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type X;
function {:builtin "MapAdd"} mapadd([X]int, [X]int) : [X]int;
function {:builtin "MapSub"} mapsub([X]int, [X]int) : [X]int;
function {:builtin "MapMul"} mapmul([X]int, [X]int) : [X]int;
function {:builtin "MapDiv"} mapdiv([X]int, [X]int) : [X]int;
function {:builtin "MapMod"} mapmod([X]int, [X]int) : [X]int;
function {:builtin "MapConst"} mapconstint(int) : [X]int;
function {:builtin "MapConst"} mapconstbool(bool) : [X]bool;
function {:builtin "MapAnd"} mapand([X]bool, [X]bool) : [X]bool;
function {:builtin "MapOr"} mapor([X]bool, [X]bool) : [X]bool;
function {:builtin "MapNot"} mapnot([X]bool) : [X]bool;
function {:builtin "MapIte"} mapiteint([X]bool, [X]int, [X]int) : [X]int;
function {:builtin "MapIte"} mapitebool([X]bool, [X]bool, [X]bool) : [X]bool;
function {:builtin "MapLe"} maple([X]int, [X]int) : [X]bool;
function {:builtin "MapLt"} maplt([X]int, [X]int) : [X]bool;
function {:builtin "MapGe"} mapge([X]int, [X]int) : [X]bool;
function {:builtin "MapGt"} mapgt([X]int, [X]int) : [X]bool;
function {:builtin "MapEq"} mapeq([X]int, [X]int) : [X]bool;
function {:builtin "MapIff"} mapiff([X]bool, [X]bool) : [X]bool;
function {:builtin "MapImp"} mapimp([X]bool, [X]bool) : [X]bool;
const FF: [X]bool;
axiom FF == mapconstbool(false);
const TT: [X]bool;
axiom TT == mapconstbool(true);
const MultisetEmpty: [X]int;
axiom MultisetEmpty == mapconstint(0);
function {:inline} MultisetSingleton(x: X) : [X]int
{
MultisetEmpty[x := 1]
}
function {:inline} MultisetPlus(a: [X]int, b: [X]int) : [X]int
{
mapadd(a, b)
}
function {:inline} MultisetMinus(a: [X]int, b: [X]int) : [X]int
{
mapiteint(mapgt(a, b), mapsub(a, b), mapconstint(0))
}
procedure foo() {
var x: X;
assert FF != TT;
assert mapnot(FF) == TT;
assert MultisetSingleton(x) != MultisetEmpty;
assert MultisetPlus(MultisetEmpty, MultisetSingleton(x)) == MultisetSingleton(x);
assert MultisetMinus(MultisetPlus(MultisetEmpty, MultisetSingleton(x)), MultisetSingleton(x)) == MultisetEmpty;
assert MultisetMinus(MultisetEmpty, MultisetSingleton(x)) == MultisetEmpty;
}
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