indexing
	description: "Prime number properties"
	names: primes

class interface
	PRIMES

feature -- Access

	all_lower_primes (n: INTEGER): ARRAY [BOOLEAN]
			-- Array of n boolean values, where the
			-- value at index i is true if and only if
			-- i is prime.

	higher_prime (n: INTEGER): INTEGER
			-- Lowest prime greater than or equal to n

	i_th (i: INTEGER): INTEGER
			-- The i-th prime number
		require -- from COUNTABLE
			positive_argument: i > 0

	index: INTEGER
			-- Index of current position
			-- (from COUNTABLE_SEQUENCE)

	index_of (v: like item; i: INTEGER): INTEGER
			-- Index of i-th occurrence of v.
			-- 0 if none.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from LINEAR
			positive_occurrences: i > 0
		ensure -- from LINEAR
			non_negative_result: Result >= 0

	is_prime (n: INTEGER): BOOLEAN
			-- Is n a prime number?
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not empty

	item: INTEGER
			-- Item at current position
			-- (from COUNTABLE_SEQUENCE)
		require -- from ACTIVE
			readable: readable
		require -- from TRAVERSABLE
			not_off: not off

	lower_prime (n: INTEGER): INTEGER
			-- Greatest prime lower than or equal to n
		require
			argument_big_enough: n >= smallest_prime

	occurrences (v: INTEGER): INTEGER
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	search (v: like item)
			-- Move to first position (at or after current
			-- position) where item and v are equal.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- If no such position ensure that exhausted will be true.
			-- (from LINEAR)
		ensure -- from LINEAR
			object_found: (not exhausted and object_comparison) implies equal (v, item);
			item_found: (not exhausted and not object_comparison) implies v = item

	Smallest_odd_prime: INTEGER is 3

	Smallest_prime: INTEGER is 2
	
feature -- Status report

	After: BOOLEAN is false
			-- Is current position past last item? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	changeable_comparison_criterion: BOOLEAN
			-- May object_comparison be changed?
			-- (Answer: yes by default.)
			-- (from CONTAINER)

	Empty: BOOLEAN is false
			-- Is structure empty? (Answer: no.)
			-- (from INFINITE)

	exhausted: BOOLEAN
			-- Has structure been completely explored?
			-- (from LINEAR)
		ensure -- from LINEAR
			exhausted_when_off: off implies Result

	Extendible: BOOLEAN is false
			-- May items be added? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	Full: BOOLEAN is true
			-- The structure is complete
			-- (from INFINITE)

	object_comparison: BOOLEAN
			-- Must search operations use equal rather than =
			-- for comparing references? (Default: no, use =.)
			-- (from CONTAINER)

	off: BOOLEAN
			-- Is there no current item?
			-- (from LINEAR)

	Prunable: BOOLEAN is false
			-- May items be removed? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	Readable: BOOLEAN is true
			-- Is there a current item that may be read?
			-- (Answer: yes.)
			-- (from COUNTABLE_SEQUENCE)

	Writable: BOOLEAN is false
			-- Is there a current item that may be written?
			-- (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)
	
feature -- Status setting

	compare_objects
			-- Ensure that future search operations will use equal
			-- rather than = for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion
		ensure -- from CONTAINER
			object_comparison

	compare_references
			-- Ensure that future search operations will use =
			-- rather than equal for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
	
feature -- Cursor movement

	forth
			-- Move to next position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from LINEAR
			not_after: not after

	start
			-- Move to first position.
			-- (from COUNTABLE_SEQUENCE)
	
invariant

		-- from GENERAL
	reflexive_equality: standard_is_equal (Current);
	reflexive_conformance: conforms_to (Current);
		-- from INFINITE
	never_empty: not empty;
	always_full: full;
		-- from ACTIVE
	writable_constraint: writable implies readable;
	empty_constraint: empty implies (not readable) and (not writable);
		-- from LINEAR
	after_constraint: after implies off;
		-- from TRAVERSABLE
	empty_constraint: empty implies off;

end -- class PRIMES