(calc.info)Conditional Syntax Rules

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8.8.8.4 Conditional Syntax Rules
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It is possible to attach a "condition" to a syntax rule.  For example,
the rules

     foo ( # ) := ifoo(#1) :: integer(#1)
     foo ( # ) := gfoo(#1)

will parse `foo(3)' as `ifoo(3)', but will parse `foo(3.5)' and
`foo(x)' as calls to `gfoo'.  Any number of conditions may be attached;
all must be true for the rule to succeed.  A condition is "true" if it
evaluates to a nonzero number.  Note: Logical Operations, for a list
of Calc functions like `integer' that perform logical tests.

   The exact sequence of events is as follows:  When Calc tries a rule,
it first matches the pattern as usual.  It then substitutes `#1', `#2',
etc., in the conditions, if any.  Next, the conditions are simplified
and evaluated in order from left to right, as if by the `a s' algebra
command (Note: Simplifying Formulas).  Each result is true if it is a
nonzero number, or an expression that can be proven to be nonzero
(Note: Declarations).  If the results of all conditions are true, the
expression (such as `ifoo(#1)') has its `#'s substituted, and that is
the result of the parse.  If the result of any condition is false, Calc
goes on to try the next rule in the syntax table.

   Syntax rules also support `let' conditions, which operate in exactly
the same way as they do in algebraic rewrite rules.  Note: Other
Features of Rewrite Rules, for details.  A `let' condition is always
true, but as a side effect it defines a variable which can be used in
later conditions, and also in the expression after the `:=' sign:

     foo ( # ) := hifoo(x) :: let(x := #1 + 0.5) :: dnumint(x)

The `dnumint' function tests if a value is numerically an integer,
i.e., either a true integer or an integer-valued float.  This rule will
parse `foo' with a half-integer argument, like `foo(3.5)', to a call
like `hifoo(4.)'.

   The lefthand side of a syntax rule `let' must be a simple variable,
not the arbitrary pattern that is allowed in rewrite rules.

   The `matches' function is also treated specially in syntax rule
conditions (again, in the same way as in rewrite rules).  Note:
Matching Commands.  If the matching pattern contains meta-variables,
then those meta-variables may be used in later conditions and in the
result expression.  The arguments to `matches' are not evaluated in
this situation.

     sum ( # , # ) := sum(#1,a,b,c) :: matches(#2, a=[b..c])

This is another way to implement the Maple mode `sum' notation.  In
this approach, we allow `#2' to equal the whole expression `i=1..10'.
Then, we use `matches' to break it apart into its components.  If the
expression turns out not to match the pattern, the syntax rule will
fail.  Note that `Z S' always uses Calc's normal language mode for
editing expressions in syntax rules, so we must use regular Calc
notation for the interval `[b..c]' that will correspond to the Maple
mode interval `1..10'.