note
	description: "Summary description for {FUN}."
	author: "JSO, Jackie Wang"
	date: "$Date$"
	revision: "$Revision$"

class interface
	FUN [G -> attached ANY, H -> attached ANY]

create 
	make_empty
			-- Initialize an empty function
		ensure
				# Current = 0
				is_empty

	make_from_array (a: ARRAY [TUPLE [fst: G; snd: H]])
			-- Initialize a function from array 'a'.
		require
			no_duplicates: across
					a.lower |..| a.upper as i
				all
					across
						a.lower |..| a.upper as j
					all
						a [i.item].fst ~ a [j.item].fst implies i.item = j.item
					end
				end
		ensure
			consistent_counts: # Current = a.count

convert
	make_from_array ({ARRAY [TUPLE [G, H]]}),
	make_from_array: {ARRAY [PAIR [G, H]]}

feature -- Access

	generating_type: TYPE [detachable FUN [G, H]]
			-- Type of current object
			-- (type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generating_type_not_void: Result /= Void

	generator: STRING_8
			-- Name of current object's generating class
			-- (base class of the type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generator_not_void: Result /= Void
			generator_not_empty: not Result.is_empty
	
feature -- Comparison

	frozen deep_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void
			-- or attached to isomorphic object structures?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			shallow_implies_deep: standard_equal (a, b) implies Result
			both_or_none_void: (a = Void) implies (Result = (b = Void))
			same_type: (Result and (a /= Void)) implies (b /= Void and then a.same_type (b))
			symmetric: Result implies deep_equal (b, a)

	frozen equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached
			-- to objects considered equal?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.is_equal (b))

	frozen is_deep_equal (other: FUN [G, H]): BOOLEAN
			-- Are Current and other attached to isomorphic object structures?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			shallow_implies_deep: standard_is_equal (other) implies Result
			same_type: Result implies same_type (other)
			symmetric: Result implies other.is_deep_equal (Current)

	frozen standard_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached to
			-- field-by-field identical objects of the same type?
			-- Always uses default object comparison criterion.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.standard_is_equal (b))

	frozen standard_is_equal (other: FUN [G, H]): BOOLEAN
			-- Is other attached to an object of the same type
			-- as current object, and field-by-field identical to it?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			same_type: Result implies same_type (other)
			symmetric: Result implies other.standard_is_equal (Current)
	
feature -- Status report

	conforms_to (other: ANY): BOOLEAN
			-- Does type of current object conform to type
			-- of other (as per Eiffel: The Language, chapter 13)?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void

	same_type (other: ANY): BOOLEAN
			-- Is type of current object identical to type of other?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			definition: Result = (conforms_to (other) and other.conforms_to (Current))
	
feature -- Conversion

	as_array: ARRAY [PAIR [G, H]]

	as_set: SET [PAIR [G, H]]
			-- Return current function as a set of pairs
	
feature -- Duplication

	copy (other: FUN [G, H])
			-- Update current object using fields of object attached
			-- to other, so as to yield equal objects.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_equal: Current ~ other

	frozen deep_copy (other: FUN [G, H])
			-- Effect equivalent to that of:
			--		copy (other . deep_twin)
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			deep_equal: deep_equal (Current, other)

	frozen deep_twin: FUN [G, H]
			-- New object structure recursively duplicated from Current.
			-- (from ANY)
		ensure -- from ANY
			deep_twin_not_void: Result /= Void
			deep_equal: deep_equal (Current, Result)

	frozen standard_copy (other: FUN [G, H])
			-- Copy every field of other onto corresponding field
			-- of current object.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_standard_equal: standard_is_equal (other)

	frozen standard_twin: FUN [G, H]
			-- New object field-by-field identical to other.
			-- Always uses default copying semantics.
			-- (from ANY)
		ensure -- from ANY
			standard_twin_not_void: Result /= Void
			equal: standard_equal (Result, Current)

	frozen twin: FUN [G, H]
			-- New object equal to Current
			-- twin calls copy; to change copying/twinning semantics, redefine copy.
			-- (from ANY)
		ensure -- from ANY
			twin_not_void: Result /= Void
			is_equal: Result ~ Current
	
feature -- Basic operations

	frozen default: detachable FUN [G, H]
			-- Default value of object's type
			-- (from ANY)

	frozen default_pointer: POINTER
			-- Default value of type POINTER
			-- (Avoid the need to write p.default for
			-- some p of type POINTER.)
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	default_rescue
			-- Process exception for routines with no Rescue clause.
			-- (Default: do nothing.)
			-- (from ANY)

	frozen do_nothing
			-- Execute a null action.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
	
feature -- Constructors

	has_duplicates (a: ARRAY [TUPLE [fst: G; snd: H]]): BOOLEAN
			-- does array a have duplicates?
			-- hence cannot construct a function

	make_empty
			-- Initialize an empty function
		ensure
				# Current = 0
				is_empty

	make_from_array (a: ARRAY [TUPLE [fst: G; snd: H]])
			-- Initialize a function from array 'a'.
		require
			no_duplicates: across
					a.lower |..| a.upper as i
				all
					across
						a.lower |..| a.upper as j
					all
						a [i.item].fst ~ a [j.item].fst implies i.item = j.item
					end
				end
		ensure
			consistent_counts: # Current = a.count
	
feature -- Equality

	is_equal (other: like Current): BOOLEAN
			-- Is current function equal to 'other'?
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			symmetric: Result implies other ~ Current
			consistent: standard_is_equal (other) implies Result
	
feature -- Iterator

	new_cursor: ITERATION_CURSOR [PAIR [G, H]]
			-- Fresh cursor associated with current structure
		ensure -- from ITERABLE
			result_attached: Result /= Void
	
feature -- Output

	Io: STD_FILES
			-- Handle to standard file setup
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			io_not_void: Result /= Void

	print (o: detachable ANY)
			-- Write terse external representation of o
			-- on standard output.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	frozen tagged_out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			tagged_out_not_void: Result /= Void
	
feature -- Outputs

	debug_output: STRING_8
			-- String that should be displayed in debugger to represent Current.
		ensure -- from DEBUG_OUTPUT
			result_not_void: Result /= Void

	out: STRING_8
			-- New string containing terse printable representation
			-- of current object
		ensure -- from ANY
			out_not_void: Result /= Void
	
feature -- Platform

	Operating_environment: OPERATING_ENVIRONMENT
			-- Objects available from the operating system
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			operating_environment_not_void: Result /= Void
	
feature -- Quantifiers

	comprehension alias "|" (exp: PREDICATE [PAIR [G, H]]): like Current
			-- Largest subset of the current fun whose elements satisfy exp
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
			is_subset: Result |<: Current
			all_satisfying_exp: Result.hold_count (exp) = # Result
			consistent_satisfying_items: Current.hold_count (exp) = # Result

	hold_count (exp: PREDICATE [PAIR [G, H]]): INTEGER_32
			-- How many items satisfying exp are in Current?
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
			maximum_result: Result <= count
	
feature -- Relation Commands

	domain_restrict (ds: SET [G])
			-- Keep all pairs whose first values are members of 'ds'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			only_ds_in_new_fun: ((old Current.deep_twin) |\ (Current)).domain ~ (old Current.deep_twin.domain |\ ds)

	domain_restrict_by (g: G)
			-- Keep pairs whose first values are 'd'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			only_g_in_new_fun: ((old Current.deep_twin) |\ (Current)).domain ~ (old Current.deep_twin.domain |\ singleton_g (g))

	domain_subtract (ds: SET [G])
			-- Subtract all pairs whose first values are members of 'ds'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			no_ds_in_new_fun: ((old Current.deep_twin) |\ (Current)).domain ~ ds.comprehension (agent in_domain (?, (old Current.deep_twin).domain))

	domain_subtract_by (g: G)
			-- Subtract the pair whose first value is 'd'
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			no_g_in_new_fun: ((old Current.deep_twin) |\ (Current)).domain ~ singleton_g (g).comprehension (agent in_domain (?, (old Current.deep_twin).domain))

	override (r: like Current)
			-- Update current function such that it aggres on 'r'.
		ensure
				Current ~ ((old Current.deep_twin |<< r.domain) |\/| r)

	override_by (t: TUPLE [g: G; h: H])
			-- Update current function such that it aggres on 'g |-> h'.
		ensure
				Current ~ ((old Current.deep_twin @<< t.g) |\/| singleton_gh (t))

	put (h: H; g: G)
		require
				domain.has (g)
		ensure
				Current [g] ~ h

	range_restrict (rs: SET [H])
			-- Keep all pairs whose second values are members of 'rs'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			only_rs_in_new_fun: ((old Current.deep_twin) |\ (Current)).range ~ (old Current.deep_twin.range |\ rs)

	range_restrict_by (h: H)
			-- Keep all pairs whose second values are 'h'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			only_h_in_new_fun: ((old Current.deep_twin) |\ (Current)).range ~ (old Current.deep_twin.range |\ singleton_h (h))

	range_subtract (rs: SET [H])
			-- Subtract all pairs whose second values are members of 'rs'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			no_rs_in_new_fun: ((old Current.deep_twin) |\ (Current)).range ~ rs.comprehension (agent in_range (?, (old Current.deep_twin).range))

	range_subtract_by (h: H)
			-- Subtract pairs whose second values are 'h'.
		ensure
			new_fun_is_a_subset: Current |<: (old Current.deep_twin)
			no_h_in_new_fun: ((old Current.deep_twin) |\ (Current)).range ~ singleton_h (h).comprehension (agent in_range (?, (old Current.deep_twin).range))
	
feature -- Relation Operation Queries

	domain_restricted alias "|<" (ds: SET [G]): like Current
			-- Return a copy of current function with
			-- all pairs whose first values are members of 'ds' kept.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			only_ds_in_new_fun: (Current |\ Result).domain ~ (domain |\ ds)

	domain_restricted_by alias "@<" (g: G): like Current
			-- Return a copy of current funcion with
			-- all pairs whose first values are 'g' kept.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			only_g_in_new_fun: (Current |\ Result).domain ~ (domain |\ singleton_g (g))

	domain_subtracted alias "|<<" (ds: SET [G]): like Current
			-- Return a new copy of current function with
			-- all pairs whose first values are members of 'ds' subtracted.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			no_ds_in_new_fun: (Current |\ Result).domain ~ ds.comprehension (agent in_domain (?, domain))

	domain_subtracted_by alias "@<<" (g: G): like Current
			-- Return a new copy of current function with
			-- all pairs whose first values 'g' subtracted.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			no_ds_in_new_fun: (Current |\ Result).domain ~ singleton_g (g).comprehension (agent in_domain (?, domain))

	item alias "[]" (g: G): H assign put
		require
				domain.has (g)
		ensure then
			current_fun_unchanged: Current ~ old Current.deep_twin
			result_in_range: range.has (Result)

	overriden alias "|<+" (r: like Current): like Current
			-- Return a copy of current function that agrres on 'r'.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
				Result ~ ((Current |<< r.domain) |\/| r)

	overriden_by alias "@<+" (t: TUPLE [g: G; h: H]): like Current
			-- Return a copy of current function that agrres on 'g |-> h'.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
				Result ~ ((Current @<< t.g) |\/| singleton_gh (t.g, t.h))

	range_as_bag: BAG [H]
			-- Returns the range of function as a bag.

	range_restricted alias "|>" (rs: SET [H]): like Current
			-- Return a copy of current function with
			-- all pairs whose second values are members of 'rs' kept.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			only_rs_in_new_fun: (Current |\ Result).range ~ (range |\ rs)

	range_restricted_by alias "@>" (h: H): like Current
			-- Return a copy of current function with
			-- all pairs whose second values are 'h' kept.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			only_h_in_new_fun: (Current |\ Result).range ~ (range |\ singleton_h (h))

	range_subtracted alias "|>>" (rs: SET [H]): like Current
			-- Return a new copy of current function with
			-- all pairs whose second values are members of 'rs' subtracted.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			no_rs_in_new_fun: (Current |\ Result).range ~ rs.comprehension (agent in_range (?, range))

	range_subtracted_by alias "@>>" (h: H): like Current
			-- Return a new copy of current function with
			-- all pairs whose second values are 'h' subtracted.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			new_fun_is_a_subset: Result |<: Current
			no_rs_in_new_fun: (Current |\ Result).range ~ singleton_h (h).comprehension (agent in_range (?, range))
	
feature -- Relation Status Queries

	domain: SET [G]
			-- Return the domain set of function.

	inverse: FUN [H, G]
		require
				is_injection

	is_function: BOOLEAN
			-- Is Current a function?

	is_injection: BOOLEAN
			-- Is Current an injective function?

	range: SET [H]
			-- Return the range set of function.
	
feature -- Set Commands

	difference (other: like Current)
			-- Subtract all mappings in 'other' from current function.
		ensure
			definition: old Current.deep_twin ~ Current |\/| (old Current.deep_twin |/\| other)

	extend (p: PAIR [G, H])
			-- Extend current function with mapping 'g |-> h'
		require
				not domain.has (p.first)
		ensure
				old Current.deep_twin ~ Current - p

	intersect (other: like Current)
			-- Intersect with mappings in 'other'
		ensure
				Current |<: old Current.deep_twin
				Current |<: other
			definition: hold_count (agent in_both_fun (?, old Current.deep_twin, other)) = count

	subtract (p: PAIR [G, H])
			-- Subtract the mapping 'g |-> h' from current function.
		ensure
			case_of_subtraction: (old Current.deep_twin).has (p) implies old Current.deep_twin ~ Current + p
			case_of_no_subtraction: not (old Current.deep_twin).has (p) implies old Current.deep_twin ~ Current

	union (other: like Current)
			-- Extend current function with pairs in 'other'
		require
				(domain |/\| other.domain).is_empty
		ensure
				old Current.deep_twin |<: Current
				other |<: Current
			definition: hold_count (agent in_either_fun (?, old Current.deep_twin, other)) = count
	
feature -- Set Queries

	count alias "#": INTEGER_32
			-- How many pair are in current function?
		ensure
				Result = # domain

	differenced alias "|\" (other: like Current): like Current
			-- Return a new function representing the difference between Current and 'other'.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			definition: Current ~ Result |\/| (Current |/\| other)

	extended alias "+" (p: PAIR [G, H]): like Current
			-- Return a new function representing the addtion of current and 'g'.
		require
				not domain.has (p.first)
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			extension: Current ~ Result - p

	has (p: PAIR [G, H]): BOOLEAN
			-- Does current contain the mapping 'g -> h'?

	intersected alias "|/\|" (other: like Current): like Current
			-- Return a new fun representing the intersection of current and 'other'.
		ensure
			current_set_unchanged: Current ~ old Current.deep_twin
			items_from_both_set: across
					Result as it
				all
					Current.has (create {PAIR [G, H]}.make (it.item.first, it.item.second)) and other.has (create {PAIR [G, H]}.make (it.item.first, it.item.second))
				end

	is_empty: BOOLEAN
			-- Does current function contain no pairs?
		ensure
				Result = (# Current = 0)

	is_subset_of alias "|<:" (other: like Current): BOOLEAN
			-- Is current function a subset of 'other'?
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
				Result = across
					Current as cur
				all
					other.has (create {PAIR [G, H]}.make (cur.item.first, cur.item.second))
				end

	subtracted alias "-" (p: PAIR [G, H]): like Current
			-- Return a new function representing the difference between Current and 't.g |-> t.h'.
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			case_of_subtraction: has (p) implies Current ~ Result + p
			case_of_no_subtraction: not has (p) implies Current ~ Result

	unioned alias "|\/|" (other: like Current): like Current
			-- Return a new function representing the union of current and 'other'.
		require
				(domain |/\| other.domain).is_empty
		ensure
			current_fun_unchanged: Current ~ old Current.deep_twin
			items_from_either_set: across
					Result as it
				all
					Current.has (create {PAIR [G, H]}.make (it.item.first, it.item.second)) or other.has (create {PAIR [G, H]}.make (it.item.first, it.item.second))
				end
	
invariant
	is_a_function: is_function

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)

end -- class FUN

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