TIP #174: Math Operators as Commands
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TIP:	174
Title:	Math Operators as Commands
Version:	$Revision: 1.21 $
Authors:	Kristoffer Lawson <setok@altparty.org>
	Donal K. Fellows <donal.k.fellows@man.ac.uk>
	David S. Cargo <escargo@skypoint.com>
	Peter Spjuth <peter.spjuth@space.se>
	Kevin B. Kenny <kennykb@acm.org>
State:	Final
Type:	Project
Tcl-Version:	8.5
Vote:	Done
Created:	Mon Mar 15 00:00:00 UTC 2004
Abstract
This TIP describes a proposal for math operators in Tcl as separate commands, acting much like the equivalent in the Lisp language. This would make simple usage of mathematics much clearer.
Rationale
While the expr command works fairly well for longer mathematical expressions, it is extremely tedious for the most common uses, such as handling indices. Take the following examples:
 set newList [lrange $list [expr $idx - 5] [expr $idx + 5]]
 .c create oval [expr $x - $r] [expr $y - $r] [expr $x + $r] [expr $y + $r]
Many find this particular aspect of Tcl unappealing. It gets increasingly difficult to read as more and more simple mathematical expressions build up. (See Example below for how these will look after the proposed change.)
Proposed Change
1.	A group of Tcl commands are added which would handle mathematical operations without the need to use expr. Most commands would take a variable amount of arguments and would work such that the operator is applied to the combination of the first and second arguments. The result of this combination is then used with the operator for the third argument, etc. If only one argument is given, it is returned as is. See below for details for each operator. An example implementation of the + command in Tcl follows:
 proc ::tcl::mathop::+ args 
     set r 0
     foreach operand $args 
         set r [expr $r + $operand]
     
     return $r
 
2.	All operator commands will be kept in the ::tcl::mathop (in line with ::tcl::mathfunc from [232]) namespace, from which they would most commonly be imported into the calling namespace (or resolved in it by means of the namespace path ([229]) command).
3.	The commands are not connected to their corresponding expr operator. Overloading or adding any command in ::tcl::mathop does not affect operators in expr or any other command that calls Tcl_ExprObj, and nor does overriding expr alter the behaviour of any command in :::tcl::mathop.
Operator Commands Details
Unary operators ~ and ! always take one argument.
Op/argc  0    1   2   3+
~       err  ~a  err  err
!       err  !a  err  err
Left-associative operators that naturally allow 0 or more arguments do so:
Op/argc  0   1   2     3+
+        0   a   a+b   a+b+c...
*        1   a   a*b   a*b*c...
&       -1   a   a&b   a&b&c...
^        0   a   a^b   a^b^c...
|        0   a   a|b   a|b|c...
Other left or right associative operators. Operator ** is right associative, which needs to be noted clearly.
Op/argc  0   1   2     3+
**       1   a   a**b  a**(b**(c...))
(This behaviour depends on the eventual modification of the ** operator in [[expr]] to have right-associativity, which is the subject of [274]. If TIP #274 fails, ** should be left- or non-associative.)
Nonassociative operators (including the list operators, "in" and "ni") must always be binary.
Op/argc   0    1    2      3+
<<       err  err  a<<b    err
>>       err  err  a>>b    err
%        err  err  a%b     err
!=       err  err  a!=b    err
ne       err  err  a ne b  err
in       err  err  a in b  err
ni       err  err  a ni b  err
Subtract and divide treat their arguments in a left-associative way except for in the unary case. Unary minus is negation, and unary divide is reciprocal.
Op/argc  0    1      2    3-
-       err  -a     a-b  ((a-b)-c)...
/       err  1.0/a  a/b  ((a/b)/c)...
Comparison operators other than != and ne test for ordering:
Op/argc  0  1   2       3+
<        1  1  a<b     ((a<b)&(b<c)&...)
<=       1  1  a<=b    ((a<=b)&(b<=c)&...)
>        1  1  a>b     ((a>b)&(b>c)&...)
>=       1  1  a>=b    ((a>=b)&(b>=c)&...)
==       1  1  a==b    ((a==b)&(b==c)&...)
eq       1  1  a eq b  ((a eq b)&(b eq c)&...)
(Note the single &; a Tcl command is not capable of "short circuit" evaluation of its arguments.)
The operators that do conditional evaluation of their arguments (&&, || and ?:) are not included. This is because their characteristic evaluation laziness is best modelled using the existing if command.
Example
As an example use, let us change the lines from above:
 set newList [lrange $list [- $idx 5] [+ $idx 5]]
 .c create oval [- $x $r] [- $y $r] [+ $x $r] [+ $y $r]
This is clearly shorter and much easier on the eyes. There is no need to consider the effects of bracing expressions.
Sum of a list becomes
 set sum [+ expand$list]
Security considerations
It is worth noting that variadic operators have no way of "short circuit" evaluation, much as putative && and || commands would not. This consideration means that they must be used with caution in cases where expressions have side effects; all their arguments will be evaluated. Commands like
   < 1 0 [don't do this!]
   / 0 0 [don't do this!]
will indeed evaluate the string in square brackets.
If expressions like these are constructed from user input, care must be taken to place them in a safe execution environment or otherwise defend against code injection attacks. (This last consideration is somewhat far-fetched, since it is implausible that an injection attack would be able to generate [[< 1 0 [[don't do this!]]]] but not [[< [[don't do this!]] 0]].)
Implementation
Efficiency
These commands can naturally be compiled and thus as efficient as their corresponding expr operators. The following lines should probably result in the same byte codes.
set x [expr $a * $b + $c]
set x [+ [* $a $b] $c]
Reference Implementation
Available online at SourceForge [http://sf.net/tracker/?func=detail&aid=1578137&group_id=10894&atid=310894]. The patch is for this TIP as it stood several versions ago; in particular, it does not implement the ordering comparators and gets associativity wrong in a couple of other cases. Nevertheless, the authors of this TIP believe it to be an adequate proof that the ideas of the TIP are implementable with good performance.
Copyright
This document has been placed in the public domain.
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