evaluates rhs and assigns the result to be the value of lhs. From then on, lhs is replaced by rhs whenever it appears.
evaluates the ri, and assigns the results to be the values of the corresponding li.
- lhs can be any expression, including a pattern.
- f[x_]=x^2 is a typical assignment for a pattern. Notice the presence of _ on the left‐hand side, but not the right‐hand side.
- An assignment of the form f[args]=rhs sets up a transformation rule associated with the symbol f.
- Different rules associated with a particular symbol are usually placed in the order that you give them. If a new rule that you give is determined to be more specific than existing rules, it is, however, placed before them. When the rules are used, they are tested in order. »
- New assignments with identical lhs overwrite old ones. »
- You can see all the assignments associated with a symbol f using ?f or Definition[f].
- If you make assignments for functions that have attributes like Flat and Orderless, you must make sure to set these attributes before you make assignments for the functions.
- Set has attribute HoldFirst.
- If lhs is of the form f[args], then args are evaluated. »
- There are some special functions for which an assignment to s[f[args]] is automatically associated with f rather than s. These functions include: Attributes, Default, Format, MessageName, Messages, N, and Options. »
- When it appears in an unevaluated symbolic form, Set is treated as a scoping construct so that variables in nested occurrences are renamed if necessary. »
- lhs=rhs returns rhs even if for some reason the assignment specified cannot be performed.
- Some global variables such as $RecursionLimit can only be assigned a certain range or class of values.
Background & Context
- Set is a function that evaluates and assigns an expression to be the value of a variable. The expression is commonly represented using the shorthand syntax . After Set is evaluated, lhs is replaced by rhs whenever it appears. Depending on the form of lhs, the result is stored as in the associated OwnValues, DownValues, or a specialized data structure.
- Set often contains patterns on the lhs that are assigned transformed values as indicated on the rhs, e.g. . evaluates rhs immediately, so in situations where rhs should be evaluated only after the assignment is made, SetDelayed (written in shorthand as :=) should be used instead.
- The assignments associated with a given symbol can be seen using Definition[f]. Individual assignments may be removed from a symbol using Unset; Clear and ClearAll remove all definitions at once.
Examplesopen allclose all
Left-Hand Sides (7)
Use Block to temporarily set variables:
Generalizations & Extensions (5)
Properties & Relations (9)
Module introduces new symbols, distinct from global ones:
Definition prints definitions associated with a symbol:
Information prints various information about a symbol, including any definitions:
OwnValues returns a list of rules corresponding to any downvalues defined:
Use Unset (=.) to clear definitions with a particular left-hand side:
Possible Issues (4)
Neat Examples (1)
Compute the arithmetic-geometric mean of two numbers [more info]:
Wolfram Research (1988), Set, Wolfram Language function, https://reference.wolfram.com/language/ref/Set.html.
Wolfram Language. 1988. "Set." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Set.html.
Wolfram Language. (1988). Set. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Set.html