Read[stream, Number] will return a single read number. We can use a number of standard, documented types instead of Number, such as String, Expression, Real, etc.
Is it possible to get Read to immediately apply a function to the expression that was just read, similarly to how ToExpression applies its third argument?
Yes! This is documented under Details:
You can use Read to get objects to insert into any expression structure, not necessarily a list. Example:
Read[stream,Hold[Expression]]gets an expression and places it insideHold.
What this means is that we can use any compound expression as the second argument of Read. Any type names (such as Number, Real, Expression, etc.) that appear in this compound expression will be replaced by the values that are read.
Suppose we have an input file containing
1 2 3+4
Then we can read and process the data at the same time this way:
Read[str, Number] --> 1 read one number
Read[str, {Number, Number}] --> {1, 2} read two numbers
Read[str, f[Number, Number]] --> f[1, 2] read two numbers and wrap them in f instead of List
Read[str, {{Number, Number}, Expression}] --> {{1, 2}, 7} two numbers and an expression
Read[str, {{Number, Number}, Hold[Expression]} --> {{1, 2}, Hold[3+4]} two numbers and a held expression
The two most prominent applications are the ones shown in the documentation:
Read values grouped into lists, Read[..., {Number, Number, Number}]
Read held expressions using Read[..., HoldComplete[Expression]]. The expression is inserted into HoldComplete before evaluation.
Read[..., Hold[Expression]]!
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