note description: "RELATION data structure for both specification and implementation." author: "JSO and JW" date: "$Date$" revision: "$Revision$" class interface REL [G -> attached ANY, H -> attached ANY] create make_empty -- Initialize an empty set. -- (from SET) ensure -- from SET is_empty make_from_tuple_array (a: ARRAY [TUPLE [fst: G; snd: H]]) convert make_from_tuple_array ({attached ARRAY [TUPLE [G, H]]}) feature -- Access generating_type: TYPE [detachable REL [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: REL [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: REL [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 -- Duplication copy (other: REL [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: REL [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: REL [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: REL [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: REL [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: REL [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 REL [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 -- Agent functions in_domain (g: G; dom: SET [G]): BOOLEAN in_range (h: H; ran: SET [H]): BOOLEAN singleton_g (g: G): SET [G] ensure # Result = 1 Result.has (g) singleton_gh (g: G; h: H): REL [G, H] ensure # Result = 1 singleton_h (h: H): SET [H] ensure # Result = 1 Result.has (h) feature -- Commands for implementation difference (other: REL [G, H]) -- Subtract the current set by 'other'. -- (from SET) ensure -- from SET definition: old Current.deep_twin ~ Current |\/| (old Current.deep_twin |/\| other) extend (g: PAIR [G, H]) -- Extend the current set by 'g'. -- (from SET) ensure -- from SET case_of_no_extension: (old Current.deep_twin).has (g) implies old Current.deep_twin ~ Current case_of_extension: not (old Current.deep_twin).has (g) implies old Current.deep_twin ~ Current - g intersect (other: REL [G, H]) -- Intersect current set with 'other'. -- (from SET) ensure -- from SET Current |<: old Current.deep_twin Current |<: other definition: hold_count (agent in_both_set (?, old Current.deep_twin, other)) = count subtract (g: PAIR [G, H]) -- Subtract the current set by 'g'. -- (from SET) ensure -- from SET case_of_subtraction: (old Current.deep_twin).has (g) implies old Current.deep_twin ~ Current + g case_of_no_subtraction: not (old Current.deep_twin).has (g) implies old Current.deep_twin ~ Current union (other: REL [G, H]) -- Extend the current set by 'other'. -- (from SET) ensure -- from SET old Current.deep_twin |<: Current other |<: Current definition: hold_count (agent in_either_set (?, old Current.deep_twin, other)) = count feature -- Commands for relational operations domain_restrict (ds: SET [G]) -- Keep all pairs whose first values are members of 'ds'. ensure new_rel_is_a_subset: Current |<: (old Current.deep_twin) only_ds_in_new_rel: ((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_rel_is_a_subset: Current |<: (old Current.deep_twin) only_g_in_new_rel: ((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_rel_is_a_subset: Current |<: (old Current.deep_twin) no_ds_in_new_rel: ((old Current.deep_twin) |\ (Current)).domain ~ ds.comprehension (agent in_domain (?, (old Current.deep_twin).domain)) domain_subtract_by (g: G) -- Subtract pairs whose first values are 'g'. ensure new_rel_is_a_subset: Current |<: (old Current.deep_twin) no_g_in_new_rel: ((old Current.deep_twin) |\ (Current)).domain ~ singleton_g (g).comprehension (agent in_domain (?, (old Current.deep_twin).domain)) override (r: like Current) -- Update current relation 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 relation such that it aggres on 'g |-> h'. ensure Current ~ ((old Current.deep_twin @<< t.g) |\/| singleton_gh (t.g, t.h)) range_restrict (rs: SET [H]) -- Keep all pairs whose second values are members of 'rs'. ensure new_rel_is_a_subset: Current |<: (old Current.deep_twin) only_rs_in_new_rel: ((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_rel_is_a_subset: Current |<: (old Current.deep_twin) only_h_in_new_rel: ((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_rel_is_a_subset: Current |<: (old Current.deep_twin) no_rs_in_new_rel: ((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_rel_is_a_subset: Current |<: (old Current.deep_twin) no_h_in_new_rel: ((old Current.deep_twin) |\ (Current)).range ~ singleton_h (h).comprehension (agent in_range (?, (old Current.deep_twin).range)) feature -- Constructor make_empty -- Initialize an empty set. -- (from SET) ensure -- from SET is_empty make_from_array (a: ARRAY [PAIR [G, H]]) -- (from SET) ensure -- from SET all_items_are_intended: across Current as it all a.has (it.item) end all_intended_items_added: across a as it all Current.has (it.item) end make_from_tuple_array (a: ARRAY [TUPLE [fst: G; snd: H]]) make_one (a_singleton: PAIR [G, H]) -- make a singleton set -- (from SET) ensure -- from SET count = 1 has (a_singleton) feature -- Conversion to array. as_array: ARRAY [TUPLE [G, H]] ensure Current ~ create {REL [G, H]}.make_from_tuple_array (Result) feature -- Conversion to array. -- as_array: ARRAY[G] -- do -- create Result.make_empty -- across -- Current as c -- loop -- Result.force (c.item, Result.upper + 1) -- end ---- Result.compare_objects -- ensure -- Current ~ create {SET[G]}.make_from_array (Result) -- -- why does this fail in {REL}.t8 -- end set_as_array: ARRAY [PAIR [G, H]] -- (from SET) feature -- Debug output debug_output: STRING_8 -- String that should be displayed in debugger to represent Current. -- (from SET) ensure -- from DEBUG_OUTPUT result_not_void: Result /= Void out: STRING_8 -- New string containing terse printable representation -- of current object -- (from SET) ensure -- from ANY out_not_void: Result /= Void feature -- Equality is_equal (other: REL [G, H]): BOOLEAN -- Is curren set equal to 'other'? -- (from SET) require -- from ANY other_not_void: other /= Void ensure -- from ANY symmetric: Result implies other ~ Current consistent: standard_is_equal (other) implies Result ensure then -- from SET Result = (Current |<: other and then other |<: Current) feature -- Iteration new_cursor: ITERATION_CURSOR [PAIR [G, H]] -- Fresh cursor associated with current structure -- (from SET) 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 -- 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]]): REL [G, H] -- Largest subset of the current set whose elements satisfy exp -- e.g. for set: MSL_SET[STRING], -- (set | agent {STRING}.has_substring ("xy")) = {g:set | g.has_substring("xy")} -- (from SET) ensure -- from SET 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? -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin maximum_result: Result <= count feature -- Queries for relational operations domain_restricted alias "|<" (ds: SET [G]): like Current -- Return a copy of current relation with -- all pairs whose first values are members of 'ds' kept. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current only_ds_in_new_rel: (Current |\ Result).domain ~ (domain |\ ds) domain_restricted_by alias "@<" (g: G): like Current -- Return a copy of current relation with -- all pairs whose first values are 'g' kept. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current only_g_in_new_rel: (Current |\ Result).domain ~ (domain |\ singleton_g (g)) domain_subtracted alias "|<<" (ds: SET [G]): like Current -- Return a new copy of current relation with -- all pairs whose first values are members of 'ds' subtracted. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current no_ds_in_new_rel: (Current |\ Result).domain ~ ds.comprehension (agent in_domain (?, domain)) domain_subtracted_by alias "@<<" (g: G): like Current -- Return a new copy of current relation with -- all pairs whose first values 'g' subtracted. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current no_ds_in_new_rel: (Current |\ Result).domain ~ singleton_g (g).comprehension (agent in_domain (?, domain)) image alias "[]" (g: G): SET [H] -- Retrieve the set of items that are associated with 'g'. ensure current_rel_unchanged: Current ~ old Current.deep_twin Result.is_empty implies not domain.has (g) across Result as r all has (create {PAIR [G, H]}.make_from_tuple ([g, r.item])) end across range.differenced (Result) as r all not has (create {PAIR [G, H]}.make_from_tuple ([g, r.item])) end inverse: REL [H, G] ensure current_rel_unchanged: Current ~ old Current.deep_twin Result.inverse.is_equal (Current) overriden alias "|<+" (r: like Current): like Current -- Return a copy of current relation that agrres on 'r'. ensure current_rel_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 relation that agrres on 'g |-> h'. ensure current_rel_unchanged: Current ~ old Current.deep_twin Result ~ ((Current @<< t.g) |\/| singleton_gh (t.g, t.h)) range_restricted alias "|>" (rs: SET [H]): like Current -- Return a copy of current relation with -- all pairs whose second values are members of 'rs' kept. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current only_rs_in_new_rel: (Current |\ Result).range ~ (range |\ rs) range_restricted_by alias "@>" (h: H): like Current -- Return a copy of current relation with -- all pairs whose second values are 'h' kept. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current only_h_in_new_rel: (Current |\ Result).range ~ (range |\ singleton_h (h)) range_subtracted alias "|>>" (rs: SET [H]): like Current -- Return a new copy of current relation with -- all pairs whose second values are members of 'ds' subtracted. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current no_rs_in_new_rel: (Current |\ Result).range ~ rs.comprehension (agent in_range (?, range)) range_subtracted_by alias "@>>" (h: H): like Current -- Return a new copy of current relation with -- all pairs whose second values are 'h' subtracted. ensure current_rel_unchanged: Current ~ old Current.deep_twin new_rel_is_a_subset: Result |<: Current no_rs_in_new_rel: (Current |\ Result).range ~ singleton_h (h).comprehension (agent in_range (?, range)) feature -- Queries for specification. count alias "#": INTEGER_32 -- Return the cardinality of the set. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin definition: Result = hold_count (agent g_to_true) differenced alias "|\" (other: REL [G, H]): REL [G, H] -- Return a new set representing the difference between Current and 'other'. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin definition: Current ~ Result |\/| (Current |/\| other) extended alias "+" (g: PAIR [G, H]): REL [G, H] -- Return a new set representing the addtion of current and 'g'. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin case_of_no_extension: has (g) implies Current ~ Result case_of_extension: not has (g) implies Current ~ Result - g has (g: PAIR [G, H]): BOOLEAN -- Does the set contain 'g'? -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin definition_1: Result = (hold_count (agent eq (?, g)) = 1) definition_2: Result = across Current as it some it.item ~ g end intersected alias "|/\|" (other: REL [G, H]): REL [G, H] -- Return a new set representing the intersection of current and 'other'. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin items_from_both_set: across Result as it all Current.has (it.item) and other.has (it.item) end is_empty: BOOLEAN -- Is the set empty? -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin Result = (# Current = 0) is_subset_of alias "|<:" (other: REL [G, H]): BOOLEAN -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin Result = across Current as cur all other.has (cur.item) end subtracted alias "-" (g: PAIR [G, H]): REL [G, H] -- Return a new set representing the difference between Current and 'other'. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin case_of_subtraction: has (g) implies Current ~ Result + g case_of_no_subtraction: not has (g) implies Current ~ Result unioned alias "|\/|" (other: REL [G, H]): REL [G, H] -- Return a new set representing the union of current and 'other'. -- (from SET) ensure -- from SET current_set_unchanged: Current ~ old Current.deep_twin items_from_either_set: across Result as it all Current.has (it.item) or other.has (it.item) end feature -- Query and command for arbitrary set members choose_item -- Choose an arbitrary element of the -- set and store it in item -- (from SET) require -- from SET not is_empty ensure -- from SET has (item) chosen chosen: BOOLEAN -- (from SET) item: PAIR [G, H] -- Return an arbitrary member from the set. -- (from SET) require -- from SET not is_empty chosen ensure -- from SET has (Result) remove_item -- Remove an arbitrary member (i.e., 'item') from the set. -- (from SET) require -- from SET not is_empty chosen ensure -- from SET Current ~ old Current.deep_twin - old item not chosen feature -- Status queries domain: SET [G] -- Return the domain set of relation. is_function: BOOLEAN -- Is current relation a function? -- i.e., each domain value maps to at most one value. ensure Result = across domain as d all # image (d.item) = 1 end is_injection: BOOLEAN -- Is current relation an injective function? -- i.e., no two domain values map to the same range vaule. ensure Result = (is_function and inverse.is_function) range: SET [H] -- Return the range set of relation. invariant -- from SET imp.object_comparison no_duplicates: across imp.Lower |..| imp.upper as i all across imp.Lower |..| imp.upper as j all imp [i.item] ~ imp [j.item] implies i.item = j.item end end -- from ANY reflexive_equality: standard_is_equal (Current) reflexive_conformance: conforms_to (Current) end -- class REL
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