() != kind2.size())
    return Substitution();
 
  for (size_t i = 0; i < kind1.size(); ++i)
    unifier = combine_unifiers(kind1[i], kind2[i], unifier);
 
  return unifier;
}
 
/* Try and construct a Kind that is a specialization of both "general" and
 * "specific", where "specific" is known _not_ to be a specialization
 * of "general" and not to contain any Leaf.
 *
 * First check whether "general" is a specialization of "specific".
 * If so, simply return "general".
 * Otherwise, rename the placeholders in the two kinds apart and
 * try and compute a unifier.
 * If this succeeds, then return the result of applying the unifier.
 */
static std::pair<bool, Kind> unify(const Kind &general, const Kind &specific)
{
  if (specializer(specific, general).first) {
    return { true, general };
  } else {
    auto rename = param_renamer(specific.params(), "T");
    auto renamed = specific.apply(rename);
    auto unifier = compute_unifier(general, renamed);
 
    if (unifier.size() == 0)
      return { false, { } };
 
    return { true, general.apply(unifier) };
  }
}
 
/* Try and add a template class specialization corresponding to "kind".
 * The new specialization needs to be a specialization of both
 * the current specialization and "kind".
 *
 * The current template class specialization is known not to be a special case
 * of "kind".
 *
 * Try and unify the two kinds and, if this succeeds, add the result
 * to this list of template class specializations.
 */
void template_cpp_generator::class_printer::add_specialization(
  const Kind &kind)
{
  auto maybe_unified = unify(kind, instance.kind);
 
  if (!maybe_unified.first)
    return;
  instance.template_class.add_specialization(maybe_unified.second);
}
 
/* Does the type of the parameter at position "i" of "method" necessarily
 * have a final Anonymous tuple?
 *
 * If the parameter is not of an isl type or if no specializations
 * have been defined for the type, then it can be considered anonymous.
 * Otherwise, if any specialization represents an anonymous function,
 * then every specialization does, so simply check
 * the first specialization.
 */
static bool param_is_anon(const Method &method, int i)
{
  ParmVarDecl *param = method.get_param(i);
  QualType type = param->getOriginalType();
 
  if (cpp_generator::is_isl_type(type)) {
    const auto &name = type->getPointeeType().getAsString();
    const auto &cpp = cpp_generator::type2cpp(name);
    const auto &tuples = lookup_class_tuples(cpp);
 
    if (tuples.empty())
      return true;
    return tuples[0].is_anon();
  }
 
  return true;
}
 
/* Replace the final tuple of "arg_kind" by Anonymous in "sig" and
 * return the update signature,
 * unless this would affect the class instance "instance_kind".
 *
 * If the original "instance_kind" is a special case
 * of the result of the substitution, then "instance_kind"
 * is not affected and the substitution can be applied
 * to the entire signature.
 */
static Signature specialize_anonymous_arg(const Signature &sig,
  const Kind &arg_kind, const Kind &instance_kind)
{
  const auto &subs = compute_unifier(arg_kind.back(), Anonymous);
  const auto &specialized_instance = instance_kind.apply(subs);
 
  if (!specializer(specialized_instance, instance_kind).first)
    return sig;
 
  return sig.apply(subs);
}
 
/* If any of the arguments of "method" is of a type that necessarily
 * has a final Anonymous tuple, but the corresponding entry
 * in the signature "sig" is not Anonymous, then replace
 * that entry by Anonymous and return the updated signature,
 * unless this would affect the class instance "instance_kind".
 */
static Signature specialize_anonymous_args(const Signature &sig,
  const Method &method, const Kind &instance_kind)
{
  auto specialized_sig = sig;
 
  method.on_cpp_arg_list([&] (int i, int arg) {
    const auto &arg_kind = sig.args[arg];
 
    if (arg_kind.is_anon())
      return;
    if (!param_is_anon(method, i))
      return;
    specialized_sig = specialize_anonymous_arg(specialized_sig,
          arg_kind, instance_kind);
  });
 
  return specialized_sig;
}
 
/* Print a declaration or definition of the method "method"
 * if the template class specialization matches "match_arg".
 * Return true if so.
 * "sig" is the complete signature, of which "match_arg" refers
 * to the first argument or the return type.
 *
 * Since "sig" may have parameters with the same names as
 * those in instance.kind, rename them apart first.
 *
 * If the template class specialization is a special case of
 * (the renamed) "match_arg"
 * then apply the specializer to the complete (renamed) signature,
 * specialize any anonymous arguments,
 * check that the return kind is allowed and, if so,
 * print the declaration or definition using the specialized signature.
 *
 * If the template class specialization is not a special case of "match_arg"
 * then add a further specialization to the list of specializations
 * of the template class.
 */
bool template_cpp_generator::class_printer::print_matching_method(
  const Method &method, const Signature &sig, const Kind &match_arg)
{
  auto rename = shared_param_renamer(sig, instance.kind);
  auto renamed_arg = match_arg.apply(rename);
  auto maybe_specializer = specializer(renamed_arg, instance.kind);
  if (maybe_specializer.first) {
    const auto &specializer = maybe_specializer.second;
    auto specialized_sig = sig.apply(rename).apply(specializer);
    specialized_sig = specialize_anonymous_args(specialized_sig,
              method, instance.kind);
    if (!is_return_kind(method, specialized_sig.ret))
      return false;
 
    print_method_sig(method, specialized_sig, false);
  } else {
    add_specialization(match_arg);
  }
  return maybe_specializer.first;
}
 
/* Is the first argument of "method" of type "isl_ctx *"?
 */
static bool first_arg_is_ctx(const Method &method)
{
  return generator::first_arg_is_isl_ctx(method.fd);
}
 
/* Is the first signature argument set to { Ctx }?
 */
static bool first_kind_is_ctx(const Signature &sig)
{
  return sig.args[0].size() > 0 && sig.args[0][0] == Ctx;
}
 
/* Print a declaration or definition of the member method "method"
 * if it matches the signature "sig".
 * Return true if so.
 *
 * First determine the part of the signature that needs to match
 * the template class specialization and
 * check that it has the same number of template arguments.
 * Also check that the number of arguments of the signature
 * matches that of the method.
 * If there is at least one argument, then check that the first method argument
 * is an isl_ctx if and only if the first signature argument is Ctx.
 *
 * If these tests succeed, proceed with the actual matching.
 */
bool template_cpp_generator::class_printer::print_matching_method(
  const Method &method, const Signature &sig)
{
  auto match_arg = matching_kind(method, sig);
  int n_args = sig.args.size();
 
  if (match_arg.size() != instance.kind.size())
    return false;
  if (n_args != total_params(method))
    return false;
  if (n_args > 0 && first_arg_is_ctx(method) != first_kind_is_ctx(sig))
    return false;
 
  return print_matching_method(method, sig, match_arg);
}
 
/* Print a declaration or definition of the member method "method"
 * for each matching signature in "signatures".
 *
 * If there is no matching signature in "signatures",
 * then explicitly delete the method (using a signature based on
 * the specialization) so that it is not inherited from the base class.
 */
void template_cpp_generator::class_printer::print_matching_method(
  const Method &method, const std::vector<Signature> &signatures)
{
  auto any = false;
 
  for (const auto &sig : signatures)
    if (print_matching_method(method, sig))
      any = true;
 
  if (!any)
    print_method_sig(method, instance_sig(method, instance), true);
}
 
/* Signatures for "at" methods applied to a multi-expression,
 * which make the final tuple anonymous.
 */
static Signature select_set = { { Anonymous }, { { Domain }, { Integer } } };
static Signature select_map =
  { { Domain, Anonymous }, { { Domain, Range }, { Integer } } };
static std::vector<Signature> at_select = { select_set, select_map };
 
/* Signatures for other "at" methods applied to a list,
 * which do not modify the tuple kind.
 */
static Signature bin_set_int = { { Domain }, { { Domain }, { Integer } } };
static Signature bin_map_int =
  { { Domain, Range }, { { Domain, Range }, { Integer } } };
static std::vector<Signature> at_keep = { bin_set_int, bin_map_int };
 
/* Print a declaration or definition of the "at" member method "method".
 *
 * There are two types of methods called "at".
 * One type extracts an element from a multi-expression and
 * the other extracts an element from a list.
 *
 * In the first case, the return type is an anonymous function
 * while the object type is not.  In this case, the return kind
 * should have a final Anonymous tuple.
 * Otherwise, the return kind should be the same as the object kind.
 */
void template_cpp_generator::class_printer::print_at_method(
  const Method &method)
{
  auto anon = instance.template_class.is_anon();
  auto return_type = plain_return_type(method);
  auto return_class = generator.template_classes.at(return_type);
 
  if (!anon && return_class.is_anon())
    return print_matching_method(method, at_select);
  else
    return print_matching_method(method, at_keep);
}
 
/* Does the string "s" contain "sub" as a substring?
 */
static bool contains(const std::string &s, const std::string &sub)
{
  return s.find(sub) != std::string::npos;
}
 
/* Print a declaration or definition of the member method "method",
 * if it has a special signature in "special_methods".
 * Return true if this is the case.
 *
 * Check if any special signatures are specified for this method and
 * if the class name matches any of those with special signatures.
 * If so, pick the one with the best match, i.e., the first match
 * since the largest keys appear first.
 */
bool template_cpp_generator::class_printer::print_special_method(
  const Method &method, const infix_map_map &special_methods)
{
  if (special_methods.count(method.name) == 0)
    return false;
 
  for (const auto &kvp : special_methods.at(method.name)) {
    if (!contains(instance.template_class.class_name, kvp.first))
      continue;
    print_matching_method(method, kvp.second);
    return true;
  }
 
  return false;
}
 
/* Print a declaration or definition of the member method "method",
 * if it has a special signature specified by special_member_methods.
 * Return true if this is the case.
 */
bool template_cpp_generator::class_printer::print_special_member_method(
  const Method &method)
{
  return print_special_method(method, special_member_methods);
}
 
/* Print a declaration or definition of the member method "method",
 * if it is named after a template class.  Return true if this is the case.
 */
bool template_cpp_generator::class_printer::print_type_named_member_method(
  const Method &method)
{
  if (generator.template_classes.count(method.name) == 0)
    return false;
 
  print_matching_method(method, constructor_sig);
 
  return true;
}
 
/* Print a declaration or definition of the member method "method"
 * using a signature associated to method name "name", if there is any.
 * Return true if this is the case.
 */
bool template_cpp_generator::class_printer::print_member_method_with_name(
  const Method &method, const std::string &name)
{
  if (member_methods.count(name) == 0)
    return false;
 
  print_matching_method(method, member_methods.at(name));
  return true;
}
 
/* If "sub" appears inside "str", then remove the first occurrence and
 * return the result.  Otherwise, simply return "str".
 */
static std::string drop_occurrence(const std::string &str,
  const std::string &sub)
{
  auto res = str;
  auto pos = str.find(sub);
 
  if (pos != std::string::npos)
    res.erase(pos, sub.length());
 
  return res;
}
 
/* If "sub" appears in "str" next to an underscore, then remove the combination.
 * Otherwise, simply return "str".
 */
static std::string drop_underscore_occurrence(const std::string &str,
  const std::string &sub)
{
  auto res = drop_occurrence(str, sub + "_");
  if (res != str)
    return res;
  return drop_occurrence(res, std::string("_") + sub);
}
 
/* Return the name of "method", with the name of the return type,
 * along with an underscore, removed, if this combination appears in the name.
 * Otherwise, simply return the name.
 */
const std::string name_without_return(const Method &method)
{
  auto return_infix = plain_return_type(method);
  return drop_underscore_occurrence(method.name, return_infix);
}
 
/* If this method has a callback, then remove the type
 * of the first argument of the first callback from the name of the method.
 * Otherwise, simply return the name of the method.
 */
const std::string callback_name(const Method &method)
{
  if (method.callbacks.size() == 0)
    return method.name;
 
  auto type = method.callbacks.at(0)->getType();
  auto callback = cpp_generator::extract_prototype(type);
  auto arg_type = plain_type(callback->getArgType(0));
  return generator::drop_suffix(method.name, "_" + arg_type);
}
 
/* Print a declaration or definition of the member method "method".
 *
 * If the method is called "at", then it requires special treatment.
 * Otherwise, check if the signature is overridden for this class or
 * if the method is named after some other type.
 * Otherwise look for an appropriate signature using different variations
 * of the method name.  First try the method name itself,
 * then the method name with the return type removed and
 * finally the method name with the callback argument type removed.
 */
void template_cpp_generator::class_printer::print_member_method(
  const Method &method)
{
  if (method.name == "at")
    return print_at_method(method);
  if (print_special_member_method(method))
    return;
  if (print_type_named_member_method(method))
    return;
  if (print_member_method_with_name(method, method.name))
    return;
  if (print_member_method_with_name(method, name_without_return(method)))
    return;
  if (print_member_method_with_name(method, callback_name(method)))
    return;
}
 
/* Print a declaration or definition of "method" based on its type.
 */
void template_cpp_generator::class_printer::print_any_method(
  const Method &method)
{
  switch (method.kind) {
  case Method::Kind::static_method:
    print_static_method(method);
    break;
  case Method::Kind::constructor:
    print_constructor(method);
    break;
  case Method::Kind::member_method:
    print_member_method(method);
    break;
  }
}
 
/* Print a declaration or definition of "method".
 *
 * Mark the method as not requiring copies of the arguments.
 */
void template_cpp_generator::class_printer::print_method(const Method &method)
{
  print_any_method(NoCopyMethod(method));
}
 
/* Print a declaration or definition of "method".
 *
 * Note that a ConversionMethod is already marked
 * as not requiring copies of the arguments.
 */
void template_cpp_generator::class_printer::print_method(
  const ConversionMethod &method)
{
  print_any_method(method);
}
 
/* Helper class for printing the declarations for
 * template class specializations.
 */
struct template_cpp_generator::class_decl_printer :
  public specialization_printer
{
  class_decl_printer(std::ostream &os,
        template_cpp_generator &generator) :
    specialization_printer(os, generator) {}
 
  void print_arg_subclass_constructor(const specialization &instance,
    const std::vector<std::string> &params) const;
  void print_super_constructor(const specialization &instance) const;
  virtual void print_class(const specialization &instance) const override;
};
 
/* Print the declaration and definition of a constructor
 * for the template class specialization "instance" taking
 * an instance with more specialized template arguments,
 * where "params" holds the template parameters of "instance".
 * It is assumed that there is at least one template parameter as otherwise
 * there are no template arguments to be specialized and
 * no constructor needs to be printed.
 *
 * In particular, the constructor takes an object of the same instance where
 * for each template parameter, the corresponding template argument
 * of the input object is a subclass of the template argument
 * of the constructed object.
 *
 * Pick fresh names for all template parameters and
 * add a constructor with these fresh names as extra template parameters and
 * a constraint requiring that each of them is a subclass
 * of the corresponding class template parameter.
 * The plain C++ interface object of the constructed object is initialized with
 * the plain C++ interface object of the constructor argument.
 */
void template_cpp_generator::class_decl_printer::print_arg_subclass_constructor(
  const specialization &instance,
  const std::vector<std::string> &params) const
{
  const auto &class_name = instance.class_name();
  auto rename = param_renamer(params, "Arg");
  auto derived = instance.kind.apply(rename);
 
  os << "  template ";
  os << "<";
  print_pure_template_args(os, derived.params());
  os << ",\n";
  os << "            typename std::enable_if<\n";
  for (size_t i = 0; i < params.size(); ++i) {
    if (i != 0)
      os << " &&\n";
    os << "              std::is_base_of<"
       << params[i] << ", "
       << rename.at(params[i])->params()[0] << ">{}";
  }
  os << ",\n";
  os << "            bool>::type = true>";
  os << "\n";
  os << "  " << class_name << "(const ";
  print_bare_template_type(os, class_name, derived);
  os << " &obj) : " << instance.base_name() << "(obj) {}\n";
}
 
/* Print the declaration and definition of a constructor
 * for the template class specialization "instance" taking
 * an instance of the base class.
 *
 * If the instance kind is that of an anonymous set
 * (i.e., it has a single tuple that is set to Anonymous),
 * then allow the constructor to be called externally.
 * This is mostly useful for being able to use isl::val and
 * isl::typed::val<Anonymous> interchangeably and similarly for isl::id.
 *
 * If the instance is of any other kind, then make this constructor private
 * to avoid objects of the plain interface being converted automatically.
 * Also make sure that it does not apply to any type derived
 * from the base class.  In particular, this makes sure it does
 * not apply to any other specializations of this template class as
 * otherwise any conflict in specializations would simply point
 * to the private constructor.
 *
 * A factory method is added to be able to perform the conversion explicitly,
 * with an explicit specification of the template arguments.
 */
void template_cpp_generator::class_decl_printer::print_super_constructor(
  const specialization &instance) const
{
  bool hide = !instance.kind.is_anon_set();
  const auto &base_name = instance.base_name();
  const auto &arg_name = hide ? "base" : base_name;
 
  if (hide) {
    os << " private:\n";
    os << "  template <typename base,\n";
    os << "            typename std::enable_if<\n";
    os << "              std::is_same<base, " << base_name
       << ">{}, bool>::type = true>\n";
  }
  os << "  " << instance.class_name()
     << "(const " << arg_name << " &obj) : "
     << base_name << "(obj) {}\n";
  if (hide)
    os << " public:\n";
  os << "  static " << instance.class_name() << " from"
     << "(const " << base_name << " &obj) {\n";
  os << "    return " << instance.class_name() << "(obj);\n";
  os << "  }\n";
}
 
/* Print a "declaration" for the given template class specialization.
 * In particular, print the class definition and the method declarations.
 *
 * The template parameters are the distinct variable names
 * in the instance kind.
 *
 * Each instance of the template class derives from the corresponding
 * plain C++ interface class.
 *
 * All (other) template classes are made friends of this template class
 * to allow them to call the private constructor taking an object
 * of the plain interface.
 *
 * Besides the constructors and methods that forward
 * to the corresponding methods in the plain C++ interface class,
 * some extra constructors are defined.
 * The default zero-argument constructor is useful for declaring
 * a variable that only gets assigned a value at a later stage.
 * The constructor taking an instance with more specialized
 * template arguments is useful for lifting the class hierarchy
 * of the template arguments to the template class.
 * The constructor taking an instance of the base class
 * is useful for (explicitly) constructing a template type
 * from a plain type.
 */
void template_cpp_generator::class_decl_printer::print_class(
  const specialization &instance) const
{
  const auto &class_name = instance.class_name();
  auto params = instance.kind.params();
 
  os << "\n";
 
  print_template(os, params);
 
  os << "struct ";
  print_bare_template_type(os, class_name, instance.kind);
  os << " : public " << instance.base_name() << " {\n";
 
  generator.print_friends(os);
  os << "\n";
 
  os << "  " << class_name << "() = default;\n";
  if (params.size() != 0)
    print_arg_subclass_constructor(instance, params);
  print_super_constructor(instance);
  method_decl_printer(instance, *this).print_all_methods();
 
  os << "};\n";
}
 
/* Helper class for printing the definitions of template class specializations.
 */
struct template_cpp_generator::class_impl_printer :
  public specialization_printer
{
  class_impl_printer(std::ostream &os,
        template_cpp_generator &generator) :
    specialization_printer(os, generator) {}
 
  virtual void print_class(const specialization &instance) const override;
};
 
/* Print a definition for the given template class specialization.
 *
 * In particular, print definitions
 * for the constructors and methods that forward
 * to the corresponding methods in the plain C++ interface class.
 * The extra constructors declared in the class definition
 * are defined inline.
 */
void template_cpp_generator::class_impl_printer::print_class(
  const specialization &instance) const
{
  method_impl_printer(instance, *this).print_all_methods();
}
 
/* Generate a templated cpp interface
 * based on the extracted types and functions.
 *
 * First print forward declarations for all template classes,
 * then the declarations of the classes, and at the end all
 * method implementations.
 */
void template_cpp_generator::generate()
{
  ostream &os = std::cout;
 
  os << "\n";
 
  print_forward_declarations(os);
  class_decl_printer(os, *this).print_classes();
  class_impl_printer(os, *this).print_classes();
}