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https://github.com/Z3Prover/z3
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Typescript high-level api for Sets (#7471)
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Yuantian Ding
GitHub
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a17d4e68eb
commit
4be4067f75
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@ -521,6 +521,133 @@ describe('high-level', () => {
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});
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});
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describe('sets', () => {
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it('Example 1', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const conjecture = set.contains(a).and(set.contains(b)).implies(Z3.EmptySet(Z3.Int.sort()).neq(set));
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await prove(conjecture);
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});
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it('Example 2', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const conjecture = set.contains(a).and(set.contains(b)).implies(Z3.Set.val([a, b], Z3.Int.sort()).subsetOf(set));
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await prove(conjecture);
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});
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it('Example 3', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const conjecture = set.contains(a).and(set.contains(b)).and(Z3.Set.val([a, b], Z3.Int.sort()).eq(set));
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await solve(conjecture);
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});
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it('Intersection 1', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const abset = Z3.Set.val([a, b], Z3.Int.sort());
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const conjecture = set.intersect(abset).subsetOf(abset);
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await prove(conjecture);
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});
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it('Intersection 2', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const abset = Z3.Set.val([a, b], Z3.Int.sort());
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const conjecture = set.subsetOf(set.intersect(abset));
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await solve(conjecture);
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});
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it('Union 1', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const abset = Z3.Set.val([a, b], Z3.Int.sort());
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const conjecture = set.subsetOf(set.union(abset));
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await prove(conjecture);
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});
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it('Union 2', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const abset = Z3.Set.val([a, b], Z3.Int.sort());
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const conjecture = set.union(abset).subsetOf(abset);
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await solve(conjecture);
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});
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it('Complement 1', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const a = Z3.Int.const('a');
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const conjecture = set.complement().complement().eq(set)
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await prove(conjecture);
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});
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it('Complement 2', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const a = Z3.Int.const('a');
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const conjecture = set.contains(a).implies(Z3.Not(set.complement().contains(a)))
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await prove(conjecture);
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});
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it('Difference', async () => {
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const Z3 = api.Context('main');
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const [set1, set2] = Z3.Set.consts('set1 set2', Z3.Int.sort());
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const a = Z3.Int.const('a');
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const conjecture = set1.contains(a).implies(Z3.Not(set2.diff(set1).contains(a)))
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await prove(conjecture);
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});
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it('FullSet', async () => {
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const Z3 = api.Context('main');
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const set = Z3.Set.const('set', Z3.Int.sort());
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const conjecture = set.complement().eq(Z3.FullSet(Z3.Int.sort()).diff(set));
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await prove(conjecture);
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});
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it('SetDel', async () => {
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const Z3 = api.Context('main');
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const empty = Z3.Set.empty(Z3.Int.sort());
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const [a, b] = Z3.Int.consts('a b');
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const conjecture = empty.add(a).add(b).del(a).del(b).eq(empty);
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await prove(conjecture);
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});
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});
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describe('quantifiers', () => {
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it('Basic Universal', async () => {
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const Z3 = api.Context('main');
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@ -86,6 +86,8 @@ import {
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CoercibleToArith,
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NonEmptySortArray,
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FuncEntry,
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SMTSetSort,
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SMTSet,
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} from './types';
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import { allSatisfy, assert, assertExhaustive } from './utils';
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@ -795,6 +797,33 @@ export function createApi(Z3: Z3Core): Z3HighLevel {
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return new ArrayImpl<[DomainSort], RangeSort>(check(Z3.mk_const_array(contextPtr, domain.ptr, value.ptr)));
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},
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};
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const Set = {
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// reference: https://z3prover.github.io/api/html/namespacez3py.html#a545f894afeb24caa1b88b7f2a324ee7e
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sort<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSetSort<Name, ElemSort> {
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return Array.sort(sort, Bool.sort());
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},
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const<ElemSort extends AnySort<Name>>(name: string, sort: ElemSort) : SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(
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check(Z3.mk_const(contextPtr, _toSymbol(name), Array.sort(sort, Bool.sort()).ptr)),
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);
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},
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consts<ElemSort extends AnySort<Name>>(names: string | string[], sort: ElemSort) : SMTSet<Name, ElemSort>[] {
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if (typeof names === 'string') {
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names = names.split(' ');
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}
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return names.map(name => Set.const(name, sort));
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},
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empty<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort> {
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return EmptySet(sort);
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},
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val<ElemSort extends AnySort<Name>>(values: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>[], sort: ElemSort): SMTSet<Name, ElemSort> {
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var result = EmptySet(sort);
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for (const value of values) {
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result = SetAdd(result, value);
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}
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return result;
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}
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}
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////////////////
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// Operations //
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@ -1249,6 +1278,49 @@ export function createApi(Z3: Z3Core): Z3HighLevel {
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>;
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}
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function SetUnion<ElemSort extends AnySort<Name>>(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_set_union(contextPtr, args.map(arg => arg.ast))));
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}
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function SetIntersect<ElemSort extends AnySort<Name>>(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_set_intersect(contextPtr, args.map(arg => arg.ast))));
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}
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function SetDifference<ElemSort extends AnySort<Name>>(a: SMTSet<Name, ElemSort>, b: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_set_difference(contextPtr, a.ast, b.ast)));
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}
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function SetHasSize<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, size: bigint | number | string | IntNum<Name>): Bool<Name> {
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const a = typeof size === 'object'? Int.sort().cast(size) : Int.sort().cast(size);
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return new BoolImpl(check(Z3.mk_set_has_size(contextPtr, set.ast, a.ast)));
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}
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function SetAdd<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort> {
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const arg = set.elemSort().cast(elem as any);
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return new SetImpl<ElemSort>(check(Z3.mk_set_add(contextPtr, set.ast, arg.ast)));
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}
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function SetDel<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort> {
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const arg = set.elemSort().cast(elem as any);
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return new SetImpl<ElemSort>(check(Z3.mk_set_del(contextPtr, set.ast, arg.ast)));
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}
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function SetComplement<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_set_complement(contextPtr, set.ast)));
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}
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function EmptySet<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_empty_set(contextPtr, sort.ptr)));
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}
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function FullSet<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort> {
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return new SetImpl<ElemSort>(check(Z3.mk_full_set(contextPtr, sort.ptr)));
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}
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function isMember<ElemSort extends AnySort<Name>>(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>, set: SMTSet<Name, ElemSort>): Bool<Name> {
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const arg = set.elemSort().cast(elem as any);
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return new BoolImpl(check(Z3.mk_set_member(contextPtr, arg.ast, set.ast)));
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}
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function isSubset<ElemSort extends AnySort<Name>>(a: SMTSet<Name, ElemSort>, b: SMTSet<Name, ElemSort>): Bool<Name> {
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return new BoolImpl(check(Z3.mk_set_subset(contextPtr, a.ast, b.ast)));
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}
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class AstImpl<Ptr extends Z3_ast> implements Ast<Name, Ptr> {
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declare readonly __typename: Ast['__typename'];
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readonly ctx: Context<Name>;
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@ -2536,6 +2608,41 @@ export function createApi(Z3: Z3Core): Z3HighLevel {
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}
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}
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class SetImpl<ElemSort extends Sort<Name>> extends ExprImpl<Z3_ast, ArraySortImpl<[ElemSort], BoolSort<Name>>> implements SMTSet<Name, ElemSort> {
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declare readonly __typename: 'Array';
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elemSort(): ElemSort {
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return this.sort.domain();
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}
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union(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort> {
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return SetUnion(this, ...args);
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}
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intersect(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort> {
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return SetIntersect(this, ...args);
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}
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diff(b: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort> {
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return SetDifference(this, b);
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}
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hasSize(size: string | number | bigint | IntNum<Name>): Bool<Name> {
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return SetHasSize(this, size);
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}
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add(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort> {
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return SetAdd(this, elem);
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}
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del(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort> {
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return SetDel(this, elem);
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}
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complement(): SMTSet<Name, ElemSort> {
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return SetComplement(this);
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}
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contains(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): Bool<Name> {
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return isMember(elem, this);
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}
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subsetOf(b: SMTSet<Name, ElemSort>): Bool<Name> {
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return isSubset(this, b);
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}
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}
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class QuantifierImpl<
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QVarSorts extends NonEmptySortArray<Name>,
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QSort extends BoolSort<Name> | SMTArraySort<Name, QVarSorts>,
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@ -2917,6 +3024,7 @@ export function createApi(Z3: Z3Core): Z3HighLevel {
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Real,
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BitVec,
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Array,
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Set,
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////////////////
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// Operations //
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@ -2979,6 +3087,18 @@ export function createApi(Z3: Z3Core): Z3HighLevel {
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// Loading //
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/////////////
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ast_from_string,
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SetUnion,
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SetIntersect,
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SetDifference,
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SetHasSize,
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SetAdd,
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SetDel,
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SetComplement,
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EmptySet,
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FullSet,
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isMember,
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isSubset,
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};
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cleanup.register(ctx, () => Z3.del_context(contextPtr));
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return ctx;
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@ -357,6 +357,8 @@ export interface Context<Name extends string = 'main'> {
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readonly BitVec: BitVecCreation<Name>;
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/** @category Expressions */
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readonly Array: SMTArrayCreation<Name>;
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/** @category Expressions */
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readonly Set: SMTSetCreation<Name>;
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////////////////
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// Operations //
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@ -611,6 +613,39 @@ export interface Context<Name extends string = 'main'> {
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substitute(t: Expr<Name>, ...substitutions: [Expr<Name>, Expr<Name>][]): Expr<Name>;
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simplify(expr: Expr<Name>): Promise<Expr<Name>>;
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/** @category Operations */
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SetUnion<ElemSort extends AnySort<Name>>(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort>;
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/** @category Operations */
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SetIntersect<ElemSort extends AnySort<Name>>(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort>;
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/** @category Operations */
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SetDifference<ElemSort extends AnySort<Name>>(a: SMTSet<Name, ElemSort>, b: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort>;
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/** @category Operations */
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SetHasSize<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, size: bigint | number | string | IntNum<Name>): Bool<Name>;
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/** @category Operations */
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SetAdd<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort>;
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/** @category Operations */
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SetDel<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>, elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort>;
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/** @category Operations */
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SetComplement<ElemSort extends AnySort<Name>>(set: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort>;
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/** @category Operations */
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EmptySet<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort>;
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/** @category Operations */
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FullSet<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort>;
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/** @category Operations */
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isMember<ElemSort extends AnySort<Name>>(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>, set: SMTSet<Name, ElemSort>): Bool<Name>;
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/** @category Operations */
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isSubset<ElemSort extends AnySort<Name>>(a: SMTSet<Name, ElemSort>, b: SMTSet<Name, ElemSort>): Bool<Name>;
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}
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export interface Ast<Name extends string = 'main', Ptr = unknown> {
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@ -1568,6 +1603,54 @@ export interface SMTArray<
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): SMTArray<Name, DomainSort, RangeSort>;
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}
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/**
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* Set Implemented using Arrays
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*
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* @typeParam ElemSort The sort of the element of the set
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* @category Sets
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*/
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export type SMTSetSort<Name extends string = 'main', ElemSort extends AnySort<Name> = Sort<Name>> = SMTArraySort<Name, [ElemSort], BoolSort<Name>>;
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/** @category Sets*/
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export interface SMTSetCreation<Name extends string> {
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sort<ElemSort extends AnySort<Name>>(elemSort: ElemSort): SMTSetSort<Name, ElemSort>;
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const<ElemSort extends AnySort<Name>>(name: string, elemSort: ElemSort): SMTSet<Name, ElemSort>;
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consts<ElemSort extends AnySort<Name>>(names: string | string[], elemSort: ElemSort): SMTSet<Name, ElemSort>[];
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empty<ElemSort extends AnySort<Name>>(sort: ElemSort): SMTSet<Name, ElemSort>;
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val<ElemSort extends AnySort<Name>>(values: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>[], sort: ElemSort): SMTSet<Name, ElemSort>;
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}
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/**
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* Represents Set expression
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*
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* @typeParam ElemSort The sort of the element of the set
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* @category Arrays
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*/
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export interface SMTSet<Name extends string = 'main', ElemSort extends AnySort<Name> = Sort<Name>> extends Expr<Name, SMTSetSort<Name, ElemSort>, Z3_ast> {
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readonly __typename: 'Array';
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elemSort(): ElemSort;
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union(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort>;
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intersect(...args: SMTSet<Name, ElemSort>[]): SMTSet<Name, ElemSort>;
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diff(b: SMTSet<Name, ElemSort>): SMTSet<Name, ElemSort>;
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hasSize(size: bigint | number | string | IntNum<Name>): Bool<Name>;
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add(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort>;
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del(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): SMTSet<Name, ElemSort>;
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complement(): SMTSet<Name, ElemSort>;
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contains(elem: CoercibleToMap<SortToExprMap<ElemSort, Name>, Name>): Bool<Name>;
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subsetOf(b: SMTSet<Name, ElemSort>): Bool<Name>;
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}
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/**
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* Defines the expression type of the body of a quantifier expression
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*
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