Text Controls and More

A text control is just a block of text (really, HTML) that gets inserted among other controls. This can be useful in interactions that are not in context, for example by providing a brief description of what the interaction does. Unfortunately, the following generates a syntax error:

def f("This function does nothing."):
    pass

Doing nothing in Python is perfectly legal, but having a non-variable in the definition isn't. My current implementation isn't pretty:

@interact
def _(t1=text_control("This function does nothing.")):
    pass

In working on the control I have come to realize that the structure of interact is indeed limited. Currently, interact takes a function, whose variables are set with defaults as control objects. The design has several major limitations:

1. All controls must be tied to a variable, which is not what we always want. For example, there is no reason to tie a block of text to a variable.
2. Functions generated for interact cannot be used outside of interact. Similarly, functions generated outside of interact do not make good interactions. One has to write a wrapper function with the right controls.

Mathematica's Manipulate command uses a more logical design: pick any function and pass along a list of controls. For example:

Current

@interact
def f(t1=text_control("Plots a function."),
l=slider(-20, 0, default=-2, label='Lower bound:'),
u=slider(0,20, default=2, label='Upper bound:')):
    plot(lambda x:sin(x)/x, l, u).show()

Versus something like:

def f(l,u):
    plot(lambda x:sin(x)/x, l, u).show()

interact(f, "Plots a function",
('l', slider(-20, 0, default=-2, label='Lower bound:')),
('u', slider(0,20, default=2, label='Upper bound:')))

Benefits:

1. We can put anything in the list: text, numbers (default values with no controls) without associating a variable.
2. We can easily make high quality (that is, with appropriate controls, text, etc.) interactions for builtin SAGE functions or any other functions not designed for interact.
3. We can nest interactions. Right now, it is possible to create a function, and then call interact on it, but this method is known to break because interactions are limited to one and nothing else per cell.
4. I think it is easier to understand for someone who knows Python well but is not familiar with interact.

Well, those were my thoughts on interact right now, but perhaps I am looking at interact from the wrong angle today after messing with text controls. I will continue to perfect the text control, with another control in mind and more long-term plans that involve something completely different. To the reader I leave this mystery and hint only that the idea for the new control came to me yesterday while I was writing the example interaction.