--- title: "TagSetDelayed" language: "en" type: "Symbol" summary: "f /: lhs := rhs assigns rhs to be the delayed value of lhs, and associates the assignment with the symbol f." keywords: - associating values - setting values - generic programming - type based programming - object programming canonical_url: "https://reference.wolfram.com/language/ref/TagSetDelayed.html" source: "Wolfram Language Documentation" related_guides: - title: "Assignments" link: "https://reference.wolfram.com/language/guide/Assignments.en.md" related_functions: - title: "TagSet" link: "https://reference.wolfram.com/language/ref/TagSet.en.md" - title: "SetDelayed" link: "https://reference.wolfram.com/language/ref/SetDelayed.en.md" - title: "UpSetDelayed" link: "https://reference.wolfram.com/language/ref/UpSetDelayed.en.md" - title: "UpValues" link: "https://reference.wolfram.com/language/ref/UpValues.en.md" - title: "DownValues" link: "https://reference.wolfram.com/language/ref/DownValues.en.md" - title: "SubValues" link: "https://reference.wolfram.com/language/ref/SubValues.en.md" - title: "TagUnset" link: "https://reference.wolfram.com/language/ref/TagUnset.en.md" related_tutorials: - title: "Associating Definitions with Different Symbols" link: "https://reference.wolfram.com/language/tutorial/TransformationRulesAndDefinitions.en.md#6972" --- # TagSetDelayed (/: :=) f/:lhs := rhs assigns rhs to be the delayed value of lhs, and associates the assignment with the symbol f. ## Details * ``TagSetDelayed`` defines upvalues, downvalues or subvalues as appropriate. * The symbol ``f`` in ``f/:lhs := rhs`` must appear in ``lhs`` as the head of ``lhs``, the head of the head, one of the elements of ``lhs`` or the head of one of the elements. * A common case is ``f/:h[f[args]] := rhs``. * You can see all the rules associated with a particular symbol by typing `` ? symbol``. * If ``f`` appears several times in ``lhs``, then ``f/:lhs := rhs`` associates the assignment with each occurrence. * When it appears in unevaluated symbolic form, ``TagSetDelayed`` is treated as a scoping construct so that variables in nested occurrences are renamed if necessary. --- ## Examples (16) ### Basic Examples (1) ```wl In[1]:= g/:f[g[x_]] := fg[x] In[2]:= {f[g[2]], f[h[2]]} Out[2]= {fg[2], f[h[2]]} ``` ### Scope (7) #### Left-Hand Sides (4) An expression with a delayed definition is evaluated every time it is used: ```wl In[1]:= int/:rand[int] := RandomInteger[] In[2]:= Table[rand[int], {5}] Out[2]= {1, 0, 0, 1, 1} ``` --- Make definitions for special and general cases using immediate and delayed assignments: ```wl In[1]:= h/:f[h[0]] = h0; h/:f[h[x_]] := 2f[h[x - 1]] In[2]:= f[h[10]] Out[2]= 1024 h0 ``` --- The tag can appear as an argument of the left side: ```wl In[1]:= sq/:area[sq, s_] := s ^ 2 In[2]:= area[sq, 2] Out[2]= 4 ``` --- The tag can appear as the head of an argument of the left side: ```wl In[1]:= sq/:area[sq[s_]] := s ^ 2 In[2]:= area[sq[3]] Out[2]= 9 ``` #### Different Kinds of Values (3) For ownvalues, the tag is redundant: ```wl In[1]:= x/:x := RandomReal[] y := RandomReal[] In[2]:= {OwnValues[x], OwnValues[y]} Out[2]= {{HoldPattern[x] :> RandomReal[]}, {HoldPattern[y] :> RandomReal[]}} ``` --- For downvalues, the tag is redundant: ```wl In[1]:= f/:f[x_] := x ^ 2; g[x_] := x ^ 2 In[2]:= {DownValues[f], DownValues[g]} Out[2]= {{HoldPattern[f[x_]] :> x^2}, {HoldPattern[g[x_]] :> x^2}} ``` --- Use a tag to define upvalues: ```wl In[1]:= g/:f[g[x_]] := f1[x] f[h[x_]] := f2[x] In[2]:= {UpValues[g], DownValues[f]} Out[2]= {{HoldPattern[f[g[x_]]] :> f1[x]}, {HoldPattern[f[h[x_]]] :> f2[x]}} ``` ### Applications (1) Implement modular arithmetic: ```wl In[1]:= mod/:mod[a_, p_] + mod[b_, p_] := mod[Mod[a + b, p], p] mod/:i_Integer mod[a_, p_] := mod[Mod[i a, p], p] In[2]:= mod[2, 5] + 3 mod[3, 5] - mod[1, 5] Out[2]= mod[0, 5] ``` ### Properties & Relations (7) `` ^:= `` defines upvalues in the same way as using a tag does: ```wl In[1]:= g/:f[g[x_]] := f1[x] In[2]:= f[h[x_]] ^:= f2[x] In[3]:= {UpValues[g], UpValues[h]} Out[3]= {{HoldPattern[f[g[x_]]] :> f1[x]}, {HoldPattern[f[h[x_]]] :> f2[x]}} ``` --- A tag defines only one upvalue; `` ^:= `` makes definitions for all symbols: ```wl In[1]:= g/:f1[g[x_], h[y_]] := gh[x y] In[2]:= f2[g[x_], h[y_]] ^:= gh[x y] In[3]:= {UpValues[g], UpValues[h]} Out[3]= {{HoldPattern[f1[g[x_], h[y_]]] :> gh[x y], HoldPattern[f2[g[x_], h[y_]]] :> gh[x y]}, {HoldPattern[f2[g[x_], h[y_]]] :> gh[x y]}} ``` --- The right side of an immediate definition is evaluated when the definition is made: ```wl In[1]:= int/:rand[int] = RandomInteger[]; In[2]:= {rand[int], rand[int]} Out[2]= {0, 0} ``` The right side of a delayed definition is evaluated each time the definition is used: ```wl In[3]:= real/:rand[real] := RandomReal[] In[4]:= {rand[real], rand[real]} Out[4]= {0.631583, 0.929159} ``` --- Definitions with the same left side overwrite earlier ones: ```wl In[1]:= h/:f[h[x_]] := f1[x] In[2]:= h/:f[h[x_]] := f2[x] In[3]:= Definition[h] Out[3]= f[h[x_]] ^:= f2[x] ``` --- ``Definition`` prints definitions associated with a symbol: ```wl In[1]:= mod/:a_mod + b_mod := modPlus[a, b] In[2]:= Definition[mod] Out[2]= a_mod + b_mod ^:= modPlus[a, b] ``` ``Information`` prints various information about a symbol, including any definitions: ```wl In[3]:= ? mod Cell$$4531`mod a_mod + b_mod ^:= modPlus[a, b] ``` ``UpValues`` returns a list of rules corresponding to any upvalues defined: ```wl In[4]:= UpValues[mod] Out[4]= {HoldPattern[a_mod + b_mod] :> modPlus[a, b]} ``` --- Use ``=.`` to clear definitions with a particular left-hand side: ```wl In[1]:= h/:f[h[x_]] := f1[x]; h/:g[h[x_]] := g1[x]; In[2]:= h/:f[h[x_]]=. In[3]:= {f[h[1]], g[h[1]]} Out[3]= {f[h[1]], g1[1]} ``` Clear all definitions: ```wl In[4]:= Clear[h] In[5]:= Definition[h] Out[5]= ``` --- Delayed assignment introduces a scope that is not affected by global variables: ```wl In[1]:= x = 5; In[2]:= h/:f[h[x_]] := x ^ 2 In[3]:= {f[h[2]], x} Out[3]= {4, 5} ``` Immediate assignment does not introduce a scope: ```wl In[4]:= h/:g[h[x_]] = x ^ 2; In[5]:= {g[h[2]], x} Out[5]= {25, 5} ``` ## See Also * [`TagSet`](https://reference.wolfram.com/language/ref/TagSet.en.md) * [`SetDelayed`](https://reference.wolfram.com/language/ref/SetDelayed.en.md) * [`UpSetDelayed`](https://reference.wolfram.com/language/ref/UpSetDelayed.en.md) * [`UpValues`](https://reference.wolfram.com/language/ref/UpValues.en.md) * [`DownValues`](https://reference.wolfram.com/language/ref/DownValues.en.md) * [`SubValues`](https://reference.wolfram.com/language/ref/SubValues.en.md) * [`TagUnset`](https://reference.wolfram.com/language/ref/TagUnset.en.md) ## Tech Notes * [Associating Definitions with Different Symbols](https://reference.wolfram.com/language/tutorial/TransformationRulesAndDefinitions.en.md#6972) ## Related Guides * [`Assignments`](https://reference.wolfram.com/language/guide/Assignments.en.md) ## History * Introduced in 1988 (1.0)