/******************************************************************************

 * Top contributors (to current version):

 *   Andrew Reynolds, Andres Noetzli, Mathias Preiner

 *

 * This file is part of the cvc5 project.

 *

 * Copyright (c) 2009-2021 by the authors listed in the file AUTHORS

 * in the top-level source directory and their institutional affiliations.

 * All rights reserved.  See the file COPYING in the top-level source

 * directory for licensing information.

 * ****************************************************************************

 *

 * Rewriter for the theory of (co)inductive datatypes.

 */

#include "cvc5_private.h"

#ifndef CVC5__THEORY__DATATYPES__DATATYPES_REWRITER_H

#define CVC5__THEORY__DATATYPES__DATATYPES_REWRITER_H

#include "theory/theory_rewriter.h"

namespace cvc5 {

namespace theory {

namespace datatypes {

/**

 * The rewriter for datatypes. An invariant of the rewriter is that

 * postRewrite/preRewrite should not depend on the options, in particular,

 * they should not depend on whether shared selectors are enabled. Thus,

 * they should not use DTypeConstructor::getSelectorInternal. Instead,

 * the conversion from external to internal selectors is done in

 * expandDefinition. This invariant ensures that the rewritten form of a node

 * does not mix multiple option settings, which would lead to e.g. shared

 * selectors being used in an SmtEngine instance where they are disabled.

 */

{

 public:

  RewriteResponse postRewrite(TNode in) override;

  RewriteResponse preRewrite(TNode in) override;

  /** normalize codatatype constant

   *

   * This returns the normal form of the codatatype constant n. This runs a

   * DFA minimization algorithm based on the private functions below.

   *

   * In particular, we first call collectRefs to setup initial information

   * about what terms occur in n. Then, we run a DFA minimization algorithm to

   * partition these subterms in equivalence classes. Finally, we call

   * normalizeCodatatypeConstantEqc to construct the normalized codatatype

   * constant that is equivalent to n.

   */

  static Node normalizeCodatatypeConstant(Node n);

  /** normalize constant

   *

   * This method returns the normal form of n, which calls the above function

   * on all top-level codatatype subterms of n.

   */

  static Node normalizeConstant(Node n);

  /**

   * Expand an APPLY_SELECTOR term n, return its expanded form. If n is

   *   (APPLY_SELECTOR selC x)

   * its expanded form is

   *   (ITE (APPLY_TESTER is-C x)

   *     (APPLY_SELECTOR_TOTAL selC' x)

   *     (f x))

   * where f is a skolem function with id SELECTOR_WRONG, and selC' is the

   * internal selector function for selC (possibly a shared selector).

   */

  static Node expandApplySelector(Node n);

  /** expand defintions */

  TrustNode expandDefinition(Node n) override;

 private:

  /** rewrite constructor term in */

  static RewriteResponse rewriteConstructor(TNode in);

  /** rewrite selector term in */

  static RewriteResponse rewriteSelector(TNode in);

  /** rewrite tester term in */

  static RewriteResponse rewriteTester(TNode in);

  /** rewrite updater term in */

  static RewriteResponse rewriteUpdater(TNode in);

  /** collect references

   *

   * This function, given as input a codatatype term n, collects the necessary

   * information for constructing a (canonical) codatatype constant that is

   * equivalent to n if one exists, or null otherwise.

   *

   * In particular it returns a term ret such that all non-codatatype datatype

   * subterms of n are replaced by a constant that is equal to them via a

   * (mutually) recursive call to normalizeConstant above. Additionally, this

   * function replaces references to mu-binders with fresh variables.

   * In detail, mu-terms are represented by uninterpreted constants of datatype

   * type that carry their Debruijn index.

   *

   * Consider the example of a codatatype representing a stream of integers:

   *   Stream := cons( head : Int, tail : Stream )

   * The stream 1,0,1,0,1,0... when written in mu-notation is the term:

   *   mu x. cons( 1, mu y. cons( 0, x ) )

   * This is represented in cvc5 by the Node:

   *   cons( 1, cons( 0, c[1] ) )

   * where c[1] is a uninterpreted constant datatype with Debruijn index 1,

   * indicating that c[1] is nested underneath 1 level on the path to the

   * term which it binds. On the other hand, the stream 1,0,0,0,0,... is

   * represented by the codatatype term:

   *   cons( 1, cons( 0, c[0] ) )

   *

   * Subterms that are references to mu-binders in n are replaced by a new

   * variable. If n contains any subterm that is a reference to a mu-binder not

   * bound in n, then we return null. For example we return null when n is:

   *   cons( 1, cons( 0, c[2] ) )

   * since c[2] is not bound by this codatatype term.

   *

   * All valid references to mu-binders are replaced by a variable that is

   * unique for the term it references. For example, for the infinite tree

   * codatatype: Tree : node( data : Int, left : Tree, right : Tree ) If n is

   * the term: node( 0, c[0], node( 1, c[0], c[1] ) ) then the return value ret

   * of this function is: node( 0, x, node( 1, y, x ) ) where x refers to the

   * root of the term and y refers to the right tree of the root.

   *

   * The argument sk stores the current set of node that we are traversing

   * beneath. The argument rf_pending stores, for each node that we are

   * traversing beneath either null or the free variable that we are using to

   * refer to its mu-binder. The remaining arguments store information that is

   * relevant when performing normalization of n using the value of ret:

   *

   * rf : maps subterms of n to the corresponding term in ret for all subterms

   * where the corresponding term in ret is different.

   * terms : stores all subterms of ret.

   * cdts : for each term t in terms, stores whether t is a codatatype.

   */

  static Node collectRef(Node n,

                         std::vector<Node>& sk,

                         std::map<Node, Node>& rf,

                         std::vector<Node>& rf_pending,

                         std::vector<Node>& terms,

                         std::map<Node, bool>& cdts);

  /** normalize codatatype constant eqc

   *

   * This recursive function returns a codatatype constant that is equivalent to

   * n based on a pre-computed partition of the subterms of n into equivalence

   * classes, as stored in the mapping eqc, which maps the subterms of n to

   * equivalence class ids. The arguments eqc_stack and depth store information

   * about the traversal in a term we have recursed, where

   *

   * eqc_stack : maps the depth of each term we have traversed to its

   * equivalence class id. depth : the number of levels which we have traversed.

   */

  static Node normalizeCodatatypeConstantEqc(Node n,

                                             std::map<int, int>& eqc_stack,

                                             std::map<Node, int>& eqc,

                                             int depth);

  /** replace debruijn

   *

   * This function, given codatatype term n, returns a node

   * where all subterms of n that have Debruijn indices that refer to a

   * term of input depth are replaced by orig. For example, for the infinite

   * Tree datatype, replaceDebruijn( node( 0, c[0], node( 1, c[0], c[1] ) ), t,

   * Tree, 0 ) returns node( 0, t, node( 1, c[0], t ) ).

   */

  static Node replaceDebruijn(Node n,

                              Node orig,

                              TypeNode orig_tn,

                              unsigned depth);

}; /* class DatatypesRewriter */

}  // namespace datatypes

}  // namespace theory

}  // namespace cvc5

#endif /* CVC5__THEORY__DATATYPES__DATATYPES_REWRITER_H */