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DownValuesFunction [sym]

represents a function that uses definitions attached to sym when compiling.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Multiple Definitions  
Multiple Declarations  
Polymorphic Declarations  
Show More Show More
Recursive Calls  
Unnamed Patterns  
Repeated Patterns  
Matching the Head  
Pattern Test  
Condition  
Except  
Alternatives  
Compound Patterns  
Sequences  
Applications  
Symbol Definitions  
Possible Issues  
Updating  
Definition Restrictions  
Type Consistency  
Unsupported Patterns  
Sequence Patterns  
See Also
Tech Notes
Related Guides
History
Cite this Page

DownValuesFunction [sym]

represents a function that uses definitions attached to sym when compiling.

Details

  • DownValuesFunction can be used directly in compiled code.
  • DownValuesFunction can be used in compiled declarations specified by FunctionDeclaration .
  • DownValuesFunction specifications typically use Typed to give type annotations.
  • When DownValuesFunction is compiled, it creates a function from symbol declarations and compiles it.
  • Declarations that use DownValuesFunction can use polymorphic types.
  • The following pattern constructs are supported:
  • _ match an argument
    x_ match an argument assigning to the name x
    _h match if the head is h
    x_?test match if test[x] evaluates to True
    p/;cond match if cond evaluates to True
    Except [p] match if p does not match
    p1|p2 match if one of pi matches
    f[g[p]] match a compound expression (for inert expressions and packed arrays)
    __,___ match a sequence (for inert expressions)

Examples

open all close all

Basic Examples  (1)

Define a squaring function and use its definition to create a compiled function for the integer-typed case:

Use the compiled function with an integer argument:

Alternatively, use FunctionDeclaration to associate the definition of a function with a type specification:

The result is the same:

Scope  (13)

Multiple Definitions  (1)

Several definitions attached to the same symbol can be used:

Compile a function that uses the definitions:

This calls the definition that uses a condition:

This calls the definition that uses a literal 2:

This calls the last catchall definition:

Multiple Declarations  (1)

Definitions attached to a symbol can be used in more than one declaration with different types:

Make two declarations with different types and compile functions that use each:

Call the integer case:

Call the real case:

Polymorphic Declarations  (1)

Definitions attached to a symbol can be declared with a polymorphic type:

Make a polymorphic declaration and compile functions that use it for different types:

Call the integer case:

Call the real case:

Recursive Calls  (1)

Function declarations that use a symbol definition can call themselves:

Make a declaration and compile a function that uses it:

Call the function:

Unnamed Patterns  (1)

A pattern argument does not need a name:

Compile a function that uses the definition:

Call the function with different values:

Repeated Patterns  (1)

If the same name appears more than once in a definition, when called, the value must be the same:

Compile a function that uses the definition:

Call the function with different values:

Call the function with the same value and it uses the definition for the same value:

Matching the Head  (1)

A pattern can be written to match the head:

Make a polymorphic declaration that uses the definition:

Compile a function that uses the declaration with an argument that does not match the head:

Call the function with an integer and that uses the definition that does not match the head:

Compile a function that uses the declaration with an argument that does match the head:

Call the function with a real and that uses the definition that matches the head:

Pattern Test  (1)

Compiled patterns can use PatternTest :

Compile a function that uses the definition:

The input is even:

The input is odd:

Condition  (1)

Compiled patterns can use Condition :

Compile a function that uses the definition:

The input has arguments in order:

The input has arguments not in order, so in the output, they are reversed:

Except  (1)

Compiled patterns can use Except :

Make a declaration and compile a function that uses it:

The argument is even, so the first definition is not used:

The argument is odd, so the first definition is used:

Compile a function that uses the definition:

The argument is even and greater than 20, so the first definition is not used:

The argument is odd and greater than 20, so the first definition is used:

The argument is odd but less than 20, so the first definition is not used:

Alternatives  (1)

Compiled patterns can use Alternatives :

Make a declaration:

Compile a function to use the declaration:

This function matches the input, so a result is generated:

Compile a function with a different type to use the declaration:

This function also matches the input, so a result is generated:

Compound Patterns  (1)

Compilation supports compounds patterns for certain types such as "InertExpression" and "PackedArray":

Compile a function that uses the definition:

This function matches the input so a result is generated:

Compile a function with a different type to use the declaration:

Sequences  (1)

Compilation supports certain sequence patterns for "InertExpression":

Compile a function that uses the definition:

This sequence gets flattened:

The pattern with a sequence does not match, so this returns a failure:

The pattern can have a compound head of any expression type:

This matches:

This does not match:

Applications  (1)

Symbol Definitions  (1)

Declarations that use symbol definitions are useful if the declaration is used more than once:

A FunctionDeclaration that refers to the symbol:

A function that uses the symbol:

Compiled code for the function:

A vector plot based on the data that was created:

The compiled version is much faster:

An animation of the output:

Possible Issues  (5)

Updating  (1)

DownValuesFunction uses the definitions used when the compilation is carried out:

The result uses the definitions in place when the compilation is done:

Definition Restrictions  (1)

If there is no definition that applies to particular arguments, a runtime error case will be added:

This returns a result:

There is no definition that works for this input and hence a runtime error results:

Type Consistency  (1)

All the branches of pattern definitions must return the same type:

All the branches of pattern definitions must compile for the arguments:

This compiles:

This does not compile:

Unsupported Patterns  (1)

Optional patterns are not supported:

Held patterns are not supported:

Verbatim patterns are not supported:

Sequence Patterns  (1)

Sequence patterns do not support polymorphic declarations:

Make a polymorphic declaration, but the compilation cannot use it:

Tech Notes

Wolfram Research (2022), DownValuesFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/DownValuesFunction.html (updated 2025).

Text

Wolfram Research (2022), DownValuesFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/DownValuesFunction.html (updated 2025).

CMS

Wolfram Language. 2022. "DownValuesFunction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/DownValuesFunction.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_downvaluesfunction, author="Wolfram Research", title="{DownValuesFunction}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/DownValuesFunction.html}", note=[Accessed: 17-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_downvaluesfunction, organization={Wolfram Research}, title={DownValuesFunction}, year={2025}, url={https://reference.wolfram.com/language/ref/DownValuesFunction.html}, note=[Accessed: 17-November-2025]}

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