Using With in combination with Graphics [duplicate]

Question

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• What are the use cases for different scoping constructs? 7 answers

Assume that we are given a symbol p={x,y} which should represent a 2D point. If x and y have numerical values then we can plot the point uisng

Graphics[Point[p]]

Next, I wanted to plot some setting for various x and y, so I thought I could use the With command and have something like:

With[{x = 1, y = 1},
 Graphics[Point[p]]
 ]

This doesn't work. I guess it has something to do with the order of evaluations, holding stuff etc. but I cannot figure out how to solve this.

So the question is how to use With together with Graphics?

Answer 1

The trivial answer is: don't use With, use Block:

p := {x, y}

Block[{x = 1, y = 1},
 Graphics[Point[p]]
]

The question remains how one can use With. It is possible with Evaluate:

With[{x = 1, y = 1},
 Graphics[Point[p]] // Evaluate
]

This contravenes the expected behavior of With which normally replaces symbols before evaluation. It works in this case because nothing (bad) happens when you evaluate the incomplete Graphics expression; errors only appear on display. In other cases you may need to prevent evaluation of the full expression, yet you wish to make a substitution. This amounts to in-place evaluation, so you will need something like the Trott-Strzebonski method for In-Place Evaluation, or this method that WReach introduced me to:

Unevaluated[Print[Hold[p]]] /. HoldPattern[p] :> RuleCondition @ Block[{x = 1, y = 1}, p]

Hold[{1,1}]

Or, since p is a Symbol and not an arbitrary pattern we may use the "injector pattern":

Block[{x = 1, y = 1}, p] /. p_ :> Print[Hold[p]]

Hold[{1,1}]

I replaced Graphics with Print, and Point with Hold so that the holding and evaluation behavior would be apparent.