Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 LocalizedByRules

Source Notebook

Use rules as local variable lists

Contributed by: Yong-an Lu

ResourceFunction["LocalizedByRules"][rules,expr]

use rules as local variable lists in expr.

Details and Options

If the rules are given in nested lists, it is effectively mapped onto the inner lists.
The following options can be given:
MethodWithmethod to use for localizing
Possible explicit settings for the Method option include: Module, Block and With.
Left-hand side in rules can be wrapped by HoldPattern.

Examples

Basic Examples (2) 

Use rules as local variable lists:

In[1]:=
ResourceFunction["LocalizedByRules"][{n -> 2, e :> RandomReal[]}, Table[e, n]]
Out[1]=
Image

Give a single rule for a localized variable:

In[2]:=
ResourceFunction["LocalizedByRules"][x -> 7, x^2]
Out[2]=
Image

Scope (1) 

Apply each rule separately:

In[3]:=
ResourceFunction["LocalizedByRules"][{{x -> 1}, {x -> 3}, {x -> 7}}, x + # &]
Out[3]=
Image

Options (2) 

Method (2) 

Localize using different Wolfram Language scoping mechanisms:

In[4]:=
Table[ResourceFunction["LocalizedByRules"][x -> 0, scope -> Hold[x], Method -> scope], {scope, {With, Block, Module}}]
Out[4]=
Image

Check this using explicit scoping:

In[5]:=
Table[scope[{x = 0}, scope -> Hold[x]], {scope, {With, Block, Module}}]
Out[5]=
Image

Applications (1) 

An easy way to apply the solutions of an equation to TemplateExpression:

In[6]:=
eqn = {(10 x + y)/(10 y + z) == x/z, 1 <= {x, y, z} <= 9, x != z}; ResourceFunction["LocalizedByRules"][Solve[eqn, {x, y, z}, Integers], TemplateApply[ "(10x+y)/(10y+z)=<*10x+y*>/<*10y+z*>=<*x*>/<*z*>=x/z, where x is <*x*>, y is <*y*>, z is <*z*>."], Method -> Block ] // Column
Out[5]=
Image

Possible Issues (2) 

Variables with assigned values cannot be used in rules:

In[7]:=
a = 1; ResourceFunction["LocalizedByRules"][a -> 2, a]
Image
Out[5]=
Image

One can use HoldPattern to keep the left-hand side unevaluated:

In[8]:=
ResourceFunction["LocalizedByRules"][HoldPattern[a] -> 2, a]
Out[8]=
Image

The left hand side of each rule must be a symbol:

In[9]:=
ResourceFunction["LocalizedByRules"][{n -> 2, f[x_] :> x}, f[n]]
Image
Out[9]=
Image

Publisher

Yong-an Lu

Version History

  • 1.0.0 – 14 October 2019

Related Resources

License Information