/*
      Copyright 2015 Atlassian
   
      Licensed under the Apache License, Version 2.0 (the "License");
      you may not use this file except in compliance with the License.
      You may obtain a copy of the License at
   
          http://www.apache.org/licenses/LICENSE-2.0
   
     Unless required by applicable law or agreed to in writing, software
     distributed under the License is distributed on an "AS IS" BASIS,
     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     See the License for the specific language governing permissions and
     limitations under the License.
   */
  
  package io.atlassian.fugue;
  
  import static io.atlassian.fugue.Either.left;
  import static io.atlassian.fugue.Either.right;
  import static io.atlassian.fugue.Iterables.concat;
  import static io.atlassian.fugue.Iterables.drop;
  import static io.atlassian.fugue.Iterables.first;
  import static io.atlassian.fugue.Iterables.join;
  import static io.atlassian.fugue.Iterables.map;
  import static io.atlassian.fugue.Option.none;
  import static io.atlassian.fugue.Option.some;
  import static io.atlassian.fugue.Options.filterNone;
  import static io.atlassian.fugue.Unit.Unit;
  import static java.util.Collections.emptyList;
  
  import java.math.BigInteger;
  import java.util.ArrayList;
  import java.util.List;
  import java.util.function.Function;
  
  /**
   * {@link io.atlassian.fugue.Monoid} instances.
   *
   * @see Semigroups
   * @since 3.0
   */
  public final class Monoids {
  
    /**
     * A monoid that adds integers.
     */
    public static final Monoid<Integer> intAddition = new Monoid<Integer>() {
      @Override public Integer append(final Integer i1, final Integer i2) {
        return i1 + i2;
      }
  
      @Override public Integer zero() {
        return 0;
      }
  
      @Override public Integer multiply(final int n, final Integer i) {
        return n <= 0 ? 0 : n * i;
      }
    };
  
    /**
     * A monoid that multiplies integers.
     */
    public static final Monoid<Integer> intMultiplication = new Monoid<Integer>() {
      @Override public Integer append(final Integer i1, final Integer i2) {
        return i1 * i2;
      }
  
      @Override public Integer zero() {
        return 1;
      }
    };
  
    /**
     * A monoid that adds big integers.
     */
    public static final Monoid<BigInteger> bigintAddition = new Monoid<BigInteger>() {
      @Override public BigInteger append(final BigInteger a1, final BigInteger a2) {
        return a1.add(a2);
      }
  
      @Override public BigInteger zero() {
        return BigInteger.ZERO;
      }
  
      @Override public BigInteger multiply(final int n, final BigInteger b) {
        return n <= 0 ? BigInteger.ZERO : b.multiply(BigInteger.valueOf(n));
      }
    };
  
    /**
     * A monoid that multiplies big integers.
     */
    public static final Monoid<BigInteger> bigintMultiplication = new Monoid<BigInteger>() {
      @Override public BigInteger append(final BigInteger a1, final BigInteger a2) {
        return a1.multiply(a2);
      }
  
     @Override public BigInteger zero() {
       return BigInteger.ONE;
     }
 
     @Override public BigInteger multiply(final int n, final BigInteger b) {
       return n <= 0 ? BigInteger.ONE : b.pow(n);
     }
   };
 
   /**
    * A monoid that adds longs.
    */
   public static final Monoid<Long> longAddition = new Monoid<Long>() {
     @Override public Long append(final Long a1, final Long a2) {
       return a1 + a2;
     }
 
     @Override public Long zero() {
       return 0L;
     }
 
     @Override public Long multiply(final int n, final Long l) {
       return n <= 0 ? 0L : l * n;
     }
   };
 
   /**
    * A monoid that multiplies longs.
    */
   public static final Monoid<Long> longMultiplication = new Monoid<Long>() {
     @Override public Long append(final Long a1, final Long a2) {
       return a1 * a2;
     }
 
     @Override public Long zero() {
       return 1L;
     }
   };
 
   /**
    * A monoid that ORs booleans.
    */
   public static final Monoid<Boolean> disjunction = new Monoid<Boolean>() {
     @Override public Boolean append(final Boolean a1, final Boolean a2) {
       return a1 || a2;
     }
 
     @Override public Boolean zero() {
       return false;
     }
 
     @Override public Boolean sum(final Iterable<Boolean> bs) {
       return Iterables.filter(bs, b -> b).iterator().hasNext();
     }
 
     @Override public Boolean multiply(final int n, final Boolean b) {
       return n <= 0 ? false : b;
     }
   };
 
   /**
    * A monoid that XORs booleans.
    */
   public static final Monoid<Boolean> exclusiveDisjunction = new Monoid<Boolean>() {
     @Override public Boolean append(final Boolean a1, final Boolean a2) {
       return (a1 ^ a2);
     }
 
     @Override public Boolean zero() {
       return false;
     }
 
     @Override public Boolean multiply(final int n, final Boolean b) {
       return b && (n == 1);
     }
   };
 
   /**
    * A monoid that ANDs booleans.
    */
   public static final Monoid<Boolean> conjunction = new Monoid<Boolean>() {
     @Override public Boolean append(final Boolean a1, final Boolean a2) {
       return a1 && a2;
     }
 
     @Override public Boolean zero() {
       return true;
     }
 
     @Override public Boolean sum(final Iterable<Boolean> bs) {
       return !Iterables.filter(bs, b -> !b).iterator().hasNext();
     }
   };
 
   /**
    * A monoid that appends strings.
    */
   public static final Monoid<String> string = new Monoid<String>() {
     @Override public String append(final String a1, final String a2) {
       return a1.concat(a2);
     }
 
     @Override public String zero() {
       return "";
     }
 
     @Override public String sum(final Iterable<String> ss) {
       final StringBuilder sb = new StringBuilder();
       for (final String s : ss) {
         sb.append(s);
       }
       return sb.toString();
     }
   };
 
   /**
    * A monoid for the Unit value.
    */
   public static final Monoid<Unit> unit = new Monoid<Unit>() {
     @Override public Unit append(final Unit a1, final Unit a2) {
       return Unit();
     }
 
     @Override public Unit zero() {
       return Unit();
     }
 
     @Override public Unit multiply(final int n, final Unit unit) {
       return Unit();
     }
 
     @Override public Unit multiply1p(final int n, final Unit unit) {
       return Unit();
     }
   };
 
   private Monoids() {}
 
   /**
    * A monoid for functions.
    *
    * @param <A> input type
    * @param <B> composable output type
    * @param mb The monoid for the function codomain.
    * @return A monoid for functions.
    */
   public static <A, B> Monoid<Function<A, B>> function(final Monoid<B> mb) {
     return new Monoid<Function<A, B>>() {
       @Override public Function<A, B> append(final Function<A, B> a1, final Function<A, B> a2) {
         return a -> mb.append(a1.apply(a), a2.apply(a));
       }
 
       @Override public Function<A, B> zero() {
         return a -> mb.zero();
       }
 
       @Override public Function<A, B> sum(final Iterable<Function<A, B>> fs) {
         return a -> mb.sum(map(fs, Functions.<A, B> apply(a)));
       }
 
       @Override public Function<A, B> multiply(final int n, final Function<A, B> f) {
         return a -> mb.multiply(n, f.apply(a));
       }
     };
   }
 
   /**
    * A monoid for lists.
    *
    * @param <A> internal type
    * @return A monoid for lists.
    */
   public static <A> Monoid<List<A>> list() {
     return new Monoid<List<A>>() {
       @Override public List<A> append(final List<A> l1, final List<A> l2) {
         final List<A> sumList;
         if (l1.isEmpty()) {
           sumList = l2;
 
         } else if (l2.isEmpty()) {
           sumList = l1;
 
         } else {
           sumList = new ArrayList<>(l1.size() + l2.size());
           sumList.addAll(l1);
           sumList.addAll(l2);
         }
         return sumList;
       }
 
       @Override public List<A> zero() {
         return emptyList();
       }
     };
   }
 
   /**
    * A monoid for iterables.
    *
    * @param <A> internal type
    * @return A monoid for iterables.
    */
   public static <A> Monoid<Iterable<A>> iterable() {
     return new Monoid<Iterable<A>>() {
       @Override public Iterable<A> append(final Iterable<A> a1, final Iterable<A> a2) {
         return concat(a1, a2);
       }
 
       @Override public Iterable<A> zero() {
         return emptyList();
       }
 
       @Override public Iterable<A> sum(final Iterable<Iterable<A>> iterable) {
         return join(iterable);
       }
     };
   }
 
   /**
    * A monoid for options (that take the first available value).
    *
    * @param <A> internal type
    * @return A monoid for options (that take the first available value).
    */
   public static <A> Monoid<Option<A>> firstOption() {
     return new Monoid<Option<A>>() {
       @Override public Option<A> append(final Option<A> a1, final Option<A> a2) {
         return a1.isDefined() ? a1 : a2;
       }
 
       @Override public Option<A> zero() {
         return none();
       }
 
       @Override public Option<A> sum(final Iterable<Option<A>> os) {
         return first(filterNone(os)).getOrElse(none());
       }
     };
   }
 
   /**
    * A monoid for options that take the last available value.
    *
    * @param <A> internal type
    * @return A monoid for options that take the last available value.
    */
   public static <A> Monoid<Option<A>> lastOption() {
     return new Monoid<Option<A>>() {
       @Override public Option<A> append(final Option<A> a1, final Option<A> a2) {
         return a2.isDefined() ? a2 : a1;
       }
 
       @Override public Option<A> zero() {
         return none();
       }
     };
   }
 
   /**
    * A monoid for options that combine inner value with a semigroup.
    *
    * @param <A> internal type
    * @return A monoid for options that combine inner value with a semigroup.
    * @param semigroup a {@link io.atlassian.fugue.Semigroup} object.
    */
   public static <A> Monoid<Option<A>> option(final Semigroup<A> semigroup) {
     return new Monoid<Option<A>>() {
       @Override public Option<A> append(final Option<A> o1, final Option<A> o2) {
         return o1.fold(() -> o2, a1 -> o2.fold(() -> o1, a2 -> some(semigroup.append(a1, a2))));
       }
 
       @Override public Option<A> zero() {
         return none();
       }
 
       @Override public Option<A> sum(final Iterable<Option<A>> os) {
         final Iterable<A> memoized = Iterables.memoize(Options.flatten(os));
         return first(memoized).fold(Option::<A> none, a -> some(semigroup.sumNonEmpty(a, drop(1, memoized))));
       }
 
       @Override public Option<A> multiply(final int n, final Option<A> as) {
         return n <= 0 ? none() : as.fold(Option::<A> none, a -> some(semigroup.multiply1p(n - 1, a)));
       }
     };
   }
 
   /**
    * A monoid Sums up values inside either
    * {@link io.atlassian.fugue.Semigroups#either}. Monoid of right values
    * provide the identity element of the resulting monoid.
    *
    * @param <L> desired left type
    * @param <R> desired right type
    * @param lS semigroup for left values
    * @param rM monoid for right values.
    * @return A monoid Sums up values inside either.
    */
   public static <L, R> Monoid<Either<L, R>> either(final Semigroup<L> lS, final Monoid<R> rM) {
     final Either<L, R> zero = right(rM.zero());
     return new Monoid<Either<L, R>>() {
 
       @Override public Either<L, R> append(final Either<L, R> e1, final Either<L, R> e2) {
         return e1.<Either<L, R>> fold(l1 -> e2.<Either<L, R>> fold(l2 -> left(lS.append(l1, l2)), r2 -> e1),
           r1 -> e2.<Either<L, R>> fold(l2 -> e2, r2 -> right(rM.append(r1, r2))));
       }
 
       @Override public Either<L, R> zero() {
         return zero;
       }
     };
   }
 
 }