Constraint Subsumption and Overload Resolution

When multiple constrained function templates are viable for a call, the compiler uses subsumption --- a partial ordering on constraints --- to select the most constrained candidate. This mechanism eliminates the ambiguity problems that plagued SFINAE-based overload sets and enables Clean, readable overloading based on concept constraints.

Partial Ordering of Constraints

The C++ standard defines a partial ordering on constraints called subsumption [N4950 §13.5.4]. Given two constraints $P$ and $Q$ We say $P$ subsumes $Q$ (written $P \succeq Q$ ) if $P$ is at least as restrictive as $Q$ --- meaning that every set of template arguments satisfying $P$ also satisfies $Q$ .

Formally, for a constraint $P$ to subsume a constraint $Q$ :

\forall \mathrm{substitutions S : P(S) \implies Q(S)

This is a structural comparison performed by the compiler, not a runtime check. The rules for Determining subsumption between constraint conjunctions and disjunctions are [N4950 §13.5.4.1]:

$P$	$Q$	$P$ subsumes $Q$ ?
$A \land B$	$A$	Yes (conjunction subsumes each conjunct)
$A$	$A \land B$	No (the conjunct is less restrictive)
$A$	$A \lor B$	Yes (disjunction is subsumed by each disjunct)
$A \lor B$	$A$	No (the disjunction is less restrictive)
$A$	$A$	Yes (identical constraints subsume each other)
$A$	$B$	Indeterminate (incomparable unless one implies the other)

Proof: Partially-Ordered Overloads Are Preferred

Claim: When two viable function templates have constraints $P$ and $Q$ And $P$ subsumes $Q$ but $Q$ does not subsume $P$ The overload with constraint $P$ is unambiguously preferred.

Proof:

By [N4950 §13.5.4/1], a constraint $P$ subsumes a constraint $Q$ if, after normalizing both constraints into sets of atomic constraints, every atomic constraint in $P$ “s normalized set is subsumed by at least one atomic constraint in $Q$ ‘s normalized set, using the template parameter mapping.
Subsumption is a preorder (reflexive and transitive) on the set of constraints. It is not a total order --- some constraints are incomparable.
The partial ordering of constraints induces a partial ordering on the set of viable function templates. If $f_1$ has constraint $P$ and $f_2$ has constraint $Q$ And $P \succ Q$ (strict subsumption), then $f_1$ is more constrained than $f_2$ [N4950 §13.10.3.2/1].
[N4950 §13.10.3.2/1] states: “a viable function $F_1$ is defined to be a better function than another viable function $F_2$ if … $F_1$ ’s associated constraints subsume $F_2$ ‘s associated constraints and $F_2$ ‘s associated constraints do not subsume $F_1$ ‘s associated constraints.”
The “better function” rule is applied in overload resolution [N4950 §13.10.3]. If exactly one viable function is better than all others, it is selected. If no unique best function exists, the call is ambiguous.
When $P \succ Q$ strictly (subsumes but is not subsumed by), $f_1$ is the unique best function. No ambiguity arises.
When $P \succeq Q$ and $Q \succeq P$ (both subsume each other, i.e., the constraints are equivalent), neither function is strictly better than the other. The call is ambiguous.
When neither $P \succeq Q$ nor $Q \succeq P$ (the constraints are incomparable), neither function is better than the other. The call is ambiguous.

Therefore, partially-ordered overloads with strict subsumption are unambiguously resolved, while Equivalent or incomparable constraints produce ambiguity. $\blacksquare$

Corollary: For subsumption to work correctly, constraints must be written in a structurally Comparable form. Two constraints that are logically equivalent but structurally different are Incomparable for subsumption purposes, leading to ambiguity.

Corollary: Negated constraints (!C) are incomparable with all other constraints because Negation does not preserve subsumption ordering. A constraint !std::integral<T> is incomparable With std::floating_point<T> even though, set-theoretically, every floating-point type is Non-integral.

Normal Form of Constraints

Before performing subsumption, the compiler normalizes constraints into a disjunctive normal form (DNF) --- a disjunction of conjunctions of atomic constraints [N4950 §13.5.4.1]:

C = (a_1 \land a_2 \land \ldots) \lor (b_1 \land b_2 \land \ldots) \lor \ldots

Each disjunct $(a_1 \land a_2 \land \ldots)$ is a conjunction of atomic constraints. The DNF Representation is unique (up to reordering) for a given constraint expression.

Normalization algorithm:

Replace each concept-id Concept<T, Args...> with its definition’s normalized constraint (recursively).
Apply the distributive law to convert to DNF:

$(A \land B) \lor C \to (A \lor C) \land (B \lor C)$

Collect atomic constraints within each conjunction.
Remove duplicate atomic constraints within each conjunction.

Example:

template<typename T>
concept A = std::integral<T>;

template<typename T>
concept B = std::signed_integral<T>;

template<typename T>
concept C = A<T> && (B<T> || std::floating_point<T>);

The normalization of C<T> proceeds as follows:

Expand A<T> to std::integral<T>.
Expand B<T> to std::signed_integral<T>.
C<T> becomes std::integral<T> && (std::signed_integral<T> || std::floating_point<T>).
Apply distributive law: (std::integral<T> && std::signed_integral<T>) || (std::integral<T> && std::floating_point<T>).

The DNF is two disjuncts:

Disjunct 1: std::integral<T> && std::signed_integral<T>
Disjunct 2: std::integral<T> && std::floating_point<T>

For subsumption, the compiler checks that every atomic constraint in each disjunct of $P$ is Subsumed by at least one atomic constraint in the corresponding disjunct of $Q$ .

Atomic Constraints and Their Combination

An atomic constraint is the smallest unit of constraint checking [N4950 §13.5.4.1]. It consists Of an expression and a template parameter mapping. The atomic constraint is satisfied if and only If:

The template arguments are successfully substituted into the expression.
The resulting expression is true.

An atomic constraint is identified by its structural form --- the expression tree, including the Template parameter mapping. Two atomic constraints are the same if and only if their expression Trees are identical (same tokens, same structure) and their template parameter mappings are Equivalent.

Critical implication: Two atomic constraints that are logically equivalent but syntactically Different are considered different constraints. For example:

template<typename T>
concept IsInt1 = std::is_same_v<T, int>;

template<typename U>
concept IsInt2 = std::is_same_v<U, int>;

When comparing IsInt1<T> and IsInt2<T>The compiler maps T (from the first concept) to T (from the second concept) and then compares the expression trees. Both reduce to std::is_same_v<T, int>So they are structurally identical and subsume each other.

But consider:

template<typename T>
concept IsIntA = std::integral<T> && std::is_same_v<T, int>;

template<typename T>
concept IsIntB = std::is_same_v<T, int> && std::integral<T>;

Both normalize to the same set of atomic constraints: {std::integral<T>, std::is_same_v<T, int>}. The ordering of conjunctions does not matter for normalization. Both subsume each other.

However:

template<typename T>
concept IsIntC = requires(T t) { requires std::is_same_v<T, int>; };

This introduces a requires-expression with a local parameter t. The atomic constraint inside the requires-expression has a different structural form than std::is_same_v<T, int>. Even though They are logically equivalent, the compiler considers them structurally different, and they are Incomparable for subsumption.

How the Compiler Selects the Most Constrained Viable Function

When resolving a call to a constrained function template, the compiler follows this process [N4950 §13.10.3]:

Name lookup finds all candidate functions.
Template argument deduction determines the template arguments for each viable candidate.
Constraint satisfaction eliminates candidates whose constraints are not satisfied.
Partial ordering by constraints selects the most constrained candidate among the remaining viable functions.

If, after constraint subsumption, exactly one candidate is more constrained than all others, that Candidate is selected. If no unique most-constrained candidate exists (i.e., two candidates are Equally constrained or incomparable), the call is ambiguous and the program is ill-formed.

#include <concepts>
#include <iostream>
#include <string>
#include <vector>

// Less constrained: only requires integral
template<std::integral T>
void process(T value) {
    std::cout << "integral: " << value << "\n";
}

// More constrained: requires integral AND signed
template<std::integral T>
    requires std::is_signed_v<T>
void process(T value) {
    std::cout << "signed integral: " << value << "\n";
}

int main() {
    process(42);            // Calls the more constrained overload (signed)
    process(42u);           // Calls the less constrained overload (unsigned)

    // process(3.14);       // Error: no viable overload (not integral)
}

Output:

signed integral: 42
integral: 42

The second overload subsumes the first because std::integral<T> && std::is_signed_v<T> implies std::integral<T>.

Interaction with Non-Template Overloads

When a non-template function competes with a constrained function template, the standard overload Resolution rules apply [N4950 §13.10.3]. A non-template function is preferred over a function Template when the signatures are otherwise equally good matches. However, if the non-template Function’s signature requires an implicit conversion that the template does not, the template may be Preferred.

#include <concepts>
#include <iostream>

void process(int x) {
    std::cout << "non-template int: " << x << "\n";
}

template<std::integral T>
void process(T x) {
    std::cout << "template integral: " << x << "\n";
}

int main() {
    process(42);    // Calls non-template: exact match on non-template preferred
    process(42L);   // Calls template: long matches T exactly; non-template requires conversion
    // process(3.14); // Error: template not viable (not integral), no non-template match
}

Output:

non-template int: 42
template integral: 42

The rule is: when both a non-template and a template are viable, the non-template is preferred if And only if the argument conversions are equally good [N4950 §13.10.3.2]. For process(42)Both Are exact matches, so the non-template wins. For process(42L)The template is an exact match (T = long) while the non-template requires a narrowing conversion (long to int), so the Template wins.

Key insight: Constraints do not make a template “better” than a non-template function. The Partial ordering rules for constraints only apply between constrained function templates. A Non-template function and a constrained template are compared using the standard overload resolution Tie-breaking rules (non-template preferred on a tie).

#include <concepts>
#include <iostream>

// Overloaded on signed vs unsigned via concepts
template<std::signed_integral T>
void classify(T x) {
    std::cout << "signed: " << x << "\n";
}

template<std::unsigned_integral T>
void classify(T x) {
    std::cout << "unsigned: " << x << "\n";
}

// Non-template overload for bool specifically
void classify(bool b) {
    std::cout << "bool: " << b << "\n";
}

int main() {
    classify(42);     // signed: 42
    classify(42u);    // unsigned: 42
    classify(true);   // bool: 1 (non-template wins; bool matches bool exactly)
}

Note that bool satisfies std::signed_integral (on most implementations where bool is treated As a signed integral type). But the non-template overload for bool is preferred because it is an Exact match without requiring template instantiation.

Subsumption with Standard Concepts

The standard library concepts in <concepts> are carefully designed so that subsumption works Correctly. For example [N4950 §18.4]:

std::integral<T> subsumes std::integral<T> (identity).
std::signed_integral<T> subsumes std::integral<T> (every signed integral is integral).
std::integral<T> does not subsume std::signed_integral<T> (not every integral is signed).
std::forward_iterator<T> subsumes std::input_iterator<T> (every forward iterator is an input iterator).

This hierarchy enables natural overload sets:

#include <concepts>
#include <forward_list>
#include <vector>
#include <iostream>

template<std::input_iterator It>
void advance(It& it, std::iter_difference_t<It> n) {
    std::cout << "single-pass advance\n";
    while (n-- > 0) ++it;
}

template<std::forward_iterator It>
void advance(It& it, std::iter_difference_t<It> n) {
    std::cout << "multi-pass advance\n";
    while (n-- > 0) ++it;
}

int main() {
    std::vector<int>::iterator vi;
    advance(vi, 3);  // Calls forward_iterator overload

    std::istream_iterator<int> ii;
    // advance(ii, 3);  // Would call input_iterator overload
}

structure of the constraint expressions (the expression trees), not by evaluating them. Two Constraints that are logically equivalent but structurally different (e.g., std::integral<T> and requires(T t) { t + 1; } requires std::integral<T>) are incomparable for subsumption purposes. To ensure correct overload resolution, use the same concept names consistently.

Complete Example: Overload Resolution with Constrained Templates

#include <concepts>
#include <iostream>
#include <string>
#include <vector>
#include <ranges>
#include <iterator>

template<typename C>
concept Container = requires(C c) {
    { c.begin() } -> std::input_or_output_iterator;
    { c.end() } -> std::sentinel_for<decltype(c.begin())>;
    { c.size() } -> std::convertible_to<std::size_t>;
};

template<typename C>
concept Sortable = Container<C> && requires(C c) {
    { c[0] } -> std::same_as<typename C::reference>;
    requires std::random_access_iterator<decltype(c.begin())>;
    requires std::totally_ordered<typename C::value_type>;
};

template<Container C>
void describe(const C& c) {
    std::cout << "generic container, size = " << c.size() << "\n";
}

template<Sortable C>
void describe(const C& c) {
    std::cout << "sortable container, size = " << c.size()
              << ", front = " << c[0] << "\n";
}

int main() {
    std::vector<int> v{1, 2, 3};
    describe(v);  // Calls Sortable overload (more constrained)

    std::vector<std::string> vs{"hello", "world"};
    describe(vs);  // Calls Sortable overload
}

Output:

sortable container, size = 3, front = 1
sortable container, size = 2, front = hello

The Sortable concept subsumes Container because it includes all of Container’s requirements Plus additional ones. Therefore, when both overloads are viable, the Sortable overload is Preferred.

Subsumption and `requires` Expressions

A requires expression introduces a local scope with template parameters that are checked for Validity. These expressions participate in subsumption based on their structural form [N4950 §7.1.8].

#include <concepts>
#include <iostream>
#include <string>

// Constraint P: uses a requires-expression
template<typename T>
concept Hashable = requires(T t) {
    { std::hash<T>{}(t) } -> std::convertible_to<std::size_t>;
};

// Constraint Q: uses a conjunction that includes P
template<typename T>
concept Serializable = Hashable<T> && requires(T t) {
    { t.serialize() } -> std::convertible_to<std::string>;
};

// Q subsumes P because Q = P && additional_requirement
template<Hashable T>
void process(const T& val) {
    std::cout << "hashable\n";
}

template<Serializable T>
void process(const T& val) {
    std::cout << "serializable and hashable\n";
}

struct MyData {
    std::string serialize() const { return "data"; }
};

namespace std {
    template<> struct hash<MyData> {
        std::size_t operator()(const MyData&) const { return 42; }
    };
}

int main() {
    MyData d;
    process(d);  // Calls Serializable overload (more constrained)
}

Atomic Constraints and Normalization

The compiler normalizes constraints into a set of atomic constraints before performing Subsumption. An atomic constraint is an expression that cannot be decomposed further into Conjunctions or disjunctions [N4950 §13.5.4.1].

For Sortable = Container && RandomAccess && TotallyOrderedThe atomic constraints are:

Container<T> (itself a normalized set of atomic constraints from its definition)
std::random_access_iterator<decltype(C::begin())>
std::totally_ordered<typename C::value_type>

Subsumption checks each atomic constraint individually: if every atomic constraint of $P$ is Subsumed by at least one atomic constraint of $Q$ Then $P$ is subsumed by $Q$ .

Parameter Mapping in Subsumption

When comparing two constrained templates, the compiler maps template parameters between the two Constraint sets. This is where structural equivalence matters:

#include <concepts>
#include <iostream>

template<typename T>
concept IsIntegral = std::integral<T>;

template<typename U>
concept AlsoIntegral = std::integral<U>;

template<IsIntegral T>
void f(T) { std::cout << "IsIntegral\n"; }

template<AlsoIntegral T>
void f(T) { std::cout << "AlsoIntegral\n"; }

Here, IsIntegral<T> and AlsoIntegral<T> are structurally identical after normalization (both Reduce to std::integral<T>). The compiler maps T (from the first template) to T (from the Second template) and determines that they are equivalent. This results in ambiguity --- neither Subsumes the other because subsumption requires strict “at least as restrictive,” not “equally Restrictive.”

To resolve this, make one more restrictive:

template<std::integral T>
void f(T) { std::cout << "integral\n"; }

template<std::signed_integral T>
void f(T) { std::cout << "signed integral\n"; }

Now std::signed_integral<T> subsumes std::integral<T> because every signed integral is also Integral.

Requires Clauses with Local Parameters

The requires clause can introduce local template parameters using a requirement-parameter-list. This is a common source of confusion because local parameters do not Participate in the outer template parameter mapping during subsumption.

#include <concepts>
#include <iostream>

// Version A: constraint on T directly
template<typename T>
    requires std::integral<T>
void f(T) { std::cout << "A: integral T\n"; }

// Version B: constraint using a requires-expression with local parameter
template<typename T>
    requires requires(T x) { x + 1; }
void f(T) { std::cout << "B: T supports + 1\n"; }

These two constraints are incomparable for subsumption purposes, even if T is an int. The Requires-expression in Version B introduces a local parameter xAnd the compiler cannot Structurally compare std::integral<T> with the compound requirement x + 1. The result is Ambiguity when T is int.

Rule: For subsumption to work correctly across overloads, use the same structural form for Constraints. Prefer concept names over ad-hoc requires-expressions when overloading.

Fold Expressions and Conjunctions in Constraints

Constraints can use fold expressions to express “all types in a parameter pack satisfy a concept”:

#include <concepts>
#include <iostream>
#include <string>

template<typename... Ts>
concept AllIntegral = (std::integral<Ts> && ...);

template<typename... Ts>
concept AllSame = (std::same_as<Ts, std::tuple_element_t<0, std::tuple<Ts...>>> && ...);

template<typename... Ts>
    requires AllIntegral<Ts>
void print_sum(Ts... args) {
    std::cout << (args + ...) << "\n";
}

int main() {
    print_sum(1, 2, 3);       // OK: all int
    // print_sum(1, 2.0, 3);  // ERROR: double is not integral
}

Subsumption with Pack Expansion Constraints

When comparing constrained variadic templates, subsumption is evaluated per-element in the pack. However, packs of different sizes are inherently incomparable --- a constraint requiring “at least Two integral types” cannot structurally subsume one requiring “at least one integral type” using Standard concept syntax.

#include <concepts>
#include <iostream>

template<std::integral T>
void f(T) { std::cout << "single integral\n"; }

template<std::integral T, std::integral U>
void f(T, U) { std::cout << "two integrals\n"; }

int main() {
    f(42);        // Calls single integral overload
    f(1, 2);      // Calls two integrals overload
    // f(42, 3.14); // ERROR: no viable overload
}

In this case, the two overloads have different arity (1 vs 2 parameters), so they don’t compete During overload resolution --- the compiler selects based on argument count before applying Constraint subsumption.

Detailed Subsumption Examples

Example 1: Three-Level Hierarchy

#include <concepts>
#include <iostream>

template<typename T>
concept Number = std::integral<T> || std::floating_point<T>;

template<typename T>
concept ExactNumber = Number<T> && std::is_signed_v<T>;

template<typename T>
concept PreciseNumber = ExactNumber<T> && std::floating_point<T>;

template<Number T>
void classify(T) { std::cout << "number\n"; }

template<ExactNumber T>
void classify(T) { std::cout << "exact number\n"; }

template<PreciseNumber T>
void classify(T) { std::cout << "precise number\n"; }

int main() {
    classify(42u);     // "number" (unsigned int: Number, not ExactNumber)
    classify(42);      // "exact number" (int: Number, ExactNumber, not PreciseNumber)
    classify(3.14);    // "precise number" (double: Number, ExactNumber, PreciseNumber)
}

The subsumption chain is: PreciseNumber $\succ$ ExactNumber $\succ$ Number. For doubleAll Three are viable, and PreciseNumber is the most constrained. For intOnly Number and ExactNumber are viable, and ExactNumber is more constrained. For unsigned intOnly Number Is viable.

Example 2: Incomparable Constraints (Ambiguity)

#include <concepts>
#include <iostream>

template<typename T>
    requires std::integral<T>
void dispatch(T) { std::cout << "integral\n"; }

template<typename T>
    requires std::same_as<T, int> || std::same_as<T, long>
void dispatch(T) { std::cout << "int or long\n"; }

int main() {
    dispatch(42);   // AMBIGUOUS
    // dispatch(42L); // AMBIGUOUS
    // dispatch(short{1}); // OK: "integral" (only first viable)
}

For T = int: the first constraint requires std::integral<int> (true). The second requires std::same_as<int, int> || std::same_as<int, long> (true). Neither subsumes the other because std::integral<T> and std::same_as<T, int> are structurally different atomic constraints.

Fix: Make one constraint more restrictive:

template<typename T>
    requires std::integral<T>
void dispatch(T) { std::cout << "integral\n"; }

template<std::same_as<int> T>
void dispatch(T) { std::cout << "exactly int\n"; }

// Now std::same_as<int> does not subsume std::integral<T>
// but std::integral<T> does not subsume std::same_as<int>
// Still ambiguous! The fix requires a proper refinement:

The correct fix uses concept refinement:

template<std::integral T>
void dispatch(T) { std::cout << "integral\n"; }

template<std::integral T>
    requires std::same_as<T, int>
void dispatch(T) { std::cout << "exactly int\n"; }

// Now the second constraint = std::integral<T> && std::same_as<T, int>
// This subsumes std::integral<T>

Example 3: Disjunction and Subsumption Failure

#include <concepts>
#include <iostream>

template<typename T>
concept A = std::integral<T>;

template<typename T>
concept B = std::integral<T> || std::floating_point<T>;

template<A T>
void f(T) { std::cout << "A\n"; }

template<B T>
void f(T) { std::cout << "B\n"; }

int main() {
    f(42);   // AMBIGUOUS: A<T> does not subsume B<T>, B<T> does not subsume A<T>
}

This is counterintuitive. Even though A<T> is “more restrictive” than B<T> (every integral type Is either integral or floating-point), the subsumption check is structural, not semantic. The Normalized form of B<T> is std::integral<T> || std::floating_point<T>Which is a disjunction. The conjunction rule for subsumption does not apply to disjunctions.

The fix: Write the refinement explicitly:

template<typename T>
concept B = std::integral<T> || std::floating_point<T>;

template<typename T>
concept A = B<T> && std::integral<T>;

// Now A = (std::integral<T> || std::floating_point<T>) && std::integral<T>
// Normalized: std::integral<T>
// A subsumes B? No, because B is a disjunction.
// B subsumes A? No, because B is less restrictive.
// Still ambiguous!

The fundamental issue is that disjunction breaks subsumption. When a concept uses ||It Creates multiple disjuncts, and the subsumption rules do not handle the case where one constraint’s Conjunct is a subset of another constraint’s disjunct.

Practical workaround: Avoid disjunction in concepts that participate in overload sets. Instead, Use mutually exclusive concepts or explicit overloads for each disjunct:

template<std::integral T>
void f(T) { std::cout << "integral\n"; }

template<std::floating_point T>
void f(T) { std::cout << "floating_point\n"; }

Interaction with SFINAE and `enable_if`

C++20 concepts were designed to replace SFINAE-based constraints. When concepts and enable_if are Mixed in the same overload set, concepts take priority in the resolution order:

Template argument deduction eliminates non-deducible candidates.
Constraint satisfaction (concepts and requires clauses) eliminates unsatisfied candidates.
Partial ordering by constraints selects the most constrained candidate.
SFINAE from enable_if / std::void_t is checked as part of template argument deduction.

Best practice: Do not mix concepts and enable_if in the same overload set. Convert all enable_if constraints to concepts for consistency and better error messages.

// BAD: mixing SFINAE and concepts
template<typename T, std::enable_if_t<std::is_integral_v<T>, int> = 0>
void f(T) {}

template<std::integral T>
void f(T) {}  // Ambiguous with the enable_if version when T is integral

// GOOD: use concepts consistently
template<std::integral T>
void f(T) { std::cout << "integral\n"; }

template<std::signed_integral T>
void f(T) { std::cout << "signed integral\n"; }

Constraint Subsumption and Class Templates

Concepts can also constrain class template partial specializations. Subsumption determines which Specialization is selected:

#include <concepts>
#include <iostream>
#include <type_traits>

template<typename T>
struct Renderer {
    static void draw() { std::cout << "default renderer\n"; }
};

template<std::integral T>
struct Renderer<T> {
    static void draw() { std::cout << "integral renderer\n"; }
};

template<std::floating_point T>
struct Renderer<T> {
    static void draw() { std::cout << "floating-point renderer\n"; }
};

int main() {
    Renderer<int>::draw();       // integral renderer
    Renderer<double>::draw();    // floating-point renderer
    Renderer<std::string>::draw(); // default renderer
}

Partial specializations are selected by the most specialized match. If two specializations are Equally specialized, the program is ill-formed.

Subsumption in Practice: Design Rules

The most reliable pattern for overload sets with concepts is the refinement hierarchy: use Conjunction (&&) to progressively refine a base concept. This guarantees that each level subsumes The previous.

Rules for reliable subsumption:

Use conjunction (&&) to refine concepts, never disjunction (||).
Use the same structural form for constraints across overloads (same concept names, same parameter positions).
Avoid requires-expressions with local parameters in overloads that need to be ordered.
Test subsumption with static_assert to catch structural mismatches early.

Intuition

Constraint subsumption is the rulebook for overload resolution when multiple templates could match. Think of it as a hierarchy of requirements — if concept A implies concept B, then a template constrained by A is more specific than one constrained by B. The compiler picks the most specific template, like choosing the most detailed map when navigating. Without subsumption, two equally-valid templates would cause ambiguity. The compiler needs a total ordering of constraints to break ties, which is why subsumption rules exist — they create a clear pecking order among competing templates.

Common Pitfalls

Structurally different but semantically equivalent constraints are incomparable. std::integral<T> and requires(T t) { t + 1; } requires std::integral<T> may be logically equivalent but structurally different. The compiler cannot determine subsumption between them, leading to ambiguity. Use the same concept name consistently.
Forgetting that subsumption requires strict “more restrictive.” Two constraints that are exactly equally restrictive (e.g., two different concept names that normalize to the same atomic constraints) result in ambiguity, not preference. One must be strictly a superset.
Using requires expressions with local parameters in overloads. Local parameters in requires(T x) { ... } do not participate in the template parameter mapping during subsumption. This makes the constraint structurally incomparable with other constraints. Prefer requires std::integral<T> (no local parameter) over requires(T x) { x + x; } (local parameter) when the constraint doesn’t need to test specific operations on a parameter.
Concepts with auto in requires expressions. requires(auto x) { x.foo(); } is less useful for subsumption because auto introduces a deduced type that may not map cleanly to the outer template parameters. Use explicit type parameters.
Negated constraints and subsumption. !std::integral<T> does not subsume std::floating_point<T> even though all floating-point types are non-integral. The compiler compares constraint structure, not set-theoretic relationships.
Disjunction in concepts breaks subsumption. A concept defined as A || B cannot be compared via subsumption with a concept defined as A. Even though A is more restrictive than A || B the structural subsumption rules do not handle this case. Avoid || in concepts used for overload resolution.
Parameter name differences across concepts. concept A = requires(T t) { ... } and concept B = requires(U u) { ... } are structurally different even if the bodies are identical, because the parameter names differ. The compiler normalizes by mapping template parameters, but the local parameter names in requires-expressions are part of the structural form. Always use consistent parameter names when you need subsumption.
Class template partial specializations with concepts. Unlike function template overloads, class template partial specializations do not use constraint subsumption for ordering. They use partial specialization ordering rules [N4950 §13.7.6.1], which are based on the template argument pattern, not the constraint expression. Do not assume that concept subsumption will select the correct class template partial specialization.

flowchart TD
    A[Constraint Subsumption] --> B[Requires Clauses]
    A --> C[Concepts]
    A --> D[Overload Resolution]
    B --> E[requires expression]
    B --> F[requires compound]
    C --> G[template parameter constraints]
    C --> H[auto parameter constraints]
    D --> I[Partial ordering]
    D --> J[Most constrained overload wins]
    E --> K[compile-time boolean]
    F --> L[nested requirements]
    G --> M[std::Sortable, std::Copyable]
    H --> N[auto&& with concept]
    J --> O[Subsumption: A > B means A is more specific]
    O --> P[Compiler selects most specific]
    D --> Q[SFINAE fallback]
    Q --> R[if no concept matches, try unconstrained]

Summary

This topic covers the core concepts of constraint subsumption and overload resolution, including underlying theory, practical implementation, and key applications.

Key concepts include:

core concepts and terminology
algorithms and computational thinking
practical implementation
security and ethical considerations
applications in the real world

Understanding these concepts thoroughly is essential for both examinations and practical programming, and requires both theoretical knowledge and hands-on practice.

Worked Examples

Worked examples demonstrating the application of key concepts are covered in the detailed sub-pages linked above.

Constraint Subsumption and Overload Resolution