############################################################################
#
#	File:     sets.icn
#
#	Subject:  Procedures for set manipulation
#
#	Author:   Alan Beale
#
#	Date:     August 7, 1999
#
############################################################################
#
#   This file is in the public domain.
#
############################################################################
#
#	Contributor:  Ralph E. Griswold
#
############################################################################
#
#	cset2set(c)	returns a set that contains the individual
#			characters in cset c.
#
#	domain(T)	returns the domain of the function defined by the
#			table T.
#
#	inverse(T, x)	returns the inverse of the function defined by the
#			table T.  If x is null, it's the functional inverse.
#			If x is an empty list, it's the relational inverse.
#			If x is an empty set, it the relational inverse, but
#			with each table member as a set instead of a list.
#
#	pairset(T)	converts the table T to an equivalent set of ordered
#			pairs.
#
#	range(T)	returns the range of the function defined by the
#			table T.
#  
#	seteq(S1, S2)	tests equivalence of sets S1 and S2.
#
#	setlt(S1, S2)	tests strict inclusion of S1 in S2.
#
#       setle(S1, S2)   tests non-strict inclusion of S1 in S2
#
#	simage(S)	string image of set
#
############################################################################

procedure cset2set(cs)			#: set of characters
   local result

   result := set()
   every insert(result, !cs)

   return result

end

procedure pairset(T)			#: set of table pairs
    return set(sort(T))
end

procedure domain(T)			#: domain of table
    local dom

    dom := set()
    every insert(dom, key(T))
    return dom
end

procedure range(T)			#: range of table
    local ran

    ran := set()
    every insert(ran, !T)
    return ran
end

procedure inverse(T, Default)		#: inverse of table function
    local inv, delem, relem

    inv := table(Default)
    every delem := key(T) do {
        if type(Default) == "list" then
          if member(inv, relem := T[delem]) then
            put(inv[relem], delem)
          else inv[relem] := [delem]
        else if type(Default) == "set" then
          if member(inv, relem := T[delem]) then
            insert(inv[relem], delem)
          else inv[relem] := set([delem])
        else inv[T[delem]] := delem
    }
    return inv
end

procedure seteq(set1, set2)		#: set equivalence
   local x

   if *set1 ~= *set2 then fail
   every x := !set1 do
      if not member(set2, x) then fail
   return set2

end

procedure setlt(set1, set2)		#: S1 is a proper subset of S2
   local x

   if *set1 >= *set2 then fail
   every x := !set1 do
      if not member(set2, x) then fail
   return set2

end


procedure setle(set1, set2)		#: S1 is a subset of S2
   local x

   if *set1 > *set2 then fail
   every x := !set1 do
      if not member(set2, x) then fail
   return set2

end

procedure simage(set)			#: string image of set
   local result

   result := ""

   every result ||:= image(!set) || ", "

   return "{ " || result[1:-2] || " }"

end