''In the spirit of [If we had no if], I wondered what would happen if there was no [expr] (it's certainly one of the more awkward Tcl commands). There are probably plenty of alternative ways to achieve the necessary functionality. -- [Lars H]''

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'''Natural number arithmetic via unary representation'''

In unary representation of natural number, one simply writes as many 
digits as the number one wants to represent. [string length] sort of
converts unary to decimal, and [string repeat] can be used to convert
decimal to unary. That way, one can do things such as the following.

 proc plus {a b} {
    string length "[string repeat 1 $a][string repeat 1 $b]"
 }
As expected, we get
 % plus 2 2
 4
 % plus 2 3
 5
Negative input seems to be accepted, but is then treated as zero.
 % plus -2 2
 2

In a similar vein, one can define
 proc minus {a b} {
    string length [string range [string repeat 1 $a] $b end]
 }
 proc times {a b} {
    string length [string repeat [string repeat 1 $a] $b]
 }
 proc div {a b} {
    string length [string map [
        list [string repeat 1 $b] N 1 {}
    ] [string repeat 1 $a]]
 }
 proc mod {a b} {
    string length [string map [
        list [string repeat 1 $b] {}
    ] [string repeat 1 $a]]
 }
From these one gets for example
 % minus 10 4
 6
 % minus 4 10
 0
 % times 6 7
 42
 % div 10 4
 2
 % mod 7 2
 1
 % mod 7 0
 7
 % div 7 0
 0
some of which are unusual, still (kind of) make sense.

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''Other approaches ...''


[[ [Arts and crafts of Tcl-Tk programming] -   ]]