lib/core/collection: add `CachedIterator` to factorize the logic of iterators with...

[nit.git] / lib / core / collection / abstract_collection.nit

# This file is part of NIT ( http://www.nitlanguage.org ).
#
# Copyright 2004-2008 Jean Privat <jean@pryen.org>
#
# This file is free software, which comes along with NIT.  This software is
# distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
# without  even  the implied warranty of  MERCHANTABILITY or  FITNESS FOR A
# PARTICULAR PURPOSE.  You can modify it is you want,  provided this header
# is kept unaltered, and a notification of the changes is added.
# You  are  allowed  to  redistribute it and sell it, alone or is a part of
# another product.

# Abstract collection classes and services.
#
# TODO specify the behavior on iterators when collections are modified.
module abstract_collection

import kernel

# The root of the collection hierarchy.
#
# Collections modelize finite groups of objects, called elements.
#
# The specific behavior and representation of collections is determined
# by the subclasses of the hierarchy.
#
# The main service of Collection is to provide a stable `iterator`
# method usable to retrieve all the elements of the collection.
#
# Additional services are provided.
# For an implementation point of view, Collection provide a basic
# implementation of these services using the `iterator` method.
# Subclasses often provide a more efficient implementation.
#
# Because of the `iterator` method, Collections instances can use
# the `for` control structure.
#
# ~~~nitish
# var x: Collection[U]
# # ...
# for u in x do
#       # u is a U
#       # ...
# end
# ~~~
#
# that is equivalent with the following:
#
# ~~~nitish
# var x: Collection[U]
# # ...
# var i = x.iterator
# while i.is_ok do
#     var u = i.item # u is a U
#     # ...
#     i.next
# end
# ~~~
interface Collection[E]
        # Get a new iterator on the collection.
        fun iterator: Iterator[E] is abstract

        # Is there no item in the collection?
        #
        #     assert [1,2,3].is_empty  == false
        #     assert [1..1[.is_empty   == true
        fun is_empty: Bool do return length == 0

        # Alias for `not is_empty`.
        #
        # Some people prefer to have conditions grammatically easier to read.
        #
        #     assert [1,2,3].not_empty  == true
        #     assert [1..1[.not_empty   == false
        fun not_empty: Bool do return not self.is_empty

        # Number of items in the collection.
        #
        #     assert [10,20,30].length == 3
        #     assert [20..30[.length   == 10
        fun length: Int
        do
                var nb = 0
                for i in self do nb += 1
                return nb
        end

        # Is `item` in the collection ?
        # Comparisons are done with ==
        #
        #     assert [1,2,3].has(2)    == true
        #     assert [1,2,3].has(9)    == false
        #     assert [1..5[.has(2)     == true
        #     assert [1..5[.has(9)     == false
        fun has(item: nullable Object): Bool
        do
                for i in self do if i == item then return true
                return false
        end

        # Is the collection contain only `item`?
        # Comparisons are done with ==
        # Return true if the collection is empty.
        #
        #     assert [1,1,1].has_only(1)         == true
        #     assert [1,2,3].has_only(1)         == false
        #     assert [1..1].has_only(1)          == true
        #     assert [1..3].has_only(1)          == false
        #     assert [3..3[.has_only(1)          == true # empty collection
        #
        # ENSURE `is_empty implies result == true`
        fun has_only(item: nullable Object): Bool
        do
                for i in self do if i != item then return false
                return true
        end

        # How many occurrences of `item` are in the collection?
        # Comparisons are done with ==
        #
        #     assert [10,20,10].count(10)         == 2
        fun count(item: nullable Object): Int
        do
                var nb = 0
                for i in self do if i == item then nb += 1
                return nb
        end

        # Return the first item of the collection
        #
        #     assert [1,2,3].first                == 1
        fun first: E
        do
                assert length > 0
                return iterator.item
        end

        # Does the collection contain at least each element of `other`?
        #
        #     assert [1,3,4,2].has_all([1..2])    == true
        #     assert [1,3,4,2].has_all([1..5])    == false
        #
        # Repeated elements in the collections are not considered.
        #
        #     assert [1,1,1].has_all([1])         == true
        #     assert [1..5].has_all([1,1,1])      == true
        #
        # Note that the default implementation is general and correct for any lawful Collections.
        # It is memory-efficient but relies on `has` so may be CPU-inefficient for some kind of collections.
        fun has_all(other: Collection[nullable Object]): Bool
        do
                if is_same_instance(other) then return true
                var ol = other.length
                var  l = length
                if ol == 0 then return true
                if l == 0 then return false
                if ol == 1 then return has(other.first)
                for x in other do if not has(x) then return false
                return true
        end

        # Does the collection contain exactly all the elements of `other`?
        #
        # The same elements must be present in both `self` and `other`,
        # but the order of the elements in the collections are not considered.
        #
        #     assert [1..3].has_exactly([3,1,2]) == true  # the same elements
        #     assert [1..3].has_exactly([3,1])   == false # 2 is not in the array
        #     assert [1..2].has_exactly([3,1,2]) == false # 3 is not in the range
        #
        # Repeated elements must be present in both collections in the same amount.
        # So basically it is a multi-set comparison.
        #
        #     assert [1,2,3,2].has_exactly([1,2,2,3]) == true  # the same elements
        #     assert [1,2,3,2].has_exactly([1,2,3])   == false # more 2 in the first array
        #     assert [1,2,3].has_exactly([1,2,2,3])   == false # more 2 in the second array
        #
        # Note that the default implementation is general and correct for any lawful Collections.
        # It is memory-efficient but relies on `count` so may be CPU-inefficient for some kind of collections.
        fun has_exactly(other: Collection[nullable Object]): Bool
        do
                if length != other.length then return false
                for e in self do if self.count(e) != other.count(e) then return false
                return true
        end

        # Does the collection contain at least one element of `other`?
        #
        #     assert [1,3,4,2].has_any([1..10])    == true
        #     assert [1,3,4,2].has_any([5..10])    == false
        #
        # Note that the default implementation is general and correct for any lawful Collections.
        # It is memory-efficient but relies on `has` so may be CPU-inefficient for some kind of collections.
        fun has_any(other: Collection[nullable Object]): Bool
        do
                for o in other do
                        if has(o) then return true
                end
                return false
        end
end

# Iterators generate a series of elements, one at a time.
#
# They are mainly used with collections and obtained from `Collection::iterator`.
interface Iterator[E]
        # The current item.
        # Require `is_ok`.
        fun item: E is abstract

        # Jump to the next item.
        # Require `is_ok`.
        fun next is abstract

        # Jump to the next item `step` times.
        #
        # ~~~
        # var i = [11, 22, 33, 44].iterator
        # assert i.item == 11
        # i.next_by 2
        # assert i.item == 33
        # ~~~
        #
        # `next_by` should be used instead of looping on `next` because is takes care
        # of stopping if the end of iteration is reached prematurely whereas a loop of
        # `next` will abort because of the precondition on `is_ok`.
        #
        # ~~~
        # i.next_by 100
        # assert not i.is_ok
        # ~~~
        #
        # If `step` is negative, this method aborts.
        # But specific subclasses can change this and do something more meaningful instead.
        #
        # Require `is_ok`
        fun next_by(step: Int)
        do
                assert step >= 0
                while is_ok and step > 0 do
                        next
                        step -= 1
                end
        end

        # Is there a current item ?
        fun is_ok: Bool is abstract

        # Iterate over `self`
        fun iterator: Iterator[E] do return self

        # Pre-iteration hook.
        #
        # Used to inform `self` that the iteration is starting.
        # Specific iterators can use this to prepare some resources.
        #
        # Is automatically invoked at the beginning of `for` structures.
        #
        # Do nothing by default.
        fun start do end

        # Post-iteration hook.
        #
        # Used to inform `self` that the iteration is over.
        # Specific iterators can use this to free some resources.
        #
        # Is automatically invoked at the end of `for` structures.
        #
        # Do nothing by default.
        fun finish do end

        # A decorator around `self` that advance self a given number of steps instead of one.
        #
        # ~~~
        # var i = [11, 22, 33, 44, 55].iterator
        # var i2 = i.to_step(2)
        #
        # assert i2.item == 11
        # i2.next
        # assert i2.item == 33
        #
        # assert i.item == 33
        # ~~~
        fun to_step(step: Int): Iterator[E] do return new StepIterator[E](self, step)
end

# A basic helper class to specialize specific Iterator decorators
abstract class IteratorDecorator[E]
        super Iterator[E]

        # The underling iterator
        protected var real: Iterator[E]

        redef fun is_ok do return real.is_ok
        redef fun item do return real.item
        redef fun finish do real.finish
        redef fun next do real.next
        redef fun next_by(step) do real.next_by(step)
end

# A decorator that advance a given number of steps
private class StepIterator[E]
        super IteratorDecorator[E]
        var step: Int

        redef fun next do real.next_by(step)
        redef fun next_by(step) do real.next_by(step * self.step)
end

# An iterator that lazyly cache the current item.
#
# This class can be used as an helper to build simple iterator with a single and simplier `next_item` method.
# The only constraint is that `next_item` returns null on the last item, so `null` cannot be a valid element.
abstract class CachedIterator[E: Object]
        super Iterator[E]

        # Get the next item if any.
        # Returns null if there is no next item.
        fun next_item: nullable E is abstract

        # The last item effectively read.
        # `null` if on start, after a next of if no more items are available.
        protected var cache: nullable E = null

        # The current item, if any.
        # If not, the cache is effectively filled (with `next_item`).
        # Return `null` iff there is no more elements.
        protected fun current_item: nullable E
        do
                var cache = self.cache
                if cache != null then return cache
                cache = next_item
                self.cache = cache
                return cache
        end

        redef fun item do return current_item.as(not null)

        redef fun is_ok do return current_item != null

        redef fun next do
                # If needed, fill the cache (an consume the current element)
                current_item
                # Empty the cache (so the next element will be read)
                cache = null
        end
end

# A collection that contains only one item.
#
# Used to pass arguments by reference.
#
# Also used when one want to give a single element when a full
# collection is expected
class Ref[E]
        super Collection[E]

        redef fun first do return item

        redef fun is_empty do return false

        redef fun length do return 1

        redef fun has(an_item) do return item == an_item

        redef fun has_only(an_item) do return item == an_item

        redef fun count(an_item)
        do
                if item == an_item then
                        return 1
                else
                        return 0
                end
        end

        redef fun iterator do return new RefIterator[E](self)

        # The stored item
        var item: E is writable
end

# This iterator is quite stupid since it is used for only one item.
private class RefIterator[E]
        super Iterator[E]
        redef fun item do return _container.item

        redef fun next do is_ok = false

        redef var is_ok = true

        var container: Ref[E]
end

# Items can be removed from this collection
interface RemovableCollection[E]
        super Collection[E]

        # Remove all items
        #
        #     var a = [1,2,3]
        #     a.clear
        #     assert a.length == 0
        #
        # ENSURE `is_empty`
        fun clear is abstract

        # Remove an occurrence of `item`
        #
        #     var a = [1,2,3,1,2,3]
        #     a.remove 2
        #     assert a == [1,3,1,2,3]
        fun remove(item: nullable Object) is abstract

        # Remove all occurrences of `item`
        #
        #     var a = [1,2,3,1,2,3]
        #     a.remove_all 2
        #     assert a == [1,3,1,3]
        fun remove_all(item: nullable Object) do while has(item) do remove(item)
end

# Items can be added to these collections.
interface SimpleCollection[E]
        super RemovableCollection[E]

        # Add `item` to this collection.
        #
        #     var a = [1,2]
        #     a.add 3
        #     assert a.has(3)  == true
        #     assert a.has(10) == false
        #
        # Ensure col.has(item)
        fun add(item: E) is abstract

        # Add each item of `coll`.
        #
        #     var a = [1,2]
        #     a.add_all([3..5])
        #     assert a.has(4)  == true
        #     assert a.has(10) == false
        fun add_all(coll: Collection[E]) do for i in coll do add(i)
end

# Abstract sets.
#
# Set is a collection without duplicates (according to `==`)
#
#      var s: Set[String] = new ArraySet[String]
#      var a = "Hello"
#      var b = "Hel" + "lo"
#      # ...
#      s.add(a)
#      assert s.has(b)      ==  true
interface Set[E]
        super SimpleCollection[E]
        super Cloneable

        redef fun has_only(item)
        do
                var l = length
                if l == 1 then
                        return has(item)
                else if l == 0 then
                        return true
                else
                        return false
                end
        end

        # Only 0 or 1
        redef fun count(item)
        do
                if has(item) then
                        return 1
                else
                        return 0
                end
        end

        # Synonym of remove since there is only one item
        redef fun remove_all(item) do remove(item)

        # Equality is defined on set and means that each set contains the same elements
        redef fun ==(other)
        do
                if not other isa Set[nullable Object] then return false
                if other.length != length then return false
                return has_all(other)
        end

        # Because of the law between `==` and `hash`, `hash` is redefined to be the sum of the hash of the elements
        redef fun hash
        do
                # 23 is a magic number empirically determined to be not so bad.
                var res = 23 + length
                # Note: the order of the elements must not change the hash value.
                # So, unlike usual hash functions, the accumulator is not combined with itself.
                for e in self do
                        if e != null then res += e.hash
                end
                return res
        end

        # Returns the union of this set with the `other` set
        fun union(other: Set[E]): Set[E]
        do
                var nhs = new_set
                nhs.add_all self
                nhs.add_all other
                return nhs
        end

        # Returns the intersection of this set with the `other` set
        fun intersection(other: Set[E]): Set[E]
        do
                var nhs = new_set
                for v in self do if other.has(v) then nhs.add(v)
                return nhs
        end

        redef fun clone do return union(self)

        # Returns a new instance of `Set`.
        #
        # Depends on the subclass, mainly used for copy services
        # like `union` or `intersection`.
        protected fun new_set: Set[E] is abstract
end

# MapRead are abstract associative collections: `key` -> `item`.
interface MapRead[K, V]
        # Get the item at `key`
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x["four"] == 4
        #     # assert x["five"] #=> abort
        #
        # If the key is not in the map, `provide_default_value` is called (that aborts by default)
        # See `get_or_null` and `get_or_default` for safe variations.
        fun [](key: nullable Object): V is abstract

        # Get the item at `key` or null if `key` is not in the map.
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x.get_or_null("four") == 4
        #     assert x.get_or_null("five") == null
        #
        # Note: use `has_key` and `[]` if you need the distinction between a key associated with null, and no key.
        fun get_or_null(key: nullable Object): nullable V
        do
                if has_key(key) then return self[key]
                return null
        end

        # Get the item at `key` or return `default` if not in map
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x.get_or_default("four", 40) == 4
        #     assert x.get_or_default("five", 50) == 50
        #
        fun get_or_default(key: nullable Object, default: V): V
        do
                if has_key(key) then return self[key]
                return default
        end

        # Is there an item associated with `key`?
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x.has_key("four") == true
        #     assert x.has_key("five") == false
        #
        # By default it is a synonymous to `keys.has` but could be redefined with a direct implementation.
        fun has_key(key: nullable Object): Bool do return self.keys.has(key)

        # Get a new iterator on the map.
        fun iterator: MapIterator[K, V] is abstract

        # Return the point of view of self on the values only.
        # Note that `self` and `values` are views on the same data;
        # therefore any modification of one is visible on the other.
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x.values.has(4) == true
        #     assert x.values.has(5) == false
        fun values: Collection[V] is abstract

        # Return the point of view of self on the keys only.
        # Note that `self` and `keys` are views on the same data;
        # therefore any modification of one is visible on the other.
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x.keys.has("four") == true
        #     assert x.keys.has("five") == false
        fun keys: Collection[K] is abstract

        # Is there no item in the collection?
        #
        #     var x = new HashMap[String, Int]
        #     assert x.is_empty  == true
        #     x["four"] = 4
        #     assert x.is_empty  == false
        fun is_empty: Bool is abstract

        # Alias for `not is_empty`.
        #
        # Some people prefer to have conditions grammatically easier to read.
        #
        #     var map = new HashMap[String, Int]
        #     assert map.not_empty == false
        #     map["one"] = 1
        #     assert map.not_empty == true
        fun not_empty: Bool do return not self.is_empty

        # Number of items in the collection.
        #
        #     var x = new HashMap[String, Int]
        #     assert x.length  == 0
        #     x["four"] = 4
        #     assert x.length  == 1
        #     x["five"] = 5
        #     assert x.length  == 2
        fun length: Int is abstract

        # Called by the underling implementation of `[]` to provide a default value when a `key` has no value
        # By default the behavior is to abort.
        #
        # Note: the value is returned *as is*, implementations may want to store the value in the map before returning it
        # @toimplement
        protected fun provide_default_value(key: nullable Object): V do abort

        # Does `self` and `other` have the same keys associated with the same values?
        #
        # ~~~
        # var a = new HashMap[String, Int]
        # var b = new ArrayMap[Object, Numeric]
        # assert a == b
        # a["one"] = 1
        # assert a != b
        # b["one"] = 1
        # assert a == b
        # b["one"] = 2
        # assert a != b
        # ~~~
        redef fun ==(other)
        do
                if not other isa MapRead[nullable Object, nullable Object] then return false
                if other.length != self.length then return false
                for k, v in self do
                        if not other.has_key(k) then return false
                        if other[k] != v then return false
                end
                return true
        end

        # A hashcode based on the hashcode of the keys and the values.
        #
        # ~~~
        # var a = new HashMap[String, Int]
        # var b = new ArrayMap[Object, Numeric]
        # a["one"] = 1
        # b["one"] = 1
        # assert a.hash == b.hash
        # ~~~
        redef fun hash
        do
                var res = length
                for k, v in self do
                        if k != null then res += k.hash * 7
                        if v != null then res += v.hash * 11
                end
                return res
        end
end

# Maps are associative collections: `key` -> `item`.
#
# The main operator over maps is [].
#
#     var map: Map[String, Int] = new ArrayMap[String, Int]
#     # ...
#     map["one"] = 1      # Associate 'one' to '1'
#     map["two"] = 2      # Associate 'two' to '2'
#     assert map["one"]             ==  1
#     assert map["two"]             ==  2
#
# Instances of maps can be used with the for structure
#
#     for key, value in map do
#         assert (key == "one" and value == 1) or (key == "two" and value == 2)
#     end
#
# The keys and values in the map can also be manipulated directly with the `keys` and `values` methods.
#
#     assert map.keys.has("one")    ==  true
#     assert map.keys.has("tree")   ==  false
#     assert map.values.has(1)      ==  true
#     assert map.values.has(3)      ==  false
#
interface Map[K, V]
        super MapRead[K, V]

        # Set the `value` at `key`.
        #
        # Values can then get retrieved with `[]`.
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     assert x["four"]   == 4
        #
        # If the key was associated with a value, this old value is discarded
        # and replaced with the new one.
        #
        #     x["four"] = 40
        #     assert x["four"]         == 40
        #     assert x.values.has(4)   == false
        #
        fun []=(key: K, value: V) is abstract

        # Add each (key,value) of `map` into `self`.
        # If a same key exists in `map` and `self`, then the value in self is discarded.
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     x["five"] = 5
        #     var y = new HashMap[String, Int]
        #     y["four"] = 40
        #     y["nine"] = 90
        #     x.add_all y
        #     assert x["four"]  == 40
        #     assert x["five"]  == 5
        #     assert x["nine"]  == 90
        fun add_all(map: MapRead[K, V])
        do
                var i = map.iterator
                while i.is_ok do
                        self[i.key] = i.item
                        i.next
                end
        end

        # Alias for `add_all`
        fun recover_with(map: MapRead[K, V]) is deprecated do add_all(map)

        # Remove all items
        #
        #     var x = new HashMap[String, Int]
        #     x["four"] = 4
        #     x.clear
        #     assert x.keys.has("four") == false
        #
        # ENSURE `is_empty`
        fun clear is abstract

        redef fun values: RemovableCollection[V] is abstract

        redef fun keys: RemovableCollection[K] is abstract
end

# Iterators for Map.
interface MapIterator[K, V]
        # The current item.
        # Require `is_ok`.
        fun item: V is abstract

        # The key of the current item.
        # Require `is_ok`.
        fun key: K is abstract

        # Jump to the next item.
        # Require `is_ok`.
        fun next is abstract

        # Is there a current item ?
        fun is_ok: Bool is abstract

        # Set a new `item` at `key`.
        #fun item=(item: E) is abstract

        # Pre-iteration hook.
        #
        # Used to inform `self` that the iteration is starting.
        # Specific iterators can use this to prepare some resources.
        #
        # Is automatically invoked at the beginning of `for` structures.
        #
        # Do nothing by default.
        fun start do end

        # Post-iteration hook.
        #
        # Used to inform `self` that the iteration is over.
        # Specific iterators can use this to free some resources.
        #
        # Is automatically invoked at the end of `for` structures.
        #
        # Do nothing by default.
        fun finish do end
end

# Iterator on a 'keys' point of view of a map
class MapKeysIterator[K, V]
        super Iterator[K]
        # The original iterator
        var original_iterator: MapIterator[K, V]

        redef fun is_ok do return self.original_iterator.is_ok
        redef fun next do self.original_iterator.next
        redef fun item do return self.original_iterator.key
end

# Iterator on a 'values' point of view of a map
class MapValuesIterator[K, V]
        super Iterator[V]
        # The original iterator
        var original_iterator: MapIterator[K, V]

        redef fun is_ok do return self.original_iterator.is_ok
        redef fun next do self.original_iterator.next
        redef fun item do return self.original_iterator.item
end

# Sequences are indexed collections.
# The first item is 0. The last is `length-1`.
#
# The order is the main caracteristic of sequence
# and all concrete implementation of sequences are basically interchangeable.
interface SequenceRead[E]
        super Collection[E]

        # Get the first item.
        # Is equivalent with `self[0]`.
        #
        #     var a = [1,2,3]
        #     assert a.first   == 1
        #
        # REQUIRE `not is_empty`
        redef fun first
        do
                assert not_empty: not is_empty
                return self[0]
        end

        # Return the index-th element of the sequence.
        # The first element is 0 and the last is `length-1`
        # If index is invalid, the program aborts
        #
        #     var a = [10,20,30]
        #     assert a[0]   == 10
        #     assert a[1]   == 20
        #     assert a[2]   == 30
        #
        # REQUIRE `index >= 0 and index < length`
        fun [](index: Int): E is abstract

        # Return the index-th element but wrap
        #
        # Whereas `self[]` requires the index to exists, the `modulo` accessor automatically
        # wraps overbound and underbouds indexes.
        #
        # ~~~
        # var a = [10,20,30]
        # assert a.modulo(1) == 20
        # assert a.modulo(3) == 10
        # assert a.modulo(-1) == 30
        # assert a.modulo(-10) == 30
        # ~~~
        #
        # REQUIRE `not_empty`
        # ENSURE `result == self[modulo_index(index)]`
        fun modulo(index: Int): E do return self[modulo_index(index)]

        # Returns the real index for a modulo index.
        #
        # ~~~
        # var a = [10,20,30]
        # assert a.modulo_index(1) == 1
        # assert a.modulo_index(3) == 0
        # assert a.modulo_index(-1) == 2
        # assert a.modulo_index(-10) == 2
        # ~~~
        #
        # REQUIRE `not_empty`
        fun modulo_index(index: Int): Int
        do
                var length = self.length
                if index >= 0 then
                        return index % length
                else
                        return length - (-1 - index) % length - 1
                end
        end

        # Try to get an element, return `null` if the `index` is invalid.
        #
        # ~~~
        # var a = [10,20,30]
        # assert a.get_or_null(1) == 20
        # assert a.get_or_null(3) == null
        # assert a.get_or_null(-1) == null
        # assert a.get_or_null(-10) == null
        # ~~~
        fun get_or_null(index: Int): nullable E
        do
                if index >= 0 and index < length then return self[index]
                return null
        end

        # Try to get an element, return `default` if the `index` is invalid.
        #
        # ~~~
        # var a = [10,20,30]
        # assert a.get_or_default(1, -1) == 20
        # assert a.get_or_default(3, -1) == -1
        # assert a.get_or_default(-1, -1) == -1
        # assert a.get_or_default(-10, -1) == -1
        # ~~~
        fun get_or_default(index: Int, default: E): E
        do
                if index >= 0 and index < length then return self[index]
                return default
        end

        # Get the last item.
        # Is equivalent with `self[length-1]`.
        #
        #     var a = [1,2,3]
        #     assert a.last   == 3
        #
        # REQUIRE `not is_empty`
        fun last: E
        do
                assert not_empty: not is_empty
                return self[length-1]
        end

        # The index of the first occurrence of `item`.
        # Return -1 if `item` is not found.
        # Comparison is done with `==`.
        #
        #     var a = [10,20,30,10,20,30]
        #     assert a.index_of(20)   == 1
        #     assert a.index_of(40)   == -1
        fun index_of(item: nullable Object): Int do return index_of_from(item, 0)

        # The index of the last occurrence of `item`.
        # Return -1 if `item` is not found.
        # Comparison is done with `==`.
        #
        #     var a = [10,20,30,10,20,30]
        #     assert a.last_index_of(20)   == 4
        #     assert a.last_index_of(40)   == -1
        fun last_index_of(item: nullable Object): Int do return last_index_of_from(item, length-1)

        # The index of the first occurrence of `item`, starting from pos.
        # Return -1 if `item` is not found.
        # Comparison is done with `==`.
        #
        #     var a = [10,20,30,10,20,30]
        #     assert a.index_of_from(20, 3)   == 4
        #     assert a.index_of_from(20, 4)   == 4
        #     assert a.index_of_from(20, 5)   == -1
        fun index_of_from(item: nullable Object, pos: Int): Int
        do
                var p = 0
                var i = iterator
                while i.is_ok do
                        if p>=pos and i.item == item then return i.index
                        i.next
                        p += 1
                end
                return -1
        end

        # The index of the last occurrence of `item` starting from `pos` and decrementing.
        # Return -1 if `item` is not found.
        # Comparison is done with `==`.
        #
        #     var a = [10,20,30,10,20,30]
        #     assert a.last_index_of_from(20, 2)   == 1
        #     assert a.last_index_of_from(20, 1)   == 1
        #     assert a.last_index_of_from(20, 0)   == -1
        fun last_index_of_from(item: nullable Object, pos: Int): Int do
                var i = pos
                while i >= 0 do
                        if self[i] == item then return i
                        i -= 1
                end
                return -1
        end

        # Two sequences are equals if they have the same items in the same order.
        #
        #     var a = new List[Int]
        #     a.add(1)
        #     a.add(2)
        #     a.add(3)
        #     assert a == [1,2,3]
        #     assert a != [1,3,2]
        redef fun ==(o)
        do
                if not o isa SequenceRead[nullable Object] then return false
                var l = length
                if o.length != l then return false
                var i = 0
                while i < l do
                        if self[i] != o[i] then return false
                        i += 1
                end
                return true
        end

        # Because of the law between `==` and `hash`, `hash` is redefined to be the sum of the hash of the elements
        redef fun hash
        do
                # The 17 and 2/3 magic numbers were determined empirically.
                # Note: the standard hash functions djb2, sbdm and fnv1 were also
                # tested but were comparable (or worse).
                var res = 17 + length
                for e in self do
                        res = res * 3 / 2
                        if e != null then res += e.hash
                end
                return res
        end

        redef fun iterator: IndexedIterator[E] is abstract

        # Gets a new Iterator starting at position `pos`
        #
        #     var iter = [10,20,30,40,50].iterator_from(2)
        #     assert iter.to_a == [30, 40, 50]
        fun iterator_from(pos: Int): IndexedIterator[E]
        do
                var res = iterator
                while pos > 0 and res.is_ok do
                        res.next
                        pos -= 1
                end
                return res
        end

        # Gets an iterator starting at the end and going backwards
        #
        #     var reviter = [1,2,3].reverse_iterator
        #     assert reviter.to_a == [3,2,1]
        fun reverse_iterator: IndexedIterator[E] is abstract

        # Gets an iterator on the chars of self starting from `pos`
        #
        #     var reviter = [10,20,30,40,50].reverse_iterator_from(2)
        #     assert reviter.to_a == [30,20,10]
        fun reverse_iterator_from(pos: Int): IndexedIterator[E]
        do
                var res = reverse_iterator
                while pos > 0 and res.is_ok do
                        res.next
                        pos -= 1
                end
                return res
        end
end

# Sequence are indexed collection.
# The first item is 0. The last is `length-1`.
interface Sequence[E]
        super SequenceRead[E]
        super SimpleCollection[E]

        # Set the first item.
        # Is equivalent with `self[0] = item`.
        #
        #     var a = [1,2,3]
        #     a.first = 10
        #     assert a == [10,2,3]
        fun first=(item: E)
        do self[0] = item end

        # Set the last item.
        # Is equivalent with `self[length-1] = item`.
        #
        #     var a = [1,2,3]
        #     a.last = 10
        #     assert a == [1,2,10]
        #
        # If the sequence is empty, `last=` is equivalent with `self[0]=` (thus with `first=`)
        #
        #     var b = new Array[Int]
        #     b.last = 10
        #     assert b == [10]
        fun last=(item: E)
        do
                var l = length
                if l > 0 then
                        self[l-1] = item
                else
                        self[0] = item
                end
        end

        # A synonym of `push`
        redef fun add(e) do push(e)

        # Add an item after the last one.
        #
        #     var a = [1,2,3]
        #     a.push(10)
        #     a.push(20)
        #     assert a  == [1,2,3,10,20]
        fun push(e: E) is abstract

        # Add each item of `coll` after the last.
        #
        #     var a = [1,2,3]
        #     a.append([7..9])
        #     assert a  == [1,2,3,7,8,9]
        #
        # Alias of `add_all`
        fun append(coll: Collection[E]) do add_all(coll)

        # Remove the last item.
        #
        #     var a = [1,2,3]
        #     assert a.pop  == 3
        #     assert a.pop  == 2
        #     assert a == [1]
        #
        # REQUIRE `not is_empty`
        fun pop: E is abstract

        # Add an item before the first one.
        #
        #     var a = [1,2,3]
        #     a.unshift(10)
        #     a.unshift(20)
        #     assert a  == [20,10,1,2,3]
        fun unshift(e: E) is abstract

        # Add all items of `coll` before the first one.
        #
        #     var a = [1,2,3]
        #     a.prepend([7..9])
        #     assert a  == [7,8,9,1,2,3]
        #
        # Alias of `insert_at(coll, 0)`
        fun prepend(coll: Collection[E]) do insert_all(coll, 0)

        # Remove the first item.
        # The second item thus become the first.
        #
        #     var a = [1,2,3]
        #     assert a.shift  == 1
        #     assert a.shift  == 2
        #     assert a == [3]
        #
        # REQUIRE `not is_empty`
        fun shift: E is abstract

        # Set the `item` at `index`.
        #
        #     var a = [10,20,30]
        #     a[1] = 200
        #     assert a  == [10,200,30]
        #
        # like with `[]`, index should be between `0` and `length-1`
        # However, if `index==length`, `[]=` works like `push`.
        #
        #     a[3] = 400
        #     assert a  == [10,200,30,400]
        #
        # REQUIRE `index >= 0 and index <= length`
        fun []=(index: Int, item: E) is abstract

        # Set the index-th element but wrap
        #
        # Whereas `self[]=` requires the index to exists, the `modulo` accessor automatically
        # wraps overbound and underbouds indexes.
        #
        # ~~~
        # var a = [10,20,30]
        # a.modulo(1) = 200
        # a.modulo(3) = 100
        # a.modulo(-1) = 300
        # a.modulo(-10) = 301
        # assert a == [100, 200, 301]
        # ~~~
        #
        # REQUIRE `not_empty`
        # ENSURE `self[modulo_index(index)] == value`
        fun modulo=(index: Int, value: E) do self[modulo_index(index)] = value

        # Insert an element at a given position, following elements are shifted.
        #
        #     var a = [10, 20, 30, 40]
        #     a.insert(100, 2)
        #     assert a      ==  [10, 20, 100, 30, 40]
        #
        # REQUIRE `index >= 0 and index <= length`
        # ENSURE `self[index] == item`
        fun insert(item: E, index: Int) is abstract

        # Insert all elements at a given position, following elements are shifted.
        #
        #     var a = [10, 20, 30, 40]
        #     a.insert_all([100..102], 2)
        #     assert a      ==  [10, 20, 100, 101, 102, 30, 40]
        #
        # REQUIRE `index >= 0 and index <= length`
        # ENSURE `self[index] == coll.first`
        fun insert_all(coll: Collection[E], index: Int)
        do
                assert index >= 0 and index < length
                if index == length then
                        add_all(coll)
                end
                for c in coll do
                        insert(c, index)
                        index += 1
                end
        end

        # Remove the item at `index` and shift all following elements
        #
        #     var a = [10,20,30]
        #     a.remove_at(1)
        #     assert a  == [10,30]
        #
        # REQUIRE `index >= 0 and index < length`
        fun remove_at(index: Int) is abstract

        # Rotates the elements of self once to the left
        #
        # ~~~nit
        # var a = [12, 23, 34, 45]
        # a.rotate_left
        # assert a == [23, 34, 45, 12]
        # ~~~
        fun rotate_left do
                var fst = shift
                push fst
        end

        # Rotates the elements of self once to the right
        #
        # ~~~nit
        # var a = [12, 23, 34, 45]
        # a.rotate_right
        # assert a == [45, 12, 23, 34]
        # ~~~
        fun rotate_right do
                var lst = pop
                unshift lst
        end
end

# Iterators on indexed collections.
interface IndexedIterator[E]
        super Iterator[E]
        # The index of the current item.
        fun index: Int is abstract
end

# Associative arrays that internally uses couples to represent each (key, value) pairs.
# This is an helper class that some specific implementation of Map may implements.
interface CoupleMap[K, V]
        super Map[K, V]

        # Return the couple of the corresponding key
        # Return null if the key is no associated element
        protected fun couple_at(key: nullable Object): nullable Couple[K, V] is abstract

        # Return a new iteralot on all couples
        # Used to provide `iterator` and others
        protected fun couple_iterator: Iterator[Couple[K,V]] is abstract

        redef fun iterator do return new CoupleMapIterator[K,V](couple_iterator)

        redef fun [](key)
        do
                var c = couple_at(key)
                if c == null then
                        return provide_default_value(key)
                else
                        return c.second
                end
        end

        redef fun has_key(key) do return couple_at(key) != null
end

# Iterator on CoupleMap
#
# Actually it is a wrapper around an iterator of the internal array of the map.
private class CoupleMapIterator[K, V]
        super MapIterator[K, V]
        redef fun item do return _iter.item.second

        #redef fun item=(e) do _iter.item.second = e

        redef fun key do return _iter.item.first

        redef fun is_ok do return _iter.is_ok

        redef fun next
        do
                _iter.next
        end

        var iter: Iterator[Couple[K,V]]
end

# Some tools ###################################################################

# Two objects in a simple structure.
class Couple[F, S]

        # The first element of the couple.
        var first: F is writable

        # The second element of the couple.
        var second: S is writable
end