extension PureXML.Schema {
/// XSD 1.0 "Particle Valid (Restriction)" for the common cases: a complex
/// type derived by restriction must have a content model that accepts a
/// subset of its base's. Covers element-vs-element name matching,
/// element-vs-wildcard admission, wildcard narrowing, occurrence-range
/// subsumption, and the group recursions (sequence/all order-preserving with
/// emptiable skips, choice mapping, sequence-into-choice, sequence-into-all).
/// The spec's effective-total-range arithmetic for MapAndSum is approximated
/// by per-particle checks, a documented simplification.
enum ParticleRestriction {
/// The reason a restriction's content is not a valid subset of its
/// base's, or nil when it is. `types` resolves an element's
/// ``ElementType/typeReference`` so element-vs-element pairs can check that
/// the restricting type derives from the base's (NameAndTypeOK).
static func violation(restricted: ContentType, base: ContentType, types: [String: ElementType], derivation: [String: TypeDerivation]) -> String? {
switch (restricted, base) {
case (.empty, .empty), (.simpleContent, _), (_, .simpleContent):
nil
case let (.empty, .elementOnly(baseParticle)), let (.empty, .mixed(baseParticle)):
emptiable(baseParticle) ? nil : "the base content is required, so the restriction cannot be EMPTY"
case (.mixed, .elementOnly):
"a restriction cannot add mixed content to an element-only base"
case let (.elementOnly(restrictedParticle), .empty):
// A content-free particle (an empty group, or one whose members all
// have maxOccurs=0) accepts only the empty sequence, so it is a valid
// restriction of EMPTY; only a particle that can contribute a child is
// adding content.
contentFree(restrictedParticle) ? nil : "the base content is EMPTY, so the restriction cannot add content"
case (.mixed, .empty):
"the base content is EMPTY, so the restriction cannot add content"
case let (.elementOnly(restrictedParticle), .elementOnly(baseParticle)),
let (.elementOnly(restrictedParticle), .mixed(baseParticle)),
let (.mixed(restrictedParticle), .mixed(baseParticle)):
// The W3C restriction algorithm is defined over the normalized content
// model (pointless particles eliminated): a `maxOccurs=0` member
// removed, a `{1,1}` single-member group unwrapped, a nested
// same-compositor `{1,1}` group spliced. Without this, e.g. a base
// `sequence(any{2,3})` is not seen as the wildcard it equals.
valid(restrictedParticle.normalized(), baseParticle.normalized(), types, derivation)
? nil
: "the restricted content model is not a subset of the base's"
}
}
/// Whether `restricted` accepts a subset of `base` (the pairwise check).
///
/// Occurrence subsumption (`rangeSubsumed`) is applied only to the
/// same-kind pairings (element/element, wildcard/wildcard, group/group) and
/// element/wildcard, where the two particles' own occurrence ranges are
/// directly comparable. For the cross-kind pairings (element/group and
/// group/element via RecurseAsIfGroup; group/wildcard via
/// NSRecurseCheckCardinality) the occurrence is matched *inside* the case,
/// against a member or as an effective total range, never the derived
/// particle's own occurrence against the base group/wildcard's. Applying the
/// outer check there over-rejects: e.g. `sequence(e1{2,3})` restricting
/// `sequence(e1{1,3},...)` once the pointless single-member group is
/// normalized to the bare `e1{2,3}` (`3 > 1` against the base sequence).
static func valid(_ restricted: Particle, _ base: Particle, _ types: [String: ElementType], _ derivation: [String: TypeDerivation]) -> Bool {
// A restriction that can never contribute a child (its own `maxOccurs=0`,
// or a group whose every member is content-free) accepts only the empty
// sequence, so it is a valid restriction of any emptiable base. Checked
// before the structural cases, which would otherwise recurse into members
// that never occur and wrongly reject (e.g. a `maxOccurs="0"` sequence
// whose members have their own non-trivial occurrences).
if contentFree(restricted) {
return emptiable(base)
}
// NameAndTypeOK clause 1 over the DECLARED references: when both particles were
// compiled from ``, section 3.9.6 pairs the declared
// element declarations, and Elt:Elt requires the same {name} and {target
// namespace}. Substitution has no allowance here: a restriction that swaps a
// head for one of its substitution-group members names a different declaration
// and is invalid (elemZ026), even though the expanded terms would line up.
return declaredReferencesCompatible(restricted, base)
&& structuralValid(restricted, base, types, derivation)
}
/// The section 3.9.6 pairing table over the compiled terms, dispatched by the
/// (derived, base) term kinds once the outer gates (content-free, declared
/// references) have run.
private static func structuralValid(_ restricted: Particle, _ base: Particle, _ types: [String: ElementType], _ derivation: [String: TypeDerivation]) -> Bool {
switch (restricted.term, base.term) {
case let (.element(rName, _, rTypeName, rValue, rBlock, rNil), .element(bName, bType, bTypeName, bValue, bBlock, bNil)):
// NameAndTypeOK: beyond name, occurrence, and type derivation, the
// restriction's {disallowed substitutions} must be a superset of the
// base's (it may block more, never fewer); if the base is fixed the
// restriction must be fixed to the same value; and it may not be
// nillable unless the base element is.
return rangeSubsumed(restricted, base)
&& sameName(rName, bName)
&& rBlock.isSuperset(of: bBlock)
&& (!rNil || bNil)
&& fixedValueOK(rValue, bValue, bType, types)
&& elementTypeRestrictionOK(rTypeName, bTypeName, types, derivation)
case let (.element(name, _, _, _, _, _), .wildcard(wildcard)):
return rangeSubsumed(restricted, base) && wildcard.admits(name)
case let (.wildcard(restrictedWildcard), .wildcard(baseWildcard)):
return rangeSubsumed(restricted, base) && narrows(restrictedWildcard, baseWildcard)
case let (.element, .group(baseGroup)):
return elementRestrictsGroup(restricted, base, baseGroup, types, derivation)
case (.group, .element):
// XSD 1.0 §3.9.6 "Particle Valid (Restriction)" defines NO case for a
// derived group against a base element: the only element/group pairing
// is the reverse (an element restricting a base group, via
// RecurseAsIfGroup). A derived group that can contribute content
// therefore never validly restricts a single base element, regardless
// of how its leaves are named or counted. (A CONTENT-FREE derived group
// was already accepted above as a valid restriction of any emptiable
// base; only a content-bearing one reaches here.) This is the spec rule
// the corpus enforces -- e.g. a `choice(seq(e1), e2, e3)` restricting a
// `choice(e1, e2, e3)` is invalid because the derived `seq(e1)` branch
// has no base element it can validly restrict (particlesHb011).
return false
case let (.group(restrictedGroup), .group(baseGroup)) where restrictedGroup.compositor == .sequence && baseGroup.compositor == .choice:
// MapAndSum (Sequence:Choice, XSD 1.0 §3.9.6): each derived particle is
// a valid restriction of some base branch, AND the derived sequence's
// occurrence count times its number of particles is within the base
// choice's occurrence range. The outer occurrence subsumption used by
// the same-compositor cases is wrong here (it would compare a derived
// `sequence{2,4}` directly to a base `choice{3,9}`); the count-product
// is the spec's measure, deliberately stricter than a pure subset.
let members = restrictedGroup.particles.filter { $0.maxOccurs != 0 }
let branches = baseGroup.particles.filter { $0.maxOccurs != 0 }
return rangeWithinWildcard(
derivedMin: restricted.minOccurs * members.count,
derivedMax: restricted.maxOccurs.map { $0 * members.count },
wildcardMin: base.minOccurs,
wildcardMax: base.maxOccurs,
)
&& members.allSatisfy { member in branches.contains { valid(member, $0, types, derivation) } }
case let (.group(restrictedGroup), .group(baseGroup)):
// A content-free derived group was already handled above; here the
// derived group can contribute content, so its outer occurrence must be
// subsumed and its members must map onto the base's.
return rangeSubsumed(restricted, base) && groupValid(restrictedGroup, baseGroup, types, derivation)
case let (.group, .wildcard(wildcard)):
// NSRecurseCheckCardinality: every leaf the group can contain is
// admitted by the wildcard (an element by name, a nested wildcard by
// narrowing), AND the group's effective total occurrence range is
// within the wildcard's occurrence range.
return leavesAdmitted(restricted, by: wildcard)
&& rangeWithinWildcard(
derivedMin: restricted.effectiveOccurrenceMin(),
derivedMax: restricted.effectiveOccurrenceMax(),
wildcardMin: base.minOccurs,
wildcardMax: base.maxOccurs,
)
default:
return false
}
}
static func groupValid(_ restricted: Group, _ base: Group, _ types: [String: ElementType], _ derivation: [String: TypeDerivation]) -> Bool {
// A particle that can never occur (maxOccurs=0) contributes nothing to the
// language, so it is removed before mapping (a "pointless particle"). Left
// in, it would wrongly consume a base particle and starve the particles
// after it (e.g. `(e1 maxOccurs=0, e2)` restricting `(any)`).
let restrictedParticles = restricted.particles.filter { $0.maxOccurs != 0 }
let baseParticles = base.particles.filter { $0.maxOccurs != 0 }
switch (restricted.compositor, base.compositor) {
case (.sequence, .sequence), (.all, .all):
return recurse(restrictedParticles, baseParticles, skippedMustBeEmptiable: true, types, derivation)
case (.choice, .choice):
// RecurseLax: an order-preserving mapping (W3C requires it; a choice
// `(b|a)` is NOT a valid restriction of `(a|b)`), but skipped base
// branches need not be emptiable. The base's substitution-group
// expansion must therefore be in document order for this to be right.
return recurse(restrictedParticles, baseParticles, skippedMustBeEmptiable: false, types, derivation)
case (.sequence, .choice):
// RecurseAsIfGroup for an element against a base choice arrives here as a
// one-particle synthetic sequence: each derived particle fits some base
// branch. (A genuine multi-particle sequence restricting a choice is
// handled by MapAndSum at the particle level, where the occurrence
// count-product is available.)
return restrictedParticles.allSatisfy { particle in
baseParticles.contains { valid(particle, $0, types, derivation) }
}
case (.sequence, .all):
// RecurseUnordered: map onto distinct base particles in any order.
return recurseUnordered(restrictedParticles, baseParticles, types, derivation)
default:
return false
}
}
/// Whether a particle can never contribute a child element or wildcard: it
/// has `maxOccurs=0`, or is a group all of whose members are content-free
/// (an empty group included). Its only legal content is the empty sequence.
static func contentFree(_ particle: Particle) -> Bool {
if particle.maxOccurs == 0 {
return true
}
switch particle.term {
case .element, .wildcard:
return false
case let .group(group):
return group.particles.allSatisfy(contentFree)
}
}
/// Order-preserving mapping of the restricted particles onto the base's.
/// A skipped base particle must be emptiable for sequence/all (Recurse);
/// for choice (RecurseLax) skipping is free.
private static func recurse(
_ restricted: [Particle],
_ base: [Particle],
skippedMustBeEmptiable: Bool,
_ types: [String: ElementType],
_ derivation: [String: TypeDerivation],
) -> Bool {
var baseIndex = 0
for particle in restricted {
var matched = false
while baseIndex < base.count {
let candidate = base[baseIndex]
baseIndex += 1
if valid(particle, candidate, types, derivation) {
matched = true
break
}
if skippedMustBeEmptiable, !emptiable(candidate) {
return false
}
}
if !matched {
return false
}
}
if skippedMustBeEmptiable {
while baseIndex < base.count {
if !emptiable(base[baseIndex]) {
return false
}
baseIndex += 1
}
}
return true
}
/// Any-order mapping onto distinct base particles; unmapped base
/// particles must be emptiable.
private static func recurseUnordered(_ restricted: [Particle], _ base: [Particle], _ types: [String: ElementType], _ derivation: [String: TypeDerivation]) -> Bool {
var used = [Bool](repeating: false, count: base.count)
for particle in restricted {
guard let index = base.indices.first(where: { !used[$0] && valid(particle, base[$0], types, derivation) }) else {
return false
}
used[index] = true
}
return base.indices.allSatisfy { used[$0] || emptiable(base[$0]) }
}
/// Occurrence-range subsumption: the restriction may not occur less often
/// than the base requires, nor more often than the base allows.
private static func rangeSubsumed(_ restricted: Particle, _ base: Particle) -> Bool {
guard restricted.minOccurs >= base.minOccurs else { return false }
guard let baseMax = base.maxOccurs else { return true }
guard let restrictedMax = restricted.maxOccurs else { return false }
return restrictedMax <= baseMax
}
/// Whether a particle can match no children at all.
static func emptiable(_ particle: Particle) -> Bool {
if particle.minOccurs == 0 {
return true
}
switch particle.term {
case .element, .wildcard:
return false
case let .group(group):
switch group.compositor {
case .sequence, .all:
return group.particles.allSatisfy(emptiable)
case .choice:
return group.particles.contains(where: emptiable)
}
}
}
/// Whether the restricted wildcard admits no namespace the base refuses.
/// Whether `restricted` is a valid subset of `base` (Wildcard Subset): its
/// processContents is at least as strong and its namespace constraint is
/// narrower or equal. Shared with attribute-wildcard restriction.
static func narrows(_ restricted: Wildcard, _ base: Wildcard) -> Bool {
// Wildcard Subset (XSD 1.0 §3.10.6): the restriction's processContents
// must be identical to or STRONGER than the base's (strict > lax > skip);
// a restriction may not weaken validation. Namespace narrowing is below.
guard processContentsRank(restricted.processContents) >= processContentsRank(base.processContents) else {
return false
}
// Wildcard Subset (XSD 1.0 §3.10.6 / Errata E1-10): the restriction's
// namespace constraint must admit only what the base does. Both `not`
// forms exclude absent.
return switch (restricted.namespace, base.namespace) {
case (_, .any):
true
case let (.enumerated(narrow), .enumerated(wide)):
narrow.isSubset(of: wide)
case let (.enumerated(narrow), .notNamespace(excluded)):
!narrow.contains(excluded) && !narrow.contains("")
case let (.enumerated(narrow), .notAbsent):
!narrow.contains("")
case let (.notNamespace(narrow), .notNamespace(wide)):
narrow == wide
case (.notNamespace, .notAbsent), (.notAbsent, .notAbsent):
true
default:
false
}
}
/// NameAndTypeOK clause 1 over the DECLARED references: when both particles were
/// compiled from ``, the declared names must match. A
/// particle without a declared reference (a local element, a group written out
/// in place) is unconstrained here and checked by its structural case instead.
private static func declaredReferencesCompatible(_ restricted: Particle, _ base: Particle) -> Bool {
guard let restrictedDeclared = restricted.declaredReference,
let baseDeclared = base.declaredReference
else {
return true
}
return sameName(restrictedDeclared, baseDeclared)
}
private static func sameName(_ lhs: PureXML.Model.QualifiedName, _ rhs: PureXML.Model.QualifiedName) -> Bool {
lhs.localName == rhs.localName && (lhs.namespaceURI ?? "") == (rhs.namespaceURI ?? "")
}
/// Whether every leaf a particle can contain is admitted by `wildcard`: an
/// element by name, a nested wildcard by narrowing.
private static func leavesAdmitted(_ particle: Particle, by wildcard: Wildcard) -> Bool {
switch particle.term {
case let .element(name, _, _, _, _, _): wildcard.admits(name)
case let .wildcard(inner): narrows(inner, wildcard)
case let .group(group): group.particles.allSatisfy { leavesAdmitted($0, by: wildcard) }
}
}
/// Whether a derived effective total range fits within a base wildcard's
/// occurrence range: at least the wildcard's minimum, at most its maximum.
static func rangeWithinWildcard(derivedMin: Int, derivedMax: Int?, wildcardMin: Int, wildcardMax: Int?) -> Bool {
guard derivedMin >= wildcardMin else { return false }
guard let wildcardMax else { return true }
guard let derivedMax else { return false }
return derivedMax <= wildcardMax
}
}
}