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Pitfalls of C# Generics and Their Solution Using Concepts



In comparison with Haskell type classes and C ++ concepts, such object-oriented languages as C# and Java provide much limited mechanisms of generic programming based on F-bounded polymorphism. Main pitfalls of C# generics are considered in this paper. Extending C# language with concepts which can be simultaneously used with interfaces is proposed to solve the problems of generics; a design and translation of concepts are outlined.
Pitfalls of C# Generics and Their Solution Using
Julia Belyakova
Institute for Mathematics, Mechanics
and Computer Science
Southern Federal University
Rostov-on-Don, Russia
Stanislav Mikhalkovich
Institute for Mathematics, Mechanics
and Computer Science
Southern Federal University
Rostov-on-Don, Russia
Abstract—In comparison with Haskell type classes and C
concepts, such object-oriented languages as C
and Java provide
much limited mechanisms of generic programming based on
F-bounded polymorphism. Main pitfalls of C
generics are
considered in this paper. Extending C
language with concepts
which can be simultaneously used with interfaces is proposed
to solve the problems of generics; a design and translation of
concepts are outlined.
Generic programming is supported in different program-
ming languages by various techniques such as C
and Java generics, Haskell type classes, etc. Some of
these techniques were found more expressive and suitable for
generic programming, other ones more verbose and worse
maintainable [1]. Thus, for example, the mechanism of ex-
pressive and flexible C
unconstrained templates suffers from
unclear error messages and a late stage of error detection [2],
[3]. New language construct called concepts
was proposed
for C
language as a possible substitution of unconstrained
templates. A design of C
conforms to main
principles of effective generic tools design [1].
In comparison with concepts and Haskell type classes [1],
[7], such mainstream object-oriented languages as C
and Java
provide much limited mechanisms of generic programming
based on F-bounded polymorphism. Pitfalls of C
are analysed in this paper in detail (Sec. II): we discuss
some known drawbacks and state the problems of subtle
semantics of recursive constraints (Sec. II-B) and constraints-
compatibility (Sec. II-C). To manage the pitfalls considered
extending of C
with concepts is proposed: a design of
concepts is briefly presented in Sec. IV. We also discuss a
translation of such extension to standard C
language is used in this paper primarily for the sake
of syntax demonstration. As for the pitfalls of C
they hold for Java as well with slight differences. However,
while the concepts design proposed in the paper could be
Term “concept” was initially introduced in a documentation of the
Standard Template Library (STL) [4] to describe requirements on template
parameters in informal way.
There were several designs of C
concepts [3], [5], [6]; all of them share
some general ideas.
(ICmp-1) interface IComparable<T> {int CompareTo(T other);}
(ICmp-2) interface IComparer<T> {int Compare(T x, T y);}
(s-1) Sort<T>(T[]) where T : IComparable<T>;
(s-2) Sort<T>(T[], IComparer<T>);
Fig. 1. IComparable<T>/IComparer<T> interfaces and its applications
easily adapted for Java (and also for any .NET-language with
interface-based generics), the technique of language extension
translation (which we consider in Sec. IV) cannot be applied
for Java directly. Unlike Java Virtual Machine, .NET Frame-
work preserves type information in its byte code, this property
being crucial for the translation method.
and Java interfaces originally developed to be an entity
of object-oriented programming were later applied to generic
programming as constraints on generic type parameters. There
are several shortcomings of this approach.
A. Lack of Retroactive Interface Implementation
Interfaces cannot be implemented retroactively, i. e. it is im-
possible to add the relationship “type T implements interface
I if type T is already defined. Consider a generic algorithm
for sorting arrays Sort<T> with the following signature:
Sort<T>(T[]) where T : IComparable<T>;
If some type Foo provides an operation of comparison but does
not implement the interface IComparable<Foo>, Sort<Foo>
is not a valid instance of Sort<>. What one can do in
this case? If type cannot be changed (it may be defined
in external .dll, for instance), the only way to cope with
sorting is to define an adapter class FooAdapter which imple-
ments Sort<FooAdapter> interface, pack all Foo objects into
FooAdapter ones, sort them and unpack back to an array of
Foo objects. Apparently, there must be a better approach.
Fortunately, in the .NET Framework standard library the
Array.Sort<T> method [8] is provided with two “branches”
of overloads:
1) For any type T which implements IComparable<T> in-
terface ((s-1) example, Fig. 1).
(1) interface IComparableTo<S> { int CompareTo(S other); }
(2) interface IComparable<T> where T : IComparable<T>
{ int CompareTo(T other); }
Fig. 2. IComparable<T> vs IComparableTo<S> example
2) For any type T with an external comparer of type
IComparer<T> provided ((s-2) example, Fig. 1).
Hence, if some type is already defined, values of this
type can be compared, but this type does not implement
IComparable<> interface (as in the Foo example above),
Sort<> with IComparer<> (branch 2) is to be used. Thus
one can simulate retroactive modeling property (in Scala the
similar approach is referred to as a programming with the
“concept pattern” [9]). Consequently, if retroactive modeling
is required, a programmer has to write a generic code twice —
in “interface-oriented” and in “concept pattern” styles. The
amount of necessary overloads grows exponentially: if one
needs two retroactively modeled constraints on generic type,
corresponding generic code would consist of four “twins”, if
three eight “twins” and so on.
B. Drawbacks of Recursive Constraints
Example 1. The following reason about the Sort<T>
method for IComparable<T> may be not obvious. The no-
tation of Sort<T> in (s-1) example (Fig. 1) looks a little
bit redundant; such a recursive constraint on type T might
look even frightening, but it is well formed. Furthermore, the
word “comparable” in this context is very likely associated
with the ability to compare values of type T with each other.
But the interface IComparable<T> ((ICmp-1), Fig. 1) does
not correspond this semantics: it designates the ability of
some type (which implements this interface) to be comparable
with type T. The same problem with Comparable<X> interface
in Java is explored in [10]. The particular role of recursive
constraints in generic programming is explored in [11].
It would be better to split the single IComparable<> inter-
face into two different interfaces (Fig. 2):
1) IComparableTo<S> which requires some type (which
implements this interface) to be comparable with S.
2) IComparable<T> which requires values of type T to be
comparable with each other.
Note that the definition of the latter interface needs the
constraint where T : IComparable<T> (q.v. Fig. 2).
Example 2. As an another example consider a generic
definition of graph with peculiar structure: graph stores some
data in vertices; every vertex contains information about its
predecessors and successors thereby defining arcs. A graph
itself consists of set of vertices instead of set of edges. Such
kind of graph is suitable for a task of data flow analysis in the
area of optimizing compilers [12] because “movement along
arcs up and down” is intensively used action in an analysis of
a control flow graph.
Fig. 3 illustrates parts of the corresponding definitions:
IDataGraph<Vertex, DataType> describes interface of a data
graph; IDataVertex<Vertex, DataType> describes interface
interface IDataVertex<Vertex, DataType>
where Vertex : IDataVertex<Vertex, DataType> // (
{ ...
IEnumerator<Vertex> OutVertices { get; }
... }
interface IDataGraph<Vertex, DataType>
where Vertex : IDataVertex<Vertex, DataType> // (#)
{ ... }
Fig. 3. IDataGraph<,> and IDataVertex<,> interfaces
static HashSet<T> GetUnion<T>(HashSet<T> s1, HashSet<T> s2)
var us = new HashSet<T>(s1, s1.Comparer);
return us;
Fig. 4. Union of HashSet<T> objects
of a vertex in such graph. While the graph interface really
depends on type parameters Vertex and DataType, we have
to include Vertex as a type parameter into the vertex interface
IDataVertex<,> as well. Similarly to IComparable<> example
the constraints (*) and (#) in Fig. 3 are not superfluous.
Suppose we have the following types:
class V1 : IDataVertex<V1, int> { ... }
class V2 : IDataVertex<V1, int> { ... }
Thanks to the constraints (*) and (#) the instantiation of
graph IDataGraph<V2, int> is not allowed, since type V2
does not implement interface IDataVertex<V2, int>. Without
these constraints we might accept some inconsistent graph
with vertices of type V2 which refer to vertices of type V1.
Vertex and graph interface definitions are unclear and non-
obvious. If programmers might be used to use interface
IComparable<>, it is more difficult to manage such things as
IDataGraph<,> example. In some cases one may prefer to
abandon writing generic code because of this awkwardness.
C. Ambiguous Semantics of Generic Types
When using flexible Sort<T> method with an external
IComparer<T> parameter (Fig. 1), a programmer has clear un-
derstanding of how elements are sorted, since such a comparer
is a parameter of an algorithm. But when one uses generic
types, this information is implicit. For instance, SortedSet<T>
class takes IComparer<T> object as a constructor parameter,
HashSet<T> class taking IEqualityComparer<T>. Therefore,
given two sets of the same generic type one cannot check
at compile time whether these sets are constraints-compatible
(in case of HashSet<T> “constraints-compatibility” means that
the given sets use the same equality comparer). And it seems
that a programmer usually does not suppose that objects of the
same type can have different comparers (or addition operators,
coercions, etc). But they can, and it leads to subtle errors.
Suppose we have a simple function GetUnion<T> (q.v.
Fig. 4) which returns a union of the two given sets. If some
arguments a and b provide different equality comparers (e.g.,
case-sensitive and case-insensitive comparers for type string),
the result of GetUnion(a, b) would differ from the result of
GetUnion(b, a). Note that Haskell type classes do not suffer
interface IObserver<O, S> where O : IObserver<O, S>
where S : ISubject<O, S>
{ void update(S subj); }
interface ISubject<O, S> where O : IObserver<O, S>
where S : ISubject<O, S>
{ List<O> getObservers();
void register(O obs);
void notify(); }
Fig. 5. Observer pattern in C#
from such an ambiguity because every type provides only one
instance of a type class.
D. The Problem of Multi-Type Constraints
The well-known problem of multi-type constraints holds
for C
interfaces. Requirements concerning on several types
cannot be naturally expressed within interfaces. The paper [10]
deals with the example of Observer pattern in Java. The
Observer pattern connects two types: Observer and Subject.
Both types has methods which take the another type of this
pair as an argument: the Observer provides update(Subject),
the Subject register(Observer).
Fig. 5 shows the interface definitions IObserver<O, S> for
Observer and ISubject<O, S> for Subject in standard C
. We
need two different interfaces and have to duplicate the con-
straints on O and S in both definitions to establish consistent
connection between type parameters O and S. And again we
face with recursive constraints on types O (which represents the
Observer) and S (which represents the Subject). This example
looks even worse than the case of vertex and graph interfaces
presented in Fig. 3. But it is the only way to define a type
family [13] of Observer pattern correctly.
E. Constraints Duplication and Verbose Type Parameters
All constraints required by a definition of generic type
are to be repeatedly specified in every generic compo-
nent which uses this type. Consider the generic algorithm
GetSubgraph<,,> depending on type parameter G which im-
plements IDataGraph<,> interface (q.v. Fig. 3).
G GetSubgraph<G, Vertex, DataType>(
G g, Predicate<DataType> p)
where G : IDataGraph<Vertex, DataType>, new()
where Vertex : IDataVertex<Vertex, DataType> { ... }
GetSubgraph<G, Vertex, DataType> method is not correct
without explicit specification of constraint on type param-
eter Vertex. This constraint is induced by the definition
of IDataGraph<Vertex, DataType> interface and should be
repeated every time one uses IDataGraph<,>.
Another property of GetSubgraph<...> definition is a
plenty of generic parameters. Clearly, vertex and data types
are fully determined by the type of specific graph. At the
level of GetSubgraph<...> signature vertex type even does
not matter at all. Such types are often referred to as asso-
ciated types. Some programming languages allow to declare
associated types explicitly (SML, C
via traits, Scala via
abstract types and some other), but in C
and Java they can
only be represented by extra type parameters. It makes generic
definitions verbose and breaks encapsulation of constraints on
associated types. Issues of repeated constraints specification
and lack of associated types are considered in [14], [1] in
more detail.
We consider two studies concerning modification of generic
interfaces in this section:
1) [14] proposes the extension of C
generics with associ-
ated types and constraint propagation.
2) [10] generalizes Java 1.5 interfaces enabling retroactive
interface implementation, multi-headed interfaces (ex-
pressing multi-type constraints) and some other features.
Both studies revise interfaces to improve interface-based
mechanism of generic programming and to approach to C
concepts and Haskell type classes, which are considered being
rather similar [7]. Some features of Scala language in respect
to problems considered in Sec. II will also be mentioned.
A. C# with Associated Types and Constraint Propagation
Member types in interfaces and classes are introduced
in [14] to provide direct support of associated types. A
mechanism of constraint propagation is also proposed to lower
verbosity of generic components and get rid of constraints
duplication as was mentioned in Sec. II-E. The example
of Incidence Graph concept from the Boost Graph Library
(BGL) [15] is considered. It is shown that features proposed
can significantly improve a support of generic programming
not only in C
language but in any object-oriented language
with F-bounded polymorphism.
But the problems of multi-type constraints and recursive
constraints cannot be solved with this extension. Thus, the
code of Observer pattern (Fig. 5) cannot be improved at
all because of recursive constraints; the same holds for
IComparable<T> interface. The issue of retroactive implemen-
tation is also not touched upon in [14]: extended interfaces are
still interfaces which cannot be implemented retroactively.
B. JavaGI: Java with Generalized Interfaces
In contrast to [14], the study [10] is mainly concentrated
on the problems of retroactive implementation, multi-type
constraints (solved with multi-headed interfaces) and recur-
sive interface definitions
. For instance, Observer pattern is
expressed in JavaGI with generalized interfaces as shown
in Fig. 6 [10]. Methods of a whole interface are grouped
by a receiver type with keyword receiver. A syntax of an
interface looks a little bit verbose but it is essentially better
than two interfaces with duplicated constraints shown in Fig. 5.
Moreover, JavaGI interfaces allow default implementation of
methods (as register and notify). Retroactive implementa-
tion of interfaces is also allowed, but it is possible to define
only one implementation of an interface for the given set of
types in a namespace.
This problem is usually connected with so-called binary methods problem.
interface ObserverPattern[O, S] {
receiver O { void update(S subj); }
receiver S {
List<O> getObservers();
void register(O obs) { getObservers().add(obs); }
void notify() { ... }
class MultiheadedTest {
<S,O> void genericUpdate(S subject, O observer)
where [S,O] implements ObserverPattern {
Fig. 6. Observer pattern in JavaGI
It turns out that interfaces become some restricted version
of C
concepts [5], [16] (in particular, they do not support as-
sociated types) and, moreover, they lose a semantics of object-
oriented interfaces
. JavaGI interfaces only act as constraints
on generic type parameters, but they cannot act as types, so
one cannot use JavaGI interfaces as in Java.
C. “Concept Pattern” and Context Bounds in Scala
The idea of programming with “concept pattern” has been
reflected in Scala language [9]. Due to the combination of
generic traits (something like interfaces with abstract types
and implementation), implicits (objects used by default as
function arguments or class fields) and context bounds (like
T : Ordering in Fig. 7) Scala provides much more powerful
mechanism of generic programming than C
or Java. Fig. 7
illustrates the examples of sorting and observer pattern.
Context bounds provide simple syntax for single-parameter
constraints: the sugared (s-s) version of Sort[T] algorithm is
translated into (s-u) one by desugaring. Retroactive modeling
is supported since one can define new Ordering[] object and
use it for sorting. And one does not need to provide two
versions of the sort algorithm as for C
language (q.v. Fig. 1):
Sort[] with one argument would use default ordering due
to implicit keyword. ObserverPattern[S, O] looks rather
similar to corresponding JavaGI interface (Fig. 6). There is no
syntactic sugar for multi-parameters traits, so the notation of
genericUpdate[S, O] cannot be shortened.
In respect to the constraints-compatibility problem dis-
cussed in Sec. II-C Scala’s “concept pattern” reveals the same
drawback as C
. Generic types take “concept objects” as con-
structor parameters. In such a way TreeSet[A] [17] implicitly
takes Ordering[A] object, therefore, for instance, the result of
intersection operation would depend on an order of arguments
if they use different ordering.
A. Interfaces and Concepts
It seems that a new language construct for generic program-
ming should be introduced into such object-oriented languages
as C
or Java. If we extend interfaces preserving their object-
oriented essence [14], a generic programming mechanism be-
comes better but still not good enough, since such problems as
The way to preserve compatibility with Java code is considered in [10],
but “real interfaces” no longer exist in JavaGI.
(s-s) def Sort[T : Ordering](elems: Array[T]) { ... }
(s-u) def Sort[T](elems: Array[T])
(implicit ord: Ordering[T]) { ... }
trait ObserverPattern[S, O] {
def update(obs: O, subj: S);
def getObservers(subj: S): Seq[O];
def setObservers(subj: S, observers: Seq[O]);
def register(subj: S, obs: O)
{ setObservers(subj, getObservers(subj) :+ obs); }
def notify(subj: S) { ... }
object MultiheadedTest {
def genericUpdate[S, O](subject: S, observer: O)
(implicit obsPat: ObserverPattern[S, O]) {
obsPat.update(observer, subject);
Fig. 7. Sort[T] and ObserverPattern[S,O] examples in Scala
retroactive modeling or constraints-compatibility remain. If we
make interfaces considerably better for generic programming
purposes [10], they lose their object-oriented essence and can
no longer be used as types.
We advocate the assertion that both features have to be
provided in an object-oriented language:
1) Object-oriented interfaces which are used as types.
2) Some new construct which is used to constrain generic
type parameters. C
like concepts are proposed to serve
this goal.
B. C# with Concepts: Design and Translation
In this section we present a sketch of C
concepts design.
Concept mechanism introduces the following constructs into
the programming language:
1) Concept. Concepts describe a named set of requirements
(or constraints) on one or more types called concept
2) Model. Models determine the manner in which specific
types satisfy concept. Models are external for types; they
can be defined later than types. It means that a type can
retroactively model a concept if it semantically conforms
to this concept. Types may have several models for the
same concept. In some cases a default model can be
implicitly generated by a compiler.
3) Constraints are used in generic code to describe re-
quirements on generic type parameters.
Concepts support the following kinds of constraints:
associated types and associated values;
function signatures (may have default implementation);
nested concept requirements (for concept parameters and
associated types);
same-type constraints;
subtype and supertype constraints;
aliases for types and nested concept requirements.
The main distinction of C
concepts proposed in compari-
son with other concepts designs (C
, G [16]) is the support of
subtype constraints and anonymous models (like anonymous
classes). Concept-based mechanism of constraining generic
type parameters surpasses the abilities of interface-based one.
Construct of extended language Construct of base language
Concept Abstract class
Concept parameter Type parameter
Associated type Type parameter
Concept refinement Subtyping
Associated value Property (only read)
Nested concept requirement Type parameter
Concept requirement in generic code Type parameter
Model Class
Fig. 8. Translation of C# extension with concepts
At the same time interfaces can be used as usual without any
Concepts can be implemented in existing compilers via the
translation to standard C
. Fig. 8 presents correspondence be-
tween main constructs of extended and standard C
To preserve maximum information about the source code
semantics, some additional metainformation has to be included
into translated code. In particular, one needs to distinguish
generic type parameters in the resultant code as far as they
may represent concept parameters, associated types or nested
concept requirements. To resolve such ambiguities we propose
using attributes.
The method of translation suggested is strongly determined
by the properties of .NET Framework. Due to preserving type
information and attributes in a .NET byte code, translated
code can be unambiguously recognized as a result of code-
with-concepts translation. Moreover, it can be restored into
its source form, what means that modularity could be pro-
vided: having the binary module with definitions in extended
language one can add it to the project (in extended language
either) and use in an ordinary way.
Fig. 9 illustrates several concept definitions (in the left
column) and their translation to standard C
(in the right
column). Basic syntax of concepts is shown: concept decla-
rations (start with keyword concept), signature constraints,
signature constraints with default implementation (NotEqual
in CEquatible[T]), refinement (concept CComparable[T] re-
fines CEquatible[T], i.e. it includes all requirements of re-
fined concept and adds some new ones), associated types
(Data in CTransferFunction[TF]), multi-type concept COb-
serverPattern[O, S], nested concept requirements (CSemi-
lattice[Data] in CTransferFunction[TF]).
Concepts are translated to generic classes. Function signa-
tures are translated to abstract or virtual (if implementation is
provided) class methods. Concept parameters and associated
types are represented by type parameters (marked with at-
tributes) of a generic abstract class as well as nested concept
requirements. For instance, CSemilattice_Data type param-
eter of CTransferFunction<> denotes CSemilattice[Data]
concept requirement because this parameter is attributed with
[IsNestedConceptReq], corresponding subtype constraint be-
ing in a where-clause.
Some examples of generic code with concept constraints are
presented in the left column of Fig. 10. Concept requirements
can be used with alias (as CComparable[T] in the class of
binary search tree). Note that a singular definition of generic
component is sufficient. Translated generic code (in the right
static bool Contains<T>(T x, IEnumerable<T> values)
where CEquatible[T] { ... }
static void TestContains
Rational[] nums = ...;
var hasNumer5 = Contains[model CEquatible[Rational] {
bool Equal(Rational x, Rational y)
{ return x.Num == y.Num; }
}](new Rational(5), nums);
Fig. 12. Anonymous model example
Feature G C
multi-type constraints + +
+ +
associated types + + + + +
same-type constraints + + + + +
subtype constraints + + + +
retroactive modeling + +
+ +
multiple models +
+ +
anonymous models +
concept-based overloading + +
constraints-compatibility + + + +
means C
with associated types [1].
“Scl” means Scala [9].
means C
with concepts.
partially supported via “concept pattern”
supported via “concept pattern”
supported via “concept pattern” and implicits
partially supported by prioritized overlapping implicits
Fig. 13. Comparison of “concepts” designs
column) demonstrates significant property of translation: con-
cept requirements are translated into extra type parameters
instead of extra method and constructor parameters (as it is
in Scala and G [16]). Therefore, constraints-compatibility can
be checked at compile time, methods and objects being saved
from unnecessary arguments and fields.
Fig. 11 presents the model of concept CComparable[] for
class Rational of rational number. It is translated to derived
class CComparable_Rational_Def of CComparable<Rational>
and then used as the second type argument of generic instance
BST<,>. Fig. 12 demonstrates using of anonymous model to
find a number with a numerator equal to 5.
Many problems of C
and Java generics seem to be well
understood now. Investigating generics and several approaches
to revising OO interfaces, we faced with some pitfalls of these
solutions which were not considered yet.
1) Recursive constraints used to solve the binary method
problem appear to be rather complex and often do not
correspond a semantics assumed by a programmer.
2) The “concept pattern” breaks constraints-compatibility.
3) Using interfaces both as types and constraints on generic
type parameters leads to awkward programs with low
To solve problems considered we proposed to extend C
language with the new language construct concepts. Keep-
ing interfaces untouched, concept mechanism provides much
better support of the features crucial for generic program-
ming [1]. The support of these features in C
with concepts
concept CEquatible[T]
{ bool Equal(T x, T y); // function signature
// function signature with default implementation
bool NotEqual(T x, T y) { return !Equal(x, y); }
// refining concept
concept CComparable[T] refines CEquatible[T]
{ int Compare(T x, T y);
// overrides Equal from refined concept CEquatible[T]
override bool Equal(T x, T y) { ... }
concept CTransferFunction[TF]
{ type Data; // associated type
// nested concept requirement
require CSemilattice[Data];
Data Apply(TF trFun, Data d);
TF Compose(TF trFun1, TF trFun2);
concept CObserverPattern[O, S]
{ void UpdateSubject(O obs, S subj);
ICollection<O> GetObservers(S subj);
void RegisterObserver(S subj, O obs)
{ GetObservers(subj).Add(obs); }
void NotifyObservers(S subj) { ... }
[Concept] abstract class CEquatible<[IsConceptParam]T>
{ public abstract bool Equal(T x, T y);
public virtual bool NotEqual(T x, T y)
{ return !this.Equal(x, y); }
[Concept] abstract class CComparable<[IsConceptParam]T>
: CEquatible<T>
{ public abstract int Compare(T x, T y);
public override bool Equal(T x, T y) { ... }
[Concept] abstract class CTransferFunction<
[IsConceptParam]TF, [IsAssocType]Data,
where CSemilattice_Data : CSemilattice<Data>, new()
{ public abstract Data Apply(TF trFun, Data d);
public abstract TF Compose(TF trFun1, TF trFun2);
[Concept] abstract class CObserverPattern<
[IsConceptParam]O, [IsConceptParam]S>
{ public abstract void UpdateSubject(O obs, S subj);
public abstract ICollection<O> GetObservers(S subj);
public virtual void RegisterObserver(S subj, O obs)
{ GetObservers(subj).Add(obs); }
public virtual void NotifyObservers(S subj) { ... }
Fig. 9. Concept examples and their translation to basic C#
static void Sort<T>(T[] values)
where CComparable[T] { ... }
class BinarySearchTree<T>
// concept requirement with alias
where CComparable[T] using cCmp
private BinTreeNode<T> root;
private bool AddAux(T x, ref BinTreeNode<T> root)
// reference to concept by alias
if (cCmp.Equal(x, return false;
[GenericFun] static void Sort<[IsGenericParam]T,
[IsRequireConceptParam]CComparable_T>(T[] values)
where CComparable_T : CComparable<T>, new() { ... }
[GenericClass] [ConceptAlias("CComparable_T", "cCmp")]
class BinarySearchTree<[IsGenericParam]T,
where CComparable_T : CComparable<T>, new()
{ private BinTreeNode<T> root;
private bool AddAux(T x, ref BinTreeNode<T> root)
{ ...
CComparable_T cCmp =
if (cCmp.Equal(x, return false;
Fig. 10. Generic code and its translation to basic C#
// class for rational number with properties
// Num for numenator and Denom for denominator
class Rational { ... }
model CComparable[Rational]
bool Equal(Rational x, Rational y)
{ return (x.Num == y.Num) && (x.Denom == y.Denom); }
int Compare(Rational x, Rational y) { ... }
BST<Rational> rations = new BST<Rational>(); //
class Rational { ... }
[ExplicitModel] class CComparable_Rational_Def
: CComparable<Rational>
public override bool Equal(Rational x, Rational y)
{ return (x.Num == y.Num) && (x.Denom == y.Denom); }
public override int Compare(Rational x, Rational y){...}
BST<Rational, CComparable_Rational_Def> rations //
= new BST<Rational, CComparable_Rational_Def>();
“BST” is used instead of “BinarySearchTree” for short.
Fig. 11. Model CComparable[Rational] and its translation to basic C#
extension and its comparison with some other generic mech-
anisms are presented in Fig. 13. The design of C
concepts is
rather similar to C
concepts designs, but it supports subtype
and supertype constraints.
We also suggested a novel way of concepts translation: in
contrast to G concepts [16] and Scala “concept pattern” [9], C
concept requirements are translated to type parameters instead
of object parameters; this lowers the run-time expenses on
passing extra objects to methods and classes.
Much further investigation is to be fulfilled. First of all,
type safety of C
concepts has to be formally proved. The
design of concepts proposed seems to be rather expressive,
but it needs an approbation. So the next step is developing of
the tool for compiling a code in C
with concepts. Currently
we are working on formalization of translation from extended
language into standard C
The authors would like to thank the participants of the study
group on the foundations of programming languages Vitaly
Bragilevsky and Artem Pelenitsyn for discussions on topics
of type theory and concepts.
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