Declaration Basics
------------------

The `s d' (`calc-declare-variable') command is the easiest way to make
a declaration for a variable.  This command prompts for the variable
name, then prompts for the declaration.  The default at the
declaration prompt is the previous declaration, if any.  You can edit
this declaration, or press `C-k' to erase it and type a new
declaration.  (Or, erase it and press RET to clear the declaration,
effectively "undeclaring" the variable.)

A declaration is in general a vector of "type symbols" and "range"
values.  If there is only one type symbol or range value, you can
write it directly rather than enclosing it in a vector.  For example,
`s d foo RET real RET' declares `foo' to be a real number, and `s d
bar RET [int, const, [1..6]] RET' declares `bar' to be a constant
integer between 1 and 6.  (Actually, you can omit the outermost
brackets and Calc will provide them for you: `s d bar RET int, const,
[1..6] RET'.)

Declarations in Calc are kept in a special variable called `Decls'.
This variable encodes the set of all outstanding declarations in
the form of a matrix.  Each row has two elements:  A variable or
vector of variables declared by that row, and the declaration
specifier as described above.  You can use the `s D' command to
edit this variable if you wish to see all the declarations at once.
See Operations on Variables, for a description of this command
and the `s p' command that allows you to save your declarations
permanently if you wish.

Items being declared can also be function calls.  The arguments in the
call are ignored; the effect is to say that this function returns
values of the declared type for any valid arguments.  The `s d'
command declares only variables, so if you wish to make a function
declaration you will have to edit the `Decls' matrix yourself.

For example, the declaration matrix

     [ [ foo,       real       ]
       [ [j, k, n], int        ]
       [ f(1,2,3),  [0 .. inf) ] ]

declares that `foo' represents a real number, `j', `k' and `n'
represent integers, and the function `f' always returns a real number
in the interval shown.

If there is a declaration for the variable `All', then that
declaration applies to all variables that are not otherwise declared.
It does not apply to function names.  For example, using the row
`[All, real]' says that all your variables are real unless they are
explicitly declared without `real' in some other row.  The `s d'
command declares `All' if you give a blank response to the
variable-name prompt.