25:
368:, do not substitute structurally in the case where an expected type is declared (i.e., not inferred), e.g., only substitute for functions that are signature-based polymorphic via type inference. Then it is not possible to accidentally subtype a non-inferred type, although it may still be possible to provide an explicit conversion to a non-inferred type, which is invoked implicitly.
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in which type compatibility and equivalence are determined by the type's actual structure or definition and not by other characteristics such as its name or place of declaration. Structural systems are used to determine if types are equivalent and whether a type is a subtype of another. It contrasts
386:
A pitfall of structural typing versus nominative typing is that two separately defined types intended for different purposes, but accidentally holding the same properties (e.g. both composed of a pair of integers), could be considered the same type by the type system, simply because they happen to
1223:# (z :> simpler_obj);; This expression cannot be coerced to type simpler_obj = < get_x : int >; it has type < blahblah : float; set_x : int -> unit > but is here used with type < get_x : int; .. > The first object type has no method get_x
323:, an element is considered to be compatible with another if, for each feature within the second element's type, a corresponding and identical feature exists in the first element's type. Some languages may differ on the details, such as whether the
383:; in particular, it permits creation of a type which is a supertype of an existing type, without modifying the definition of the latter. However, this may not be desirable where the programmer wishes to create closed abstractions.
552:) is defined only by its methods. In other words, the type of x is defined by the method types "get_x : int" and "set_x : int -> unit" rather than by any name.
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must match in name. This definition is not symmetric, and includes subtype compatibility. Two types are considered to be identical if each is compatible with the other.
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Checking that two types are compatible, based on structural typing, is a non-trivial operation, e.g., requires maintaining a stack of previous checked types.
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of the base type, or subtypes thereof. The subtype may contain added features, such as members not present in the base type, or stronger invariants.
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can be formed based on how the subtype relationship is defined. One type is a subtype of another if and only if it contains all the
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So they must be the same type, or else this wouldn't even type-check. This shows that equivalence of types is structural.
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OCaml considers them the same type. For example, the equality operator is typed to only take two values of the same type:
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A distinction exists between structural substitution for inferred and non-inferred polymorphism. Some languages, such as
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Another object can be made that happens to have that method and method type; the other methods are irrelevant:
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means that the first argument can be any object which has a "set_x" method, which takes an int as argument.
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Here the OCaml interactive runtime prints out the inferred type of the object for convenience. Its type (
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Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on
Principles of programming languages - POPL '90
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416:) without going through a nominative class. Classes only serve as functions for creating objects.
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This shows that compatibility for things like method invocation is determined by structure.
311:, in which only the part of the structure accessed at runtime is checked for compatibility.
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Let us define a type synonym for objects with only a "get_x" method and no other methods:
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uses structural typing on methods to determine compatibility of a type with an interface.
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Cook, W.R.; Hill, W.L.; Canning, P.S. (January 1990). "Inheritance is not subtyping".
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Objects in OCaml are structurally typed by the names and types of their methods.
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have identical structure. One way this can be avoided is by creating one
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This shows that compatibility for widening coercions are structural.
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uses structural typing on methods for compatibility of object types.
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uses structural typing, but classes are not structurally subtyped.
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functions exhibit structural typing on type arguments.
1315:"Type compatibility: name vs structural equivalence"
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Structural subtyping is arguably more flexible than
49:. Unsourced material may be challenged and removed.
726:One can define a function that invokes a method:
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1261:. San Francisco, California. pp. 125–135.
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1011:The "set_to_10" function also works on it:
1299:: CS1 maint: location missing publisher (
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825:The inferred type for the first argument (
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109:Learn how and when to remove this message
1123:contains a superset of its methods. So
1115:is not of this type; but structurally,
827:< set_x : int -> 'a; .. >
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1341:Pierce, Benjamin C. (2002). "19.3".
1119:is of a subtype of this type, since
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47:adding citations to reliable sources
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394:In 1990, Cook, et al., proved that
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412:Objects can be created directly (
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836:So it can be used on object
396:inheritance is not subtyping
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288:structural type system
144:Strong vs. weak typing
16:Class of type systems
373:nominative subtyping
351:subtype polymorphism
43:improve this article
1268:10.1145/96709.96721
389:algebraic data type
302:nominative systems
1354:978-0-262-16209-8
414:immediate objects
321:structural typing
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1363:External links
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60: –
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54:Find sources:
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38:
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32:This article
30:
26:
21:
20:
1388:Type systems
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353:, a similar
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340:C++ template
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296:type systems
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223:Intersection
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125:Type systems
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41:Please help
36:verification
33:
1373:WikiWikiWeb
1185:simpler_obj
1157:simpler_obj
1144:simpler_obj
1111:The object
1087:simpler_obj
1062:simpler_obj
315:Description
308:duck typing
187:Duck typing
139:Type safety
1230:References
379:types and
233:Refinement
182:structural
69:newspapers
1295:cite book
1019:set_to_10
848:set_to_10
765:set_to_10
737:set_to_10
381:protocols
355:dichotomy
208:Dependent
99:July 2011
1382:Category
966:blahblah
935:"%d
899:blahblah
608:"%d
359:features
325:features
203:Abstract
173:inferred
169:Manifest
1287:8225906
439:mutable
405:Example
366:Haskell
248:Session
218:Gradual
178:Nominal
164:dynamic
83:scholar
1351:
1285:
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1080:>;;
941:"
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926:Printf
914:method
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605:printf
599:Printf
587:method
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377:ad hoc
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160:Static
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332:OCaml
299:with
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854:;;
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487:;;
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
