/******************************************************************************
 * Top contributors (to current version):
 *   Abdalrhman Mohamed, Mudathir Mohamed, Aina Niemetz
 *
 * 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.
 * ****************************************************************************
 *
 * A simple demonstration of the Sygus API.
 *
 * A simple demonstration of how to use the Sygus API to synthesize max and min
 * functions. Here is the same problem written in Sygus V2 format:
 *
 * (set-logic LIA)
 *
 * (synth-fun max ((x Int) (y Int)) Int
 *   ((Start Int) (StartBool Bool))
 *   ((Start Int (0 1 x y
 *                (+ Start Start)
 *                (- Start Start)
 *                (ite StartBool Start Start)))
 *    (StartBool Bool ((and StartBool StartBool)
 *                     (not StartBool)
 *                     (<= Start Start)))))
 *
 * (synth-fun min ((x Int) (y Int)) Int)
 *
 * (declare-var x Int)
 * (declare-var y Int)
 *
 * (constraint (>= (max x y) x))
 * (constraint (>= (max x y) y))
 * (constraint (or (= x (max x y))
 *                 (= y (max x y))))
 * (constraint (= (+ (max x y) (min x y))
 *                (+ x y)))
 *
 * (check-synth)
 *
 * The printed output for this example should be equivalent to:
 * (
 *   (define-fun max ((x Int) (y Int)) Int (ite (<= x y) y x))
 *   (define-fun min ((x Int) (y Int)) Int (ite (<= x y) x y))
 * )
 */

import static io.github.cvc5.api.Kind.*;

import io.github.cvc5.api.*;

public class SygusFun
{
  public static void main(String args[]) throws CVC5ApiException
  {
    try (Solver slv = new Solver())
    {
      // required options
      slv.setOption("sygus", "true");
      slv.setOption("incremental", "false");

      // set the logic
      slv.setLogic("LIA");

      Sort integer = slv.getIntegerSort();
      Sort bool = slv.getBooleanSort();

      // declare input variables for the functions-to-synthesize
      Term x = slv.mkVar(integer, "x");
      Term y = slv.mkVar(integer, "y");

      // declare the grammar non-terminals
      Term start = slv.mkVar(integer, "Start");
      Term start_bool = slv.mkVar(bool, "StartBool");

      // define the rules
      Term zero = slv.mkInteger(0);
      Term one = slv.mkInteger(1);

      Term plus = slv.mkTerm(ADD, start, start);
      Term minus = slv.mkTerm(SUB, start, start);
      Term ite = slv.mkTerm(ITE, start_bool, start, start);

      Term And = slv.mkTerm(AND, start_bool, start_bool);
      Term Not = slv.mkTerm(NOT, start_bool);
      Term leq = slv.mkTerm(LEQ, start, start);

      // create the grammar object
      Grammar g = slv.mkSygusGrammar(new Term[] {x, y}, new Term[] {start, start_bool});

      // bind each non-terminal to its rules
      g.addRules(start, new Term[] {zero, one, x, y, plus, minus, ite});
      g.addRules(start_bool, new Term[] {And, Not, leq});

      // declare the functions-to-synthesize. Optionally, provide the grammar
      // constraints
      Term max = slv.synthFun("max", new Term[] {x, y}, integer, g);
      Term min = slv.synthFun("min", new Term[] {x, y}, integer);

      // declare universal variables.
      Term varX = slv.declareSygusVar(integer, "x");
      Term varY = slv.declareSygusVar(integer, "y");

      Term max_x_y = slv.mkTerm(APPLY_UF, max, varX, varY);
      Term min_x_y = slv.mkTerm(APPLY_UF, min, varX, varY);

      // add semantic constraints
      // (constraint (>= (max x y) x))
      slv.addSygusConstraint(slv.mkTerm(GEQ, max_x_y, varX));

      // (constraint (>= (max x y) y))
      slv.addSygusConstraint(slv.mkTerm(GEQ, max_x_y, varY));

      // (constraint (or (= x (max x y))
      //                 (= y (max x y))))
      slv.addSygusConstraint(
          slv.mkTerm(OR, slv.mkTerm(EQUAL, max_x_y, varX), slv.mkTerm(EQUAL, max_x_y, varY)));

      // (constraint (= (+ (max x y) (min x y))
      //                (+ x y)))
      slv.addSygusConstraint(
          slv.mkTerm(EQUAL, slv.mkTerm(ADD, max_x_y, min_x_y), slv.mkTerm(ADD, varX, varY)));

      // print solutions if available
      if (slv.checkSynth().isUnsat())
      {
        // Output should be equivalent to:
        // (
        //   (define-fun max ((x Int) (y Int)) Int (ite (<= x y) y x))
        //   (define-fun min ((x Int) (y Int)) Int (ite (<= x y) x y))
        // )
        Term[] terms = new Term[] {max, min};
        Utils.printSynthSolutions(terms, slv.getSynthSolutions(terms));
      }
    }
  }
}