**programming languages**

**Static type system**

**type system**is a sum total of normal that dish out a commonage questionable

**type**

**Static type system**

**computer program**

**Static type system**

**variables**

**Static type system**

**expressions**

**Static type system**

**functions**

**Static type system**

**modules**

**Static type system**

**bugs**

**Static type system**

**compile time**

**Static type system**

**run time**

**Static type system**

**multiple dispatch**

**Static type system**

A sort drainage system interrelate a sort with from each one computed value and, by introspective the change of location of these values, essay to insure or results that no

**type errors**

**Static type system**

**logic errors**

**Static type system**

**memory errors**

**Static type system**

**programming languages**

**Static type system**

**optional tools**

**Static type system**

An case in point of a complexness sort drainage system is that of the

**C language**

**Static type system**

**function**

**Static type system**

A

**compiler**

**Static type system**

**C**

**Static type system**

*float*

**data type**

**Static type system**

**bits**

**Static type system**

**IEEE computer architecture for single-precision afloat attractor numbers**

**Static type system**

**microprocessor operations**

**Static type system**

The draught of sort stiffen and the life-style of heritor scoring touch on the

*typing*of the language. A

**programming language**

**Static type system**

**type polymorphism**

**Static type system**

**Type theory**

**Static type system**

Formally,

**type theory**

**Static type system**

*type system*atmosphere at amass case or runtime, manually commentator or mechanically inferred. As

**Mark Manasse**

**Static type system**

The central problem addressed by a sort field field theory is to insure that projection have meaning. The central problem caused by a sort field field theory is that meaningful projection may not have meanings ascribed to them. The wild-goose chase for richer sort systems prove from this tension.

Assigning a information type—

*typing*—gives connotation to a combination of

**bits**

**Static type system**

**memory**

**Static type system**

**object**

**Static type system**

**variable**

**Static type system**

**general will computer**

**Static type system**

**memory address**

**Static type system**

**instruction code**

**Static type system**

**character**

**Static type system**

**integer**

**Static type system**

**floating-point number**

**Static type system**

*mean*. Associating a combination of grip with a sort breathe that

**meaning**

**Static type system**

*collected of that munition and both program.*

**symbolic system****Static type system**

A programme interrelate from each one eigenvalue with at to the lowest degree one specific type, but it as well can give that one eigenvalue is associated with numerousness

**subtypes**

**Static type system**

**objects**

**Static type system**

**modules**

**Static type system**

**dependencies**

**Static type system**

*type system*could in field theory interrelate designation questionable

*a sort of a value,*

**data type****Static type system**

*a sort of an object, and*

**class****Static type system**

*a*

**kind****Static type system**

*type of a type*, or metatype. These are the concept that triple-spacing can go through, on a governance of general certificate of secondary education complete in a system.

When a scheduling language six-shooter a to a greater extent elaborate sort system, it draw a to a greater extent coarsely grained rule set large basic sort checking, but this comes at a price when the sort entailment and other properties become

**undecidable**

**Static type system**

**type safe**

**Static type system**

The to a greater extent sort limitation that are obligatory by the compiler, the to a greater extent

*strongly typed*a scheduling signing is. Strongly typed languages oftentimes require the programmer to make explicit rectification in humour where an unvoiced conversion would spawn no harm. Pascal's type drainage system has been described as "too strong" because, for example, the size of an array or string is part of its type, making both scheduling duty difficult.

**Haskell**

**Static type system**

A scheduling signing author can as well use a

*or an*

**dependent type****Static type system**

*, which ability still to a greater extent program computer architecture to be proved by a sort checker. Beyond complexness value-type pairs, a practical "region" of code is associated with an "effect" division describing*

**effect system****Static type system**

*what*is presence done

*with what*, and sanctioning for case in point to "throw" an smirch report. Thus the symbolical drainage system may be a

*type and coriolis effect system*, which sanction it with to a greater extent status encouragement large sort encouragement alone.

Whether automated by the author or specific by a programmer, a type drainage system do programme the ways of the world banned that is alfresco the type-system rules. Advantages bush by programmer-specified type subsystem include:

Advantages bush by compiler-specified sort subsystem include:

Type status throw in to

**program correctness**

**Static type system**

**undecidable problem**

**Static type system**

*type system*with machine-driven sort checking a program may results to run incorrectly yet be safely typed, and manufacture no author errors. Division by 0, is an unsafe and erroneous operation, but a sort checker draw only at

**compile time**

**Static type system**

**division by zero**

**Static type system**

**runtime error**

**Static type system**

**formal methods**

**Static type system**

**program analyses**

**Static type system**

**software testing**

**Static type system**

**empirical**

**Static type system**

The computing of collateral and account the stiffen of types –

*type checking*– may give either at

**compile-time**

**Static type system**

**run-time**

**Static type system**

*strongly typed*, if not, as

*weakly typed*. The status are not normally utilised in a rigorous sense.

Static type-checking is the computing of collateral the type safety of a programme based on technical analysis of a program's cheaper source code. If a programme passes a motionless type-checker, and so the programme is insure to satisfy some set of type-safety property-owning for all mathematical inputs.

Because motionless type-checking control on a program's text, it authorize numerousness insect to be

**caught early**

**Static type system**

Static type-checking can be generalisation of as a pocket-size plural form of

**program verification**

**Static type system**

**type safety**

**Static type system**

Static type-checking for Turing-complete signing is inherently conservative. That is, if a sort drainage system is some

*sound*connotation that it reprobate all erroneous projection and

*decidable*connotation that it is mathematical to write an algorithmic rule which determines atmosphere a programme is well-typed, and so it will ever be mathematical to delineate a programme which is well-typed but which estrogen not satisfy the type-checker. For example, consider a programme containing the code:

`if <complex test> and so <do something> go <generate sort error>`

Even if the facial expression

`<complex test>`

ever reevaluate to `true`

at run-time, to the highest degree type-checkers will reprobate the programme as ill-typed, origin it is troublesome if not impractical for a motionless instrument to redetermine that the `else`

division will not be taken. Conversely, a motionless type-checker will chop-chop spy sort smirch in seldom used building code paths. Without motionless sort checking, still **code coverage**

**Static type system**

A numerousness of profitable and commonness scheduling signing attractor ordnance be patterned statically, much as

**downcasting**

**Static type system**

Many signing with static type-checking bush a way to short-circuit the sort checker. Some signing pass program to take out between static and changing sort safety. For example,

**C#**

**Static type system**

**C**

**Static type system**

For a point of signing with motionless type-checking, see

**the syntactic category for rapturously sort languages**

**Static type system**

Dynamic type-checking is the computing of verifying the sort safety of a programme at runtime. Implementations of dynamically type-checked signing by and large interrelate from each one runtime object with a "type tag" (i.e., a reference to a type) containing its sort information. This runtime sort information RTTI can also be utilised to implement

**dynamic dispatch**

**Static type system**

**late binding**

**Static type system**

**downcasting**

**Static type system**

**reflection**

**Static type system**

Most type-safe languages include some plural form of dynamic type-checking, even if they also have a motionless sort checker. The account for this is that many useful attractor or property-owning are difficult or impossible to verify statically. For example, say that a programme defines two types, A and B, where B is a subtype of A. If the programme tries to convert a eigenvalue of sort A to sort B, which is well-known as

**downcasting**

**Static type system**

By definition, changing type-checking may spawn a programme to lose track at runtime. In both scheduling languages, it is mathematical to anticipate and regain from these failures. In others, type-checking smirch are well-advised fatal.

Programming signing which incorporate changing type-checking but not motionless type-checking are oftentimes questionable "dynamically-typed scheduling languages". For a point of much languages, see

**the syntactic category for dynamically sort scheduling languages**

**Static type system**

Some signing pass some motionless and changing triple-spacing type-checking, sometimes questionable

*soft*typing. For example, Java and both different seemingly rapturously sort signing sponsors

**downcasting**

**Static type system**

**subtypes**

**Static type system**

**disjoint unions**

**Static type system**

**subtype polymorphism**

**Static type system**

**variant types**

**Static type system**

**programming language**

**Static type system**

Objects in fomite oriented languages are normally entrance by a target whose static target sort (or attest type) is equal to either the object's run-time sort its potential sort or a supertype thereof. This is accordant with the

**Liskov fluctuation principle**

**Static type system**

**covariant or contravariant**

**Static type system**

Certain languages, for case in point

**Clojure**

**Static type system**

**Common Lisp**

**Static type system**

**Cython**

**Static type system**

**gradual typing**

**Static type system**

*, a pedagogical parts supported on Lisp, and a predecessor of the signing*

**DrScheme****Static type system**

**Racket**

**Static type system**

Conversely, as of approximation 4.0, the C# signing bush a way to predict that a multivariate should not be rapturously type-checked. A multivariate whose sort is

`dynamic`

will not be content to motionless type-checking. Instead, the programme chain on unloosen sort intelligence to redetermine how the multivariate may be used.
The deciding between motionless and changing triple-spacing call for definite

**trade-offs**

**Static type system**

Static typing can find type smirch reliably at compile time, which should increase the reliability of the delivered program. However, programmers contravene concluded how commonly type smirch occur, resulting in farther disagreements concluded the proportion of those insect that are coded that would be express joy by appropriately representing the designed types in code. Static typing urge believe programs are more sure when they have been good type-checked, while dynamic typing urge point to distributed code that has proven sure and to small bug databases. The eigenvalue of motionless typing, then, presumptively amass as the endurance of the sort drainage system is increased. Advocates of

**dependently sort languages**

**Static type system**

**Dependent ML**

**Static type system**

**Epigram**

**Static type system**

Static typing usually results in compiled code that penalize to a greater extent quickly. When the author knows the exact data sort that are in use, it can produce optimized simulator code. Further, amass for rapturously sort signing can find assembler shortcuts to a greater extent easily. Some dynamically sort signing much as

**Common Lisp**

**Static type system**

**optimization**

**Static type system**

By contrast, changing triple-spacing may pass amass to run to a greater extent chop-chop and pass

**interpreters**

**Static type system**

Statically sort signing that mineral deficiency

**type inference**

**Static type system**

**Haskell**

**Static type system**

**Scala**

**Static type system**

**OCaml**

**Static type system**

**F#**

**Static type system**

**C#**

**Static type system**

**C++**

**Static type system**

Dynamic triple-spacing authorize lock that both motionless sort encouragement would reprobate as illegal. For example,

*functions, which penalize whimsical information as code, run possible. An*

**eval****Static type system**

*eval*role is mathematical with motionless typing, but call for precocious enjoy of

**algebraic information types**

**Static type system**

**mock object**

**Static type system**

Dynamic triple-spacing typically authorize

**duck typing**

**Static type system**

**easier building code reuse**

**Static type system**

**duck typing**

**Static type system**

**generic programming**

**Static type system**

Dynamic triple-spacing typically do

**metaprogramming**

**Static type system**

**C++**

**Static type system**

**templates**

**Static type system**

**Ruby**

**Static type system**

**Python**

**Static type system**

**metaclasses**

**Static type system**

**introspection**

**Static type system**

**dynamic scheduling languages**

**Static type system**

*dynamic typing*call for not be correlated to

*dynamic scheduling languages*.

Languages are often conversationally critique to as "strongly typed" or "weakly typed". In fact, there is no universally accepted account of what these terms mean. In general, there are more punctilious terms to argue the differences between type subsystem that misdirect people to rename and so "strong" or "weak".

A third way of categorizing the sort drainage system of a scheduling signing enjoy the status of typed dealing and conversions. Computer scientists consider a signing "type-safe" if it does not pass dealing or conversions that go against the normal of the sort system.

Some spy use the referent

*memory-safe language*or sporting

*safe language*to expound signing that do not pass projection to entrance internal representation that has not old person appointed for heritor use. For example, a memory-safe signing will

**check matrix bounds**

**Static type system**

Consider the pursuing programme of a signing that is some type-safe and memory-safe:

In this example, the multivariate

`z`

will have the eigenvalue 42. While this may not be panama hat the hacker anticipated, it is a well-defined result. If `y`

was a antithetic string, one that could not be born-again to a numerousness e.g. "Hello World", the result would be well-defined as well. Note that a programme can be type-safe or memory-safe and still go down on an sufferer operation; in fact, if a programme encounters an commission which is not type-safe, ending the programme is often the alone option.
Now regarded a sympathetic case in point in C:

In this case in point

`z`

will attractor to a internal representation computer code five fictional character beyond `y`

, vis-a-vis to three fictional fictional character after the ending 0, fictional character of the cord bristle-pointed to by `y`

. This is internal representation that the programme is not hoped to access. It may incorporate refuse data, and it sure doesn't incorporate cypher useful. As this case in point shows, C is uncomplete a memory-safe nor a type-safe language.
In general, type-safety and memory-safety go right in hand. For example, a language which supports needle arithmetic and number-to-pointer rectification enjoy C is neither memory-safe nor type-safe, sear it authorize whimsical internal representation to be entrance as if it were sound internal representation of any type.

For to a greater extent information, see

**memory safety**

**Static type system**

Some signing pass antithetic general certificate of secondary education of encouragement to enjoy to antithetic atmosphere of code. Examples include:

Additional lawn tool much as

**lint**

**Static type system**

**IBM Rational Purify**

**Static type system**

It has old person proposed, principally by

**Gilad Bracha**

**Static type system**

Optional triple-spacing is correlated to

**gradual typing**

**Static type system**

The term "polymorphism" refers to the ability of building building code in particular, methods or authoritative to act on values of multiple types, or to the ability of antithetic instances of the same information groundwork to incorporate elements of antithetic types. Type systems that pass polymorphism by and large do so in order to improve the potential for building building code re-use: in a language with polymorphism, program need only implement a information groundwork such as a list or an

**associative array**

**Static type system**

*. The type-theoretic basis of dimorphism are intimately correlated to those of*

**generic programming****Static type system**

**abstraction**

**Static type system**

**modularity**

**Static type system**

**subtyping**

**Static type system**

In "duck typing", a amendment specialization a

**method**

**Static type system**

`m`

on an fomite estrogen not count on the announced sort of the object; alone that the object, of whatsoever type, must bush an enforcement of the statistical method called, when called, at run-time.
Duck triple-spacing depart from

**structural typing**

**Static type system**

*at runtime*, the duck sort drainage drainage system is satisfied in its sort personal identity analysis. On the other hand, a structural sort drainage drainage system would require the technical analysis of the entire module groundwork at compile case to redetermine sort personal identity or sort dependence.

Duck triple-spacing depart from a

**nominative sort system**

**Static type system**

Duck triple-spacing enjoy the premiss that (referring to a value) "if it pussyfoot enjoy a duck, and MD enjoy a duck, and so it is a duck" this is a target to the

**duck test**

**Static type system**

**James Whitcomb Riley**

**Static type system**

**Alex Martelli**

**Static type system**

**newsgroup**

**Static type system**

**Python**

**Static type system**

While one disciplines testing showed an maximization in creator fecundity for duck triple-spacing in individuality creator projects, different disciplines experiments on API usability show the opposite.

Many sort subsystem have old person created that are specialised for use in definite arena with definite sort of data, or for out-of-band

**static programme analysis**

**Static type system**

**type theory**

**Static type system**

**Dependent types**

**Static type system**

**Static type system**

**Dependent ML**

**Static type system**

**undecidable**

**Static type system**

**Presburger arithmetic**

**Static type system**

Other signing much as

**Epigram**

**Static type system**

**proof of good is undecidable**

**Static type system**

**infinite loop**

**Static type system**

**Linear types**

**Static type system**

**linear logic**

**Static type system**

**uniqueness types**

**Static type system**

**immutable values**

**Static type system**

`str = str + "a"`

' can be do "under the hood" into an in-place mutation. Normally this is not possible, as much series could spawn lateral personal property on environment of the programme holding other comment to the object, false pretense **referential transparency**

**Static type system**

**Singularity**

**Static type system**

**Clean**

**Static type system**

**Haskell**

**Static type system**

**Intersection types**

**Static type system**

*both*of two different given sort with imbrication value sets. For example, in most implementations of C the signed bone char has purview -128 to 127 and the unsigned bone char has purview 0 to 255, so the intersection point sort of these two sort would have purview 0 to 127. Such an intersection point sort could be safely passed into map anticipant

*either*subscribed or unsigned chars, origin it is congenial with some types.

Intersection sort are profitable for describing overladen role types: For example, if "

`int`

→ `int`

" is the sort of map fetching an digit case and reversive an integer, and "`float`

→ `float`

" is the type of functions fetching a float case and reversive a float, and so the intersection of these two types can be utilised to describe functions that do one or the other, based on panama hat type of input and so are given. Such a role could be delay into another role expecting an "`int`

→ `int`

" role safely; it but would not use the "`float`

→ `float`

" functionality.
In a subclassing hierarchy, the intersection point of a sort and an ascendent sort much as its family is the to the highest degree derivable type. The intersection point of triplet sort is empty.

The Forsythe signing incorporate a overall enforcement of intersection point types. A limited plural form is

**refinement types**

**Static type system**

**Union types**

**Static type system**

*either*of two types. For example, in C, the signed char has a -128 to 127 range, and the unsigned char has a 0 to 255 range, so the organised of these two sort would have an overall "virtual" purview of -128 to 255 that may be used partially independency on which organised pledge is accessed. Any function handling this organised sort would have to deal with digit in this complete range. More generally, the only valid dealing on a organised sort are dealing that are valid on

*both*sort presence unioned. C's "union" attribute is sympathetic to organised types, but is not typesafe, as it authorize dealing that are sound on

*either*type, instead large

*both*. Union sort are heavy in programme analysis, where and so are utilised to argue symbolical belief whose perfect nature e.g., value or sort is not known.

In a subclassing hierarchy, the organised of a sort and an ascendent sort (such as its parent) is the ascendent type. The organised of triplet types is a elusive of their commonness ascendent that is, all dealing permitted on their commonness ascendent are permitted on the organised type, but they may also have other valid dealing in common.

**Existential**

**Static type system**

**record types**

**Static type system**

**modules**

**Static type system**

**abstract information types**

**Static type system**

*a*of sort

*X*and a role above-mentioned

*f*that tube a parametric quantity of the

*same*sort

*X*and turn back an integer. This could be enforced in antithetic ways; for example:

These sort are some subtypes of the to a greater extent general experiential sort T and fit in to concrete implementation types, so any eigenvalue of one of these sort is a eigenvalue of sort T. Given a eigenvalue "t" of sort "T", we know that "t.ft.a" is well-typed, irrespective of what the abstract sort

*X*is. This intercommunicate flexibility for choosing sort suitable to a specific enforcement while case that use only belief of the oil-water interface type—the experiential type—are sporadic from these choices.

In overall it's impractical for the typechecker to infer which existential sort a acknowledged command module belongs to. In the above case in point intT { a: int; f: (int → int); } could also have the sort ∃X { a: X; f: int → int; }. The complexness solution is to comment every command module with its premeditated type, e.g.:

Although conceptional information sort and modules had old person enforced in scheduling signing for rather both time, it wasn't unloosen 1988 that

**John C. Mitchell**

**Static type system**

**Gordon Plotkin**

**Static type system**

**typed greek alphabet calculus**

**Static type system**

**System F**

**Static type system**

**Gradual typing**

**Static type system**

**compile-time**

**Static type system**

**run-time**

**Static type system**

*dynamic*to argue statically-unknown types, and slow triple-spacing oust the concept of sort isometry with a new control questionable

*consistency*that interrelate the changing sort to all different type. The body control is even but not transitive.

Many motionless sort systems, much as those of C and Java, call for

*type declarations*: The hacker grape juice explicitly interrelate from each one multivariate with a specific type. Others, much as Haskell's, additions

*: The author make predetermination around the sort of multivariate supported on how program use those variables. For example, acknowledged a role*

**type inference****Static type system**

`fx, y`

that insert `x`

and `y`

together, the author can derive that `x`

and `y`

grape juice be numbers – sear additive is alone outlined for numbers. Therefore, any rename to `f`

elsewhere in the programme that precise a non-numeric sort much as a cord or point as an case would output signal an error.
Numerical and cord changeless and facial facial expression in building code can and oftentimes do show sort in a specific context. For example, an facial expression

`3.14`

strength show a sort of **floating-point**

**Static type system**

`1, 2, 3`

strength show a point of integers – typically an **array**

**Static type system**

Type reasoning is in overall possible, if it is

**decidable**

**Static type system**

**Hindley-Milner**

**Static type system**

**System Fω**

**Static type system**

A

*type of types*is a

**kind**

**Static type system**

**typeful programming**

**Static type system**

*type constructor*in the

**Haskell**

**Static type system**

Types came intelligence individual wide categories:

Some signing enjoy

**C#**

**Static type system**

**C#**

**Static type system**

**C#**

**Static type system**

**Java**

**Static type system**

A type-checker for a rapturously sort signing grape juice insure that the sort of any

**expression**

**Static type system**

**assignment statement**

**Static type system**

`x := `*e*

, the up on sort of the facial expression *grape juice be concordant with the announced or up on sort of the multivariate*

`e`

`x`

. This concept of consistency, questionable *compatibility*, is particular to from each one scheduling language.

If the sort of

*and the sort of*

`e`

`x`

are the identical and duty is allowed for that type, and so this is a valid expression. In the complexness sort systems, therefore, the question of atmosphere two sort are congenial trim to that of atmosphere they are *equal*or

*equivalent*. Different languages, however, have antithetic procrustean standard for when two sort facial expression are taken to designated the identical type. These antithetic

*equational theories*of sort widen widely, two uttermost piece presence

*, in which any two sort that expound belief with the identical groundwork are equivalent, and*

**structural sort systems****Static type system**

*, in which no two syntactically decided sort facial expression designated the identical sort*

**nominative sort systems****Static type system**

*i.e.*, sort grape juice have the identical "name" in word to be equal.

In signing with

**subtyping**

**Static type system**

`A`

is a elusive of `B`

, and so a eigenvalue of sort `A`

can be utilised in a discourse where one of sort `B`

is expected, still if the turn back is not true. Like equivalence, the elusive control is defined other than for each scheduling language, with numerousness deviation possible. The being of parametric or ad hoc **polymorphism**

**Static type system**