ForAllType

ForAllType[x,type]

represents a type parameterized by x.

ForAllType[x,cond,type]

represents a type satisfying cond.

ForAllType[{x1,x1,…},cond,type]

represents a type with multiple parameters.

Details

  • ForAllType does not evaluate on its own but can be used inside functions that accept types including Typed, FunctionDeclaration, etc.
  • ForAllType is used to specify the type of polymorphic functions.
  • Possible forms for cond include:
  • Element[x,"absType"]assert that x is a member of an abstract type
    TypeEvaluate[…]run an arbitrary function
  • cond can take the form Element[xi,"absType"], where "absType" is an abstract type. »
  • TypeEvaluate can be used in cond. »
  • cond can be given as a list of conditions.

Examples

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Basic Examples  (1)

Represent the type of a function that accepts a list of objects with type t and returns a single object with type t:

Represent a declaration of a polymorphic function with this type:

Compile a program using the polymorphic function:

Compile another program using the polymorphic function with a different concrete type:

Scope  (4)

Represent the type of a function that takes any packed array and returns an array of higher rank:

Declare a function with that type and call that function on a concrete example:

Represent the type of a function that is polymorphic in its output:

Compile a function with the type:

Represent the type of a function that only accepts integers:

Represent a function with the type:

Compile a program that calls the function on an integer type:

Compilation fails when the function is given a noninteger type:

Represent the type of a function that only accepts packed arrays with a rank less than 3:

Represent a function with the type:

Compile a program that applies the function to a packed array with rank 2:

Compilation fails when the inputted packed array has rank 3:

Wolfram Research (2022), ForAllType, Wolfram Language function, https://reference.wolfram.com/language/ref/ForAllType.html.

Text

Wolfram Research (2022), ForAllType, Wolfram Language function, https://reference.wolfram.com/language/ref/ForAllType.html.

CMS

Wolfram Language. 2022. "ForAllType." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ForAllType.html.

APA

Wolfram Language. (2022). ForAllType. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ForAllType.html

BibTeX

@misc{reference.wolfram_2023_foralltype, author="Wolfram Research", title="{ForAllType}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ForAllType.html}", note=[Accessed: 30-September-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_foralltype, organization={Wolfram Research}, title={ForAllType}, year={2022}, url={https://reference.wolfram.com/language/ref/ForAllType.html}, note=[Accessed: 30-September-2023 ]}