note
	description: "[
		Finite sequences of some elements of type G.
		A valid index is 1..count.
		Array notation can be used, as well as iteration (across).
		Empty sequences can be created, or creation can be from an array. 
		Sequences have a first item (the head), a tail and last item.
		Infix notation for prepended_by where x is of generic type G:
			seq1 |< x
		Infix notation for appended_by where x is of generic type G:
			seq1 |> x
		For concatenation we use infix: seq1 |++| seq2
		For queries, to assert that the state is not changed, 
		the postcondition is
			Current ~ old Current.deep_twin
		Class also has an inefficient implementation:
	]"
	author: "JSO"
	date: "$Date$"
	revision: "$Revision$"

class 
	SEQ [G -> attached ANY]

inherit
	ITERABLE [G]
		redefine
			is_equal,
			out
		end

	DEBUG_OUTPUT
		undefine
			is_equal,
			out
		end

create 
	make_empty,
	make_from_array

convert
	make_from_array ({ARRAY [G]}),
	as_array: {ARRAY [G]}

feature -- 2-level copy

	twin2: like Current
		do
			Result := Current.twin
			Result.set_imp (Current.imp.twin)
		end
	
feature -- Constructors

	make_empty
			-- create empty list
		do
			create imp.make (10)
			imp.compare_objects
		ensure
			is_empty: is_empty
		end

	make_from_array (a: ARRAY [G])
			-- Create list from array a.
		do
			create imp.make_from_array (a)
			imp.compare_objects
		ensure
				# Current = a.count
				across
					a.lower |..| a.upper as i
				all
					Current [i.item - a.lower + 1] ~ a [i.item]
				end
		end
	
feature -- Iteration

	new_cursor: ITERATION_CURSOR [G]
			-- A new cursor for iterating through current sequence
		do
			Result := imp.new_cursor
		end
	
feature -- Status Queries

	count alias "#": INTEGER_32
			-- Return the number of elements in current sequence
		do
			Result := imp.count
		ensure
				Result = as_array.count
				Result = # as_function
		end

	lower: INTEGER_32
			-- Starting position of current sequence
		do
			Result := 1
		ensure
				Result = 1
		end

	upper: INTEGER_32
			-- Ending position of current sequence
		do
			Result := count
		ensure
				Result = # Current
		end

	is_empty: BOOLEAN
			-- Is the current sequence empty?
		do
			Result := count = 0
		ensure
				Result = (# Current = 0)
				Result = as_array.is_empty
				Result = as_function.is_empty
		end

	has (v: G): BOOLEAN
			-- Does 'v' exist in current sequence?
		do
			Result := imp.has (v)
		ensure
				Result = across
					1 |..| count as i
				some
					Current [i.item] ~ v
				end
		end

	first: G
			-- Return the 1st element in current sequence
		require
				not is_empty
		do
			Result := imp [imp.Lower]
		ensure
				Result ~ as_array [1]
				Result ~ as_function [1]
		end

	front: like Current
			-- Return current sequence except the last element
		require
				not is_empty
		do
			if count > 1 then
				Result := subsequenced (1, count - 1)
			else
				create Result.make_empty
			end
		ensure
			case_of_empty_init: # Current = 1 implies Result.is_empty
			case_of_nonempty_init: # Current > 1 implies Result ~ subsequenced (1, count - 1)
		end

	last: G
			-- Return the last element in current sequence
		require
				not is_empty
		do
			Result := imp [imp.upper]
		ensure
				Result ~ as_array [count]
				Result ~ as_function [count]
		end

	tail: like Current
			-- Return current sequence except the first element
		require
				not is_empty
		do
			if count > 1 then
				Result := subsequenced (2, count)
			else
				create Result.make_empty
			end
		ensure
			case_of_empty_tail: # Current = 1 implies Result.is_empty
			case_of_nonempty_tail: # Current > 1 implies Result ~ subsequenced (2, count)
		end

	item alias "[]" (i: INTEGER_32): G assign override
			-- Element at i-th position
		require
				valid_position (i)
		do
			Result := imp.i_th (i)
		ensure
				Result ~ as_function [i]
				Result ~ as_array [i]
		end

	is_subsequence_of alias "|<:" (other: like Current): BOOLEAN
			-- Is current a contiguous subsequence of 'other'?
			-- subsequences are not necessarily contiguous
			-- e.g. subsequences of <2, 3, 8, 5, 2> are:
			-- <>, <3, 5> <3, 5, 2> etc.
		local
			proj: SEQ [G]
			ran: SET [G]
			element: G
		do
			ran := Current.as_function.range
			create proj.make_empty
			across
				other as o
			loop
				element := o.item
				if ran.has (element) then
					proj.append (element)
				end
			end
			Result := is_augmented_subseq_of (augmented_with_collapsed_rep, proj.augmented_with_collapsed_rep)
		end

	is_contiguous_subseq_of (other: like Current): BOOLEAN
			-- Is current a contiguous subsequence of 'other'?
			-- e.g. contiguous subsequences of <2, 3, 8, 5, 2> are:
			-- <>, <2, 3> <3, 8, 5> etc.
		do
			Result := is_augmented_subseq_of (augmented_without_collapsed_rep, other.augmented_without_collapsed_rep)
		ensure
			case_current_empty: is_empty implies Result
			case_other_empty: other.is_empty implies Result = is_empty
			case_both_non_empty: not (is_empty or other.is_empty) implies Result = (across
					1 |..| # other as start_pos
				some
					across
						1 |..| # other as end_pos
					some
						end_pos.item >= start_pos.item and Current ~ other.subsequenced (start_pos.item, end_pos.item)
					end
				end)
		end
	
feature -- Commands

	append (v: G)
			-- Add v to end.
		do
			imp.extend (v)
		ensure
				Current ~ old Current.deep_twin.appended (v)
		end

	prepend (v: G)
			-- Add v to beginning.
		do
			imp.put_front (v)
		ensure
				Current ~ old Current.deep_twin.prepended (v)
		end

	subsequence (i, j: INTEGER_32)
			-- Cut down current seq so that segment i..j remains
		require
				valid_position (i)
				valid_position (j)
		local
			pos: INTEGER_32
		do
			if i <= j then
				from
					pos := 1
					imp.start
				until
					imp.after
				loop
					if pos < i or pos > j then
						imp.remove
					else
						imp.forth
					end
					pos := pos + 1
				end
			else
				make_empty
			end
		ensure
				Current ~ old Current.deep_twin.subsequenced (i, j)
		end

	concatenate (other: like Current)
			-- Append 'other' to the end of current sequence
		do
			across
				other as cur
			loop
				append (cur.item)
			end
		ensure
				Current ~ old Current.deep_twin.concatenated (other)
		end

	override (v: G; i: INTEGER_32)
			-- Replace i-th entry, if in index interval, by v.
		require
				valid_position (i)
		do
			imp.put_i_th (v, i)
		ensure
				Current ~ old Current.deep_twin.overriden (v, i)
		end

	insert (v: G; i: INTEGER_32)
			-- Insert 'v' as the i-th entry, if in index interval
			-- e.g., insert(1) on an empty sequence is forbidden.
		require
				valid_position (i)
		local
			j: INTEGER_32
			done: BOOLEAN
		do
			from
				imp.start
				j := 1
			until
				done
			loop
				if j = i then
					imp.put_left (v)
					done := True
				end
				imp.forth
				j := j + 1
			end
		ensure
				Current ~ old Current.deep_twin.inserted (v, i)
		end

	remove (i: INTEGER_32)
			-- Remove i-th entry, if in index interval
		require
				valid_position (i)
		do
			imp.start
			if imp.count > 1 then
				imp.move (i - 1)
			end
			imp.remove
		ensure
				Current ~ old Current.deep_twin.removed (i)
		end

	reverse
			-- Reverse the order of current sequence
		local
			new_imp: like imp
		do
			create new_imp.make_filled (count)
			new_imp.compare_objects
			across
				1 |..| count as i
			loop
				new_imp [count - i.item + 1] := Current [i.item]
			end
			set_imp (new_imp)
		ensure
				Current ~ old Current.deep_twin.reversed
		end
	
feature -- Specification Queries

	appended alias "|->" (v: G): like Current
			-- Return a sequence representing current with 'v' added to end
		do
			Result := Current.deep_twin
			Result.append (v)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_incremented: # Result = # Current + 1
				Result.front ~ Current
				Result.last ~ v
		end

	prepended alias "|<-" (v: G): like Current
			-- Return a sequence representing current with 'v' added to beginning
		do
			Result := Current.deep_twin
			Result.prepend (v)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_incremented: # Result = # Current + 1
				Result.first ~ v
				Result.tail ~ Current
		end

	subsequenced (i, j: INTEGER_32): like Current
			-- Segment of sequence i..j
		require
				valid_position (i)
				valid_position (j)
		do
			Result := Current.deep_twin
			Result.subsequence (i, j)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
				j >= i implies # Result = j - i + 1
				j < i implies # Result = 0
				across
					i |..| j as pos
				all
					Current [pos.item] ~ Result [pos.item - i + 1]
				end
		end

	concatenated alias "|++|" (other: like Current): like Current
			-- Return a sequence representing current with 'other' appended
		do
			Result := Current.deep_twin
			Result.concatenate (other)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_incremented: # Result = # Current + # other
				across
					1 |..| (# Current + # other) as pos
				all
					pos.item <= # Current implies Result [pos.item] ~ Current [pos.item] and pos.item > # Current implies Result [pos.item] ~ other [pos.item - # Current]
				end
		end

	overriden (v: G; i: INTEGER_32): like Current
		require
				valid_position (i)
		do
			Result := Current.deep_twin
			Result.override (v, i)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_incremented: # Current = # Result
				across
					1 |..| count as pos
				all
					pos.item = i implies Result [pos.item] ~ v and pos.item /= i implies Result [pos.item] ~ Current [pos.item]
				end
		end

	inserted (v: G; i: INTEGER_32): like Current
			-- Return a new sequence representing current with
			-- v inserted as the i-th entry, if in index interval
		require
				valid_position (i)
		do
			Result := Current.deep_twin
			Result.insert (v, i)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_incremented: # Result = # Current + 1
				Result ~ subsequenced (1, i - 1).appended (v) |++| subsequenced (i, count)
		end

	removed (i: INTEGER_32): like Current
			-- Return a new sequence representing current with
			-- i-th entry, if in index interval, removed
		require
				valid_position (i)
		do
			Result := Current.deep_twin
			Result.remove (i)
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			count_decremented: # Result = # Current - 1
				Result ~ subsequenced (1, i - 1) |++| subsequenced (i + 1, count)
		end

	reversed: like Current
			-- Return an reversed version of current sequence
		do
			Result := Current.deep_twin
			Result.reverse
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			same_count: # Current = # Result
			reverse_property_1: Current ~ Result.reversed
			reverse_property_2: across
					1 |..| count as i
				all
					Current [i.item] ~ Result [count - i.item + 1]
				end
		end

	slice (a_start, a_end, a_step: INTEGER_32): like Current
		require
				lower <= a_start and a_start <= a_end and a_end <= upper
				a_step >= 0
		local
			i: INTEGER_32
		do
			create Result.make_empty
			from
				i := a_start
			until
				i > a_end
			loop
				Result.append (item (i))
				i := i + a_step
			end
		end
	
feature -- Quantification

	hold_count (exp: PREDICATE [PAIR [INTEGER_32, G]]): INTEGER_32
			-- How many items satisfying exp are in Current?
		local
			i: INTEGER_32
			p: PAIR [INTEGER_32, G]
		do
			i := 1
			across
				Current as c
			loop
				create p.make (i, c.item)
				if exp.item ([p]) then
					Result := Result + 1
				end
				i := i + 1
			end
		ensure
			current_seq_unchanged: Current ~ old Current.deep_twin
			maximum_result: Result <= count
		end

	comprehension alias "|" (exp: PREDICATE [PAIR [INTEGER_32, G]]): like Current
			-- Form elements of current sequence that satisfy exp
			-- as a new sequence
		local
			i: INTEGER_32
			p: PAIR [INTEGER_32, G]
		do
			create Result.make_empty
			i := 1
			across
				Current as c
			loop
				create p.make (i, c.item)
				if exp.item ([p]) then
					Result.append (c.item)
				end
				i := i + 1
			end
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
			all_satisfying_items_exist: across
					Result as cur
				all
					Current.has (cur.item)
				end
			all_satisfying_exp: Result.hold_count (exp) = # Result
			consistent_satisfying_items: Current.hold_count (exp) = # Result
		end
	
feature -- Equality

	is_equal (other: like Current): BOOLEAN
			-- Is current sequence equal to other?
		do
			Result := imp ~ other.imp
		ensure then
				Result = (as_function ~ other.as_function)
		end
	
feature -- Output

	out: STRING_8
			-- Return string representation of current sequence.
		local
			i: INTEGER_32
		do
			create Result.make_empty
			Result.append ("< ")
			from
				i := 1
			until
				i > count
			loop
				check
						attached {G} imp.i_th (i) as e
				then
					Result.append (e.out)
				end
				if i < count then
					Result.append (", ")
				end
				i := i + 1
			end
			Result.append (" >")
		end

	debug_output: STRING_8
			-- Return string representation of current sequence for debugging
		do
			Result := out
		end
	
feature -- Conversion

	as_array: ARRAY [G]
			-- Return current sequence as an array
		do
			create Result.make_empty
			across
				Current as cur
			loop
				Result.force (cur.item, Result.upper + 1)
			end
			Result.compare_objects
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
				Result.lower = 1
				Result.upper = count
				across
					1 |..| count as pos
				all
					Current [pos.item] ~ Result [pos.item]
				end
		end

	as_function: FUN [INTEGER_32, G]
			-- Return current sequence as a function
			-- with its domain being the set of positions
		local
			i: INTEGER_32
			pair: PAIR [INTEGER_32, G]
		do
			create Result.make_empty
			i := 1
			across
				Current as cur
			loop
				create pair.make (i, cur.item)
				Result.extend (pair)
				i := i + 1
			end
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
			all_positions_included: # Result.domain = # Current
				across
					Result.domain as pos
				all
					valid_position (pos.item)
				end
				across
					Result.domain as pos
				all
					Current [pos.item] ~ Result [pos.item]
				end
		end
	
feature -- Auxiliary functions for contracts

	valid_position (pos: INTEGER_32): BOOLEAN
			-- Is 'pos' a valid position in current sequence
		do
			Result := 1 <= pos and then pos <= count
		ensure
				Result = (1 <= pos and pos <= # Current)
		end
	
feature {SEQ} -- Auxiliary functions for checking subsequences

	is_augmented_subseq_of (s1, s2: SEQ [TUPLE [g: G; i: INTEGER_32]]): BOOLEAN
			-- Given that both 's1' and 's2' are augmented sequences,
			-- is 's1' a contiguous subsequence of 's2'?
			-- e.g., <<[a, 1], [b, 2]>> is a contiguous subsequence of
			--       <<[a, 3], [b, 3]>>
		local
			i: INTEGER_32
		do
			if s1.is_empty then
				Result := True
			else
				from
					Result := False
					i := 1
				until
					Result or else s2.count - i + 1 < s1.count
				loop
					if s1 [1].g ~ s2 [i].g then
						Result := across
							i |..| (i + s1.count - 1) as j
						all
							s1 [j.item - i.item + 1].g ~ s2 [j.item].g and then s1 [j.item - i.item + 1].i <= s2 [j.item].i
						end
					end
					i := i + 1
				end
			end
		end

	augmented_with_collapsed_rep: SEQ [TUPLE [g: G; i: INTEGER_32]]
			-- e.g., <<a, b, b, c, d>> augmented to
			-- <<[a, 1], [b, 2], [c, 1], [d, 1]>>
		local
			i: INTEGER_32
			element: G
		do
			create Result.make_empty
			from
				i := 1
				imp.start
			until
				imp.after
			loop
				element := imp.item
				if i > 1 then
					if imp [i - 1] ~ element then
						Result [Result.count] := [Result.last.g, Result.last.i + 1]
					else
						Result.append ([element, 1])
					end
				else
					Result.append ([element, 1])
				end
				i := i + 1
				imp.forth
			end
		end

	augmented_without_collapsed_rep: SEQ [TUPLE [G, INTEGER_32]]
			-- e.g., <<a, b, b, c, d>> augmented to
			-- <<[a, 1], [b, 1], [b, 1], [c, 1], [d, 1]>>
		do
			create Result.make_empty
			across
				Current as cur
			loop
				Result.append ([cur.item, 1])
			end
		end
	
feature {SEQ} -- Implementation

	imp: ARRAYED_LIST [G]

	set_imp (new_imp: like imp)
		do
			imp := new_imp
		ensure
				imp = new_imp
		end
	
invariant
	value_semantics: imp.object_comparison
		lower = 1
		imp.Lower = lower
		is_empty = (upper < lower)
	properties: not is_empty implies Current ~ tail.prepended (first) and Current ~ front.appended (last)

end -- class SEQ

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