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Re: [Clip] VanWeerthuizenian Expressions

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  • flo.gehrke
    ... Thanks for your explanations, Art! This is certainly a great help for users trying to go further into that topic. However, I would like to get back to my
    Message 1 of 12 , Sep 18, 2013
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      --- In ntb-clips@yahoogroups.com, Art Kocsis <artkns@...> wrote:
      >
      > At 9/10/2013 05:11 PM, Flo wrote:
      >> It has been discussed several times that NT doesn't master Boolean
      >> Expressions (cf message #21773)...
      > Flo, If I can jump in here.(...)
      > In testing boolean expressions...

      Thanks for your explanations, Art!

      This is certainly a great help for users trying to go further into that topic.

      However, I would like to get back to my question concerning the specific concept that was introduced by Wayne VanWeerthuizen (where is he?) with his abovementioned 'NoteTab Tutorial Control Structures v003.OTL'...

      > Is anyone (also Wayne himself) still using such expressions and
      > could give us more examples. Regrettably, Wayne's Tutorial was
      > never finished and has remained a highly instructive fragment
      > only. Also, it's lacking complete working examples

      So far, Wayne gave us the solution for only five conditions.

      Given a simple list...

      A B
      A B C
      A C D
      B
      D E F

      we could test Wayne's five expressions against that list with the following clip...

      ^!Set %Lines%=^$GetTextLineCount$
      ^!Set %Row%=1
      ^!Goto ^?{(H=5)Find lines matching...==A AND B|A OR B|A NOT B|A XOR B|NOT A}

      :A AND B
      :Loop_1
      ^!Set %A%=0; %B%=0
      ^!Jump ^%Row%
      ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
      ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
      ^!If ^$Calc(MIN(^%A%;^%B%))$=1 Next Else Skip
      ^!Set %Hits%=^%Hits%^$GetLine$^P
      ^!Inc %Row%
      ^!If ^$GetRow$ < ^%Lines% Loop_1
      ^!Info [L]Expression: A AND B^P^PMatches:^P^%Hits%
      ^!Goto Out

      :A OR B
      :Loop_2
      ^!Set %A%=0; %B%=0
      ^!Jump ^%Row%
      ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
      ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
      ^!If ^$Calc(MAX(^%A%;^%B%))$=1 Next Else Skip
      ^!Set %Hits%=^%Hits%^$GetLine$^P
      ^!Inc %Row%
      ^!If ^$GetRow$ < ^%Lines% Loop_2
      ^!Info [L]Expression: A OR B^P^PMatches:^P^%Hits%
      ^!Goto Out

      :A NOT B
      :Loop_3
      ^!Set %A%=0; %B%=0
      ^!Jump ^%Row%
      ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
      ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
      ^!If ^$Calc(MIN(^%A%;1-^%B%))$=1 Next Else Skip
      ^!Set %Hits%=^%Hits%^$GetLine$^P
      ^!Inc %Row%
      ^!If ^$GetRow$ < ^%Lines% Loop_3
      ^!Info [L]Expression: A NOT B^P^PMatches:^P^%Hits%
      ^!Goto Out

      :A XOR B
      :Loop_4
      ^!Set %A%=0; %B%=0
      ^!Jump ^%Row%
      ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
      ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
      ^!If ^$Calc(ABS(^%A%-^%B%))$=1 Next Else Skip
      ^!Set %Hits%=^%Hits%^$GetLine$^P
      ^!Inc %Row%
      ^!If ^$GetRow$ < ^%Lines% Loop_4
      ^!Info [L]Expression: A XOR B^P^PMatches:^P^%Hits%
      ^!Goto Out

      :NOT A
      :Loop_5
      ^!Set %A%=0
      ^!Jump ^%Row%
      ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
      ^!If ^$Calc(1-^%A%)$=1 Next Else Skip
      ^!Set %Hits%=^%Hits%^$GetLine$^P
      ^!Inc %Row%
      ^!If ^$GetRow$ < ^%Lines% Loop_5
      ^!Info [L]Expression: NOT A^P^PMatches:^P^%Hits%
      ^!Goto Out

      :Out
      ^!ClearVariables

      As far as I can see, the clip gets to correct results.

      Nevertheless, for me the question remains: Is there any way to enlarge Wayne's concept to conditions like 'A AND B AND NOT (E OR D)', for example? Or is there no way to get beyond the borders of those five conditions?


      Regards,
      Flo

      P.S. Regarding...

      > Too often help is solicited and answers posted with nary a word
      > of feedback or thanks. That is not a motivator for continuing
      > to offer help.

      How right you are.... :-(
    • joy8388608
      ... Thanks for your explanations, Art! This is certainly a great help for users trying to go further into that topic. However, I would like to get back to my
      Message 2 of 12 , Sep 19, 2013
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        >Nevertheless, for me the question remains: Is there any way to enlarge Wayne's concept to conditions like 'A AND B AND NOT (E OR D)', for example? Or is there no way to get beyond the borders of those five conditions?


        I'm still not quite sure exactly what the desired end results of this topic is (subroutines? other way to write this type of code?) but here are my thoughts which might help. Sorry if I repeat what has been said before. You will find that I would try to avoid functions like MAX and MIN except for simply cases simply because the syntax gets messy so quickly.


        Assume five vars A,B,C,D,E which have each been set to 0 (false) or 1 (true).

        We want to manipulate the values to give an answer of 0 or 1.


        A OR B OR C OR D OR E

          MAX(A:B:C:D:E)

          also equivalent to NOT( (NOT A) AND (NOT B) AND (NOT C) AND (NOT D) AND (NOT E)  )

          which is equivalent to 1 - ( (1 - A) * (1 - B) * (1 - C) * (1 - D) * (1 - E) )


          also equivalent to IfTrue (A+B+C+D+E) > 0


        A AND B AND C AND D AND E

          MIN(A;B;C;D;E)

          also equivalent to A*B*C*D*E


        NOT A

          1-A


        So, if I were to calculate A AND B AND NOT (E OR D), I would do

          A * B * (1 - MAX(D:E)) since it is really ANDing three values.


        It often (but not always) helps to create an equivalent logical statement.

        For Example, A AND B AND NOT (D OR E) is the same as A AND B AND (NOT D) AND (NOT E) which equates to A * B * (1 - D) * (1 - E) which I like even better since it does away with the MAX and MIN functions with the error prone function syntax (all the dollar signs and nested parens).


        I double checked this all on paper. Hope I didn't make any mistakes and that it is useful.


        Joy




         



        --- In ntb-clips@yahoogroups.com, <flo.gehrke@...> wrote:

        --- In ntb-clips@yahoogroups.com, Art Kocsis <artkns@...> wrote:
        >
        > At 9/10/2013 05:11 PM, Flo wrote:
        >> It has been discussed several times that NT doesn't master Boolean
        >> Expressions (cf message #21773)...
        > Flo, If I can jump in here.(...)
        > In testing boolean expressions...

        Thanks for your explanations, Art!

        This is certainly a great help for users trying to go further into that topic.

        However, I would like to get back to my question concerning the specific concept that was introduced by Wayne VanWeerthuizen (where is he?) with his abovementioned 'NoteTab Tutorial Control Structures v003.OTL'...

        > Is anyone (also Wayne himself) still using such expressions and
        > could give us more examples. Regrettably, Wayne's Tutorial was
        > never finished and has remained a highly instructive fragment
        > only. Also, it's lacking complete working examples

        So far, Wayne gave us the solution for only five conditions.

        Given a simple list...

        A B
        A B C
        A C D
        B
        D E F

        we could test Wayne's five expressions against that list with the following clip...

        ^!Set %Lines%=^$GetTextLineCount$
        ^!Set %Row%=1
        ^!Goto ^?{(H=5)Find lines matching...==A AND B|A OR B|A NOT B|A XOR B|NOT A}

        :A AND B
        :Loop_1
        ^!Set %A%=0; %B%=0
        ^!Jump ^%Row%
        ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
        ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
        ^!If ^$Calc(MIN(^%A%;^%B%))$=1 Next Else Skip
        ^!Set %Hits%=^%Hits%^$GetLine$^P
        ^!Inc %Row%
        ^!If ^$GetRow$ < ^%Lines% Loop_1
        ^!Info [L]Expression: A AND B^P^PMatches:^P^%Hits%
        ^!Goto Out

        :A OR B
        :Loop_2
        ^!Set %A%=0; %B%=0
        ^!Jump ^%Row%
        ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
        ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
        ^!If ^$Calc(MAX(^%A%;^%B%))$=1 Next Else Skip
        ^!Set %Hits%=^%Hits%^$GetLine$^P
        ^!Inc %Row%
        ^!If ^$GetRow$ < ^%Lines% Loop_2
        ^!Info [L]Expression: A OR B^P^PMatches:^P^%Hits%
        ^!Goto Out

        :A NOT B
        :Loop_3
        ^!Set %A%=0; %B%=0
        ^!Jump ^%Row%
        ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
        ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
        ^!If ^$Calc(MIN(^%A%;1-^%B%))$=1 Next Else Skip
        ^!Set %Hits%=^%Hits%^$GetLine$^P
        ^!Inc %Row%
        ^!If ^$GetRow$ < ^%Lines% Loop_3
        ^!Info [L]Expression: A NOT B^P^PMatches:^P^%Hits%
        ^!Goto Out

        :A XOR B
        :Loop_4
        ^!Set %A%=0; %B%=0
        ^!Jump ^%Row%
        ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
        ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1
        ^!If ^$Calc(ABS(^%A%-^%B%))$=1 Next Else Skip
        ^!Set %Hits%=^%Hits%^$GetLine$^P
        ^!Inc %Row%
        ^!If ^$GetRow$ < ^%Lines% Loop_4
        ^!Info [L]Expression: A XOR B^P^PMatches:^P^%Hits%
        ^!Goto Out

        :NOT A
        :Loop_5
        ^!Set %A%=0
        ^!Jump ^%Row%
        ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
        ^!If ^$Calc(1-^%A%)$=1 Next Else Skip
        ^!Set %Hits%=^%Hits%^$GetLine$^P
        ^!Inc %Row%
        ^!If ^$GetRow$ < ^%Lines% Loop_5
        ^!Info [L]Expression: NOT A^P^PMatches:^P^%Hits%
        ^!Goto Out

        :Out
        ^!ClearVariables

        As far as I can see, the clip gets to correct results.

        Nevertheless, for me the question remains: Is there any way to enlarge Wayne's concept to conditions like 'A AND B AND NOT (E OR D)', for example? Or is there no way to get beyond the borders of those five conditions?


        Regards,
        Flo

        P.S. Regarding...

        > Too often help is solicited and answers posted with nary a word
        > of feedback or thanks. That is not a motivator for continuing
        > to offer help.

        How right you are.... :-(
      • flo.gehrke
        Joy, ... As I wrote, so far, Wayne gave us five expressions... Boolean -- Wayne s equivalent ... A AND B -- ^$Calc(MIN(A;B))$=1 A OR B --
        Message 3 of 12 , Sep 19, 2013
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          Joy,

          > I'm still not quite sure exactly what the desired end results of
          > this topic is (subroutines? other way to write this type of code?)

          As I wrote, so far, Wayne gave us five expressions...

          Boolean --> Wayne's equivalent
          -------------------------------
          A AND B --> ^$Calc(MIN(A;B))$=1
          A OR B --> ^$Calc(MAX(A;B))$=1
          A NOT B --> ^$Calc(MIN(A;1-B))$=1
          A XOR B --> ^$Calc(ABS(A-B))$=1
          NOT A --> ^$Calc(1-A)$=1

          See my clip as an example how to make use of these expressions -- if I understand Wayne's concept correctly.

          So my simple question is: Could anyone give me, say, four or five more "Waynean expressions" like that for executing even more complicated Boolean expressions? And best show us how to test them against the list...

          A B
          A B C
          A C D
          B
          D E F

          For example: What is the "Waynean expression" to be used with my clip in order to match lines where 'A NOT (B OR C)' is true? Or '(C OR D) AND NOT A' etc...

          > You will find that I would try to avoid functions like MAX and
          > MIN except for simply cases simply because the syntax gets
          > messy so quickly.

          Are we free to "avoid" these functions here? I think they are a basic element of Wayne's concept. 'A NOT B', for example, says: If A is true and if B is true then 'A NOT B' is true if ^$Calc(MIN(A;1-B))$=1. So I can't see how your calculations like...

          > IfTrue (A+B+C+D+E) > 0
          > MIN(A;B;C;D;E)
          > also equivalent to A*B*C*D*E

          could conform with Wayne's concept. I think ^$Calc is just used for sequentially testing for 0 or 1 (true or false) here.

          Regards,
          Flo
        • Art Kocsis
          Sorry, another long post. But there s a lot to cover. On Wed 11 Sep 2013 08:10:08 -0700 Flo said: ...what matters here is this specific approach which - as
          Message 4 of 12 , Sep 19, 2013
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            Sorry, another long post. But there's a lot to cover.

            On Wed 11 Sep 2013 08:10:08 -0700 Flo said:
            "...what matters here is this specific approach which - as Wayne explained -
            could apply to much more complex queries (with AND, OR, XOR, NOT etc). In
            cases like that, it would be difficult to use RegEx, and compound loops
            would end in extremely long "IF, ELSE IF, ELSE IF Chains" (Wayne)."

            On Thu, 19 Sep 2013 03:52:04 -0000 Flo said:
            "Nevertheless, for me the question remains: Is there any way to enlarge Wayne's
            concept to conditions like 'A AND B AND NOT (E OR D)', for example? Or is there
            no way to get beyond the borders of those five conditions?"

            BTW Five???  I only see four: NOT, OR, AND, XOR. And those are operators,
            not conditions. What am I missing>
            #############################################

            Flo, I think what you are asking is: given the absence of logical operators
            in Notetab Clip Code, how can I generalize the use of arithmetic operators
            to apply them to complex logical expressions without obtuse and lengthy
            If - Then - Else trees.

            The answer has two parts:
              1: The mapping of the logical operations to arithmetical operations
              2: The transformation of complex logical expressions into canonical form

            Regarding #1, there are a number of different mapping of logical to arithmetical
            operations as Wayne and I have discussed and with no major standouts among them.
            They all suffer from the inherent limitation of being strictly binary operations
            in Notetab, (i.e., MAX (A,B,C,D...) is not allowed). To recap two mappings:

            Operation             Addition only            Allowing Subtraction
            ============          ======================   =====================
              NOT A        <==>   (A + 1) MOD 2             (1 - A)
            A AND B        <==>   A * B                     MIN (A, B)
            A OR  B        <==>   MAX (A, B)                MAX (A, B)
            A XOR B        <==>   (A + B) MOD 2             ABS (A-B)
            NOT A AND B    <==>   (MIN (A, B) + 1) MOD 2    1 - MIN (A,B)
            NOT A OR  B    <==>   (MAX (A, B) + 1) MOD 2    1 - MAX (A,B)
            NOT A XOR B    <==>   (A + B + 1) MOD 2         1 - ABS (A-B)

            Regarding #2 as Joy and I discussed, any logical expression can be transformed
            into an equivalent DNF (an OR of ANDs), or CNF (an AND of ORs), expression. These
            canonical expressions use only the three logical operators: NOT, AND and OR.

            You can do that transform either by a series of transformations using
            DeMorgan's laws or - easier for very complicated expressions - by using truth tables. Each row in a truth table is a conjunction (AND) of the state of the columns (conditions). The disjunction (OR) of all the rows resulting in a true (=1) state is the DNF (Disjunctive Normal Form) of the system. For example:

                ##  A B C D E   X     Y1  Y2  Y3    Y     DNF Term
                ==  = = = = =   =     ==  ==  ==    =     ======================
                01  0 0 x 0 0   0     0   0   0     0    
                02  0 0 x 0 1   0     0   0   0     0    
                03  0 0 x 1 0   0     0   0   1     1     ¬A AND ¬B AND D AND ¬E
                04  0 0 x 1 1   0     0   0   0     0
                05  0 1 x 0 0   0     0   0   1     1     ¬A AND B AND ¬D AND ¬E
                06  0 1 x 0 1   0     0   1   0     1     ¬A AND B AND ¬D AND E
                07  0 1 x 1 0   0     0   1   1     1     ¬A AND B AND D AND ¬E
                08  0 1 x 1 1   0     0   0   0     0    
                09  1 0 x 0 0   0     0   0   0     0    
                10  1 0 x 0 1   0     0   0   0     0    
                11  1 0 x 1 0   0     0   0   0     0    
                12  1 0 x 1 1   0     0   0   0     0    
                13  1 1 x 0 0   1     1   0   0     1     A AND B AND ¬D AND ¬E
                14  1 1 x 0 1   0     0   0   0     0    
                15  1 1 x 1 0   0     0   0   0     0    
                16  1 1 x 1 1   0     0   0   0     0    

            For instance, taking your example, A AND B AND NOT (E OR D), (Col X),
            the DNF form for X is simply row 13: X = A AND B AND ¬D AND ¬E
            (where ¬ is the NOT operator). That seems like a lot of work compared
            to the trivial DeMorgan transformation but this is meant to illustrate
            a process so let's add some complication:

            Let Y = [A AND B AND NOT (E OR D)]
                       OR {¬A AND [B AND (¬D OR E) OR B AND (D OR ¬E)]}
                       OR [(¬A AND ¬E AND (B OR D)]
                  = Y1 OR Y2 OR Y3

            Where Y1 = A AND B AND NOT (E OR D)
                  Y2 = ¬A AND [B AND (¬D OR E) OR B AND (D OR ¬E)]
                  Y3 = (¬A AND ¬E AND (B OR D)

            The Y column is the conjunction of the Y1, Y2 and Y3 columns and the final DNF
            expression is just the OR (Sum), of the Y rows with true values:

            Y = R3 OR R5 OR R6 OR R7 OR R13
              = (¬A AND ¬B AND D AND ¬E) OR (¬A AND B AND ¬D AND ¬E) OR (¬A AND B AND ¬D AND E)
                     OR (¬A AND B AND D AND ¬E) OR (A AND B AND ¬D AND ¬E)

            This logical expression can now be evaluated in six clear and easily followed steps,
            none of which involve an If test:
               Evaluate each of the five row expressions using the canonical AND operations
               Evaluate the final result using the canonical OR operation on those five results.

            Alternatively, the expression could be coded directly using my functions. I did find
            it necessary to first transform the expression from embedded binary notation to prefix
            notation. Even then I had to be very careful not to introduce an error. I could then
            use NTB's replace dialog to convert to Clip syntax. Without a parser to analyze and
            convert an arbitrary expression with nested parentheses to Notetab format it still is
            a bit tricky. The functions work well for short or medium complexity expressions but
            a truth table is easier and more reliable for anything more complex.

            Y1 = and(A,B,¬or(E,D))
            Y2 = and(¬A,¬E,or(B,D))
            Y3 = and(¬A,or(and(B,or(¬D,E)),and(B,or(D,¬E))))

            ^!Set %Y1%^$AND(^%A%,^%B%,^$NOR(^%E%,^%D%)$)$
            ^!Set %Y2%^$AND(^$NOT(^%A%)$$,^$NOT(^%E%)$$,^$OR(^%B%,^%D%)$)$
            ^!Set %Y3%^$AND(^$NOT(^%A%)$$,^$OR(^$AND(^%B%,^$OR(^$NOT(^%D%)$$,^%E%)$)$,^$AND(^%B%,^$OR(^%D%,^$NOT(^%E%)$$)$)$
            ^!Set %Y%=^$OR(^%Y1%;^%Y2%;^%Y3%)$


            Some things to notice/consider:
            • The astute reader will notice that Y2 is equivalent to ¬A AND B AND (D XOR E)
                 However, remember we are limiting ourselves to NOT, AND and OR operators.
            • Separating the terms into partial result columns makes it easier and less
                 error prone to generate the truth table.
            • There can be some overlap in the partial results (e.g., row 7, col Y2 and Y3)
            • The growth of terms (and complexity) is linear, not exponential
            • Changes to the system criteria (truth table), are easily and fairly reliably
                 propagated to the DNF expression terms (this is much, much less error prone
                 than If - Then - Else logic trees.
            • Additional columns can easily be added to record the results of alternate
                 logical expressions using the same worksheet and input parameters states.
            • The truth table is independent and external to any program language or code.
                 It is simply prep work prior to program implementation.
            • A truth table is easy to generate, easy to understand and concise in execution
            • Most important, using a truth table to analyze and code logic expressions is
                 the most reliable and least error prone method available.

            OTOH, Trying to implement complex expressions by means of If - Then - Else
            trees is a recipe for frustration and errors. Clear computation and  program
            flow is a basic requirement for generating error free code as well for
            downstream maintainability. The VanWeerthuizenian Expressions get very messy
            very, very quickly once you go beyond the trivial two parameter, binary
            condition unless you restrict yourself to canonical forms. This is primarily
            due to the restriction of the MAX and MIN functions to two operands. That is
            why I removed that restriction from my AND and OR functions. However, in
            canonical form the benefit of my functions is much less dramatic than I expected.

            For example for R3 = ¬A AND ¬B AND D AND ¬E

            ^!Set %R3%=^$Calc(min((1-^%A%),min((1-^%B%),min(^%D%,(1-^%E%))));0)$
            vs
            ^!Set %R3%=^$AND(^$NOT(^%A%)$;^$NOT(^%B%)$;^%D%;^$NOT(^%E%)$)$

            I think the functions are clearer and less error prone than all the nested
            parentheses and remembering the correct mappings but not earth shakingly so.

            However, the major point and lesson here is the transformation to DNF
            form. Whether you use the VanWeerthuizenian constructs or my functions,
            the best path to error free coding and ease of maintenance is to transform
            your test criteria into canonical form using a single variable for each
            criteria, generate the DNF expression (by either Boolean transformations
            or via a truth table), and then evaluate the resulting products and sums.
            Do not use an If test until the final result.


            Applying this paradigm to your example:

            {A AND B|A OR B|A NOT B|A XOR B|NOT A}

            Let Y1 = A AND B; Y2 = A OR B; Y3 = A NOT B; Y4 = A XOR B; Y5 = NOT A

            The truth table is:

            #  A  B  Y1  Y2  Y3  Y4  Y5
            =  =  =  ==  ==  ==  ==  ==
            1  0  0  0   0   0   0   1
            2  0  1  0   1   0   1   1
            3  1  0  0   1   1   1   0
            4  1  1  1   1   0   0   0

            And the DNFs for the five cases are:

            Y1 = A AND B
            Y2 = A OR B
            Y3 = A AND ¬B
            Y4 = ¬A AND B OR A AND ¬B
            Y5 = ¬A

            It doesn't seem like we gained much but yours is a fairly trivial test and
            remember, I am illustrating a generalized process, not content.
            Implementing this in a clip:
            ;######################### Start of Clip Code ###############################
            ;^!SetDebug On
            ^!Set %Lines%=^$GetTextLineCount$
            ^!Set %Row%=1; %Hits%=^%Empty%
            ^!Set %Case%=^?{(H=5)Find lines matching...==_A AND B|A OR B|A NOT B|A XOR B|NOT A}

            :Loop
            ^!Jump ^%Row%
            ^!Set %A%=0; %B%=0; %Y%=0
            ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
            ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1

            ^!Set %Y1%=^$Calc(MIN(^%A%;^%B%))$
            ^!Set %Y2%=^$Calc(MAX(^%A%;^%B%))$
            ^!Set %Y3%=^$Calc(MIN(^%A%;1-^%B%))$
            ^!Set %Y41%=^$Calc(MIN(1-^%A%;^%B%))$
            ^!Set %Y42%=^$Calc(MIN(^%A%;1-^%B%))$
            ^!Set %Y4%=^$Calc(MAX(^%Y41%;^%Y42%))$
            ^!Set %Y5%=^$Calc(1-^%A%)$

            ^!IfMatch "^%Case%" "A AND B" ^!Set %Y%=^%Y1%
            ^!IfMatch "^%Case%" "A OR B" ^!Set %Y%=^%Y2%
            ^!IfMatch "^%Case%" "A NOT B" ^!Set %Y%=^%Y3%
            ^!IfMatch "^%Case%" "A XOR B" ^!Set %Y%=^%Y4%
            ^!IfMatch "^%Case%" "NOT A" ^!Set %Y%=^%Y5%

            ^!IfTrue ^%Y% ^!Set %Hits%=^%Hits%^$GetLine$^P
            ^!Inc %Row%
            ^!If ^$GetRow$ < ^%Lines% Loop
            ^!Info [L]Expression: ^%Case%^P^PMatches:^P^%Hits%

            ^!GoTo End

            ;Alternate set of logic expression calculations
            ^!Set %Y1%=^$AND(^%A%;^%B%)$
            ^!Set %Y2%=^$OR(%A%;^%B%)$
            ^!Set %Y3%=^$AND(^%A%;^$NOT(^%B%)$)$
            ^!Set %Y41%=^$AND(^$NOT(^%A%);^%B%)$;)$
            ^!Set %Y42%=^$AND(^%A%;^$NOT(^%B%)$)$
            ^!Set %Y4%=^$OR(^%Y41%;^%Y42%)$
            ^!Set %Y5%=^$NOT(^%A%)$
            ;######################### End of Clip Code ###############################

            This, of course, could be rearranged to use your computed GoTos, the DNF
            computations could be moved to the %case% tests with only %Y41% and %Y42%
            pre-computed or other optimizations which might or might not be significant
            depending on the application but would probably be at the cost of clarity
            and generalization. Remember, the emphasis here is on clarity of program
            flow (primarily linear), to minimize coding errors and to ease maintenance.
            The various sections are segregated, similar operations are consolidated, and
            program branches are minimized. A flow chart of this clip would not have any
            crossed lines.

            I hope this answers your questions.  Art
          • joy8388608
            Hi Art. Uh, wow. Just... wow. I wish I had time to look through your post in detail to see if it covers what I just logged on to post. But I don t so, again,
            Message 5 of 12 , Sep 20, 2013
            • 0 Attachment

              Hi Art. 


              Uh, wow. Just... wow. I wish I had time to look through your post in detail to see if it covers what I just logged on to post. But I don't so, again, sorry if I repeat.


              I did notice something that seems to me to be incorrect but I did not have time to see if it was a one time thing or was repeated.


              In your first table, you have

              NOT A AND B    <==>   (MIN (A, B) + 1) MOD 2    1 - MIN (A,B)   and

              NOT A OR  B    <==>   (MAX (A, B) + 1) MOD 2    1 - MAX (A,B)


              Order of operations are NOT then AND then OR 

              http://en.wikipedia.org/wiki/Logical_connective#Order_of_precedence

              so NOT A AND B is really (NOT A)  AND B but your third column interprets it as NOT (A AND B).

              Anyway, what I was going to say to Flo is this...

              I think I now see what you are really asking and I think not quite understanding. You want to find out how to do this Wayne's way and I'm saying this is a big mistake except for the simplest of cases. The second thing I'm not sure you see is that the way I'm showing is equivalent and simpler for complicated cases - easier to read, write and understand. The third point is that it seems like you are looking for a step by step method of converting logic into code. I say every case is different and sometimes Wayne's way is fine, sometimes my way is better and sometimes a combination of both is the best way. The key is to learn how to convert logical statements into the easiest form to work with and do away with MAX and MIN when possible. In other words, use my way. :)  Example. A OR NOT(C AND D) is the same as A OR NOT C OR NOT D.

              Here are real clips to show your simple case of A NOT B which I am interpreting as A AND NOT B which is really A AND (NOT B). In this one, Wayne's way is fine since it is simple enough.

              The second clip is for A NOT (B OR C) which I'm reading as A AND NOT (B OR C). It took me a few tries to get the parens matched up with the MINs and MAXs for even this simple case. Add a few conditions or more variables and it's a mess.

              Note my use of an actual test for If A=1 AND B=1 AND C=1 AND D=1 AND E=1 in both clips. I also designed the clips for up to 5 vars so the output has extra lines for simpler cases. Just ignore them.

              I think you will see the results are the same and why I like my way better.

              You can modify these clips to test your own stuff. I'd be happy to try to help if you want to see the way I would code a specific case. Every test is different and people see things in different ways. Obviously, if it's code that only you see and you see it one way better than another and it works... no problem.

              Joy

              ^!InsertText Testing A AND NOT B^%NL%^%NL%

              ^!Set %A%=0;%B%=0;%C%=0;%D%=0;%E%=0
              ^!Set %Meth1%="Calc(MIN(A;(1 - B)))"
              ^!Set %Meth2%="Calc(A * (1 - B))"
              ;^!Set %Meth3%="Calc(A * (1 - B) * (1 - C))"
              ^!InsertText Method 1 is ^%Meth1%^%NL%Method 2 is ^%Meth2%^%NL%Method 3 is ^%Meth3%^%NL%^%NL%

              :AGAIN
              ^!Set %M1%=^$Calc(MIN(^%A%;(1 - ^%B%)))$
              ^!Set %M2%=^$Calc(^%A% * (1 - ^%B%))$
              ;^!Set %M3%=^$Calc()$
              ^!InsertText A B C D E = ^%A% ^%B% ^%C% ^%D% ^%E%  Method1,2,3 gives ^%M1%  ^%M2%  ^%M3%^%NL%

              ; Note the test of If A=1 AND B=1 AND C=1 AND D=1 AND E=1
              ^!IfTrue ^$Calc(^%A%*^%B%*^%C%*^%D%*^%E%)$ ^!Goto DONE
              ^!Inc %A%
              ^!If ^%A%=1 AGAIN
              ^!Set %A%=0
              ^!Inc %B%
              ^!If ^%B%=1 AGAIN
              ^!Set %B%=0
              ^!Inc %C%
              ^!If ^%C%=1 AGAIN
              ^!Set %C%=0
              ^!Inc %D%
              ^!If ^%D%=1 AGAIN
              ^!Set %D%=0
              ^!Inc %E%
              ^!If ^%E%=1 AGAIN

              :DONE
              ^!Jump TEXT_START
              ^!ClearVariable %A%
              ^!ClearVariable %B%
              ^!ClearVariable %C%
              ^!ClearVariable %D%
              ^!ClearVariable %E%
              ^!ClearVariable %M1%
              ^!ClearVariable %M2%
              ^!ClearVariable %M3%
              ^!ClearVariable %METH1%
              ^!ClearVariable %METH2%
              ^!ClearVariable %METH3%


              <--->

              Testing A AND NOT B

              Method 1 is Calc(MIN(A;(1 - B)))
              Method 2 is Calc(A * (1 - B))
              Method 3 is 

              A B C D E = 0 0 0 0 0  Method1,2,3 gives 0  0  
              A B C D E = 1 0 0 0 0  Method1,2,3 gives 1  1  
              A B C D E = 0 1 0 0 0  Method1,2,3 gives 0  0  
              A B C D E = 1 1 0 0 0  Method1,2,3 gives 0  0  
              A B C D E = 0 0 1 0 0  Method1,2,3 gives 0  0  
              A B C D E = 1 0 1 0 0  Method1,2,3 gives 1  1  
              A B C D E = 0 1 1 0 0  Method1,2,3 gives 0  0  
              A B C D E = 1 1 1 0 0  Method1,2,3 gives 0  0  
              A B C D E = 0 0 0 1 0  Method1,2,3 gives 0  0  
              A B C D E = 1 0 0 1 0  Method1,2,3 gives 1  1  
              A B C D E = 0 1 0 1 0  Method1,2,3 gives 0  0  
              A B C D E = 1 1 0 1 0  Method1,2,3 gives 0  0  
              A B C D E = 0 0 1 1 0  Method1,2,3 gives 0  0  
              A B C D E = 1 0 1 1 0  Method1,2,3 gives 1  1  
              A B C D E = 0 1 1 1 0  Method1,2,3 gives 0  0  
              A B C D E = 1 1 1 1 0  Method1,2,3 gives 0  0  
              A B C D E = 0 0 0 0 1  Method1,2,3 gives 0  0  
              A B C D E = 1 0 0 0 1  Method1,2,3 gives 1  1  
              A B C D E = 0 1 0 0 1  Method1,2,3 gives 0  0  
              A B C D E = 1 1 0 0 1  Method1,2,3 gives 0  0  
              A B C D E = 0 0 1 0 1  Method1,2,3 gives 0  0  
              A B C D E = 1 0 1 0 1  Method1,2,3 gives 1  1  
              A B C D E = 0 1 1 0 1  Method1,2,3 gives 0  0  
              A B C D E = 1 1 1 0 1  Method1,2,3 gives 0  0  
              A B C D E = 0 0 0 1 1  Method1,2,3 gives 0  0  
              A B C D E = 1 0 0 1 1  Method1,2,3 gives 1  1  
              A B C D E = 0 1 0 1 1  Method1,2,3 gives 0  0  
              A B C D E = 1 1 0 1 1  Method1,2,3 gives 0  0  
              A B C D E = 0 0 1 1 1  Method1,2,3 gives 0  0  
              A B C D E = 1 0 1 1 1  Method1,2,3 gives 1  1  
              A B C D E = 0 1 1 1 1  Method1,2,3 gives 0  0  
              A B C D E = 1 1 1 1 1  Method1,2,3 gives 0  0  


              <--->

              ^!InsertText Testing A AND NOT (B OR C)^%NL%^%NL%

              ^!Set %A%=0;%B%=0;%C%=0;%D%=0;%E%=0
              ^!Set %Meth1%="Calc(MIN(A;(1 - MAX(B;C))))"
              ^!Set %Meth2%="Calc(A * (1 - MAX(B;C)))"
              ^!Set %Meth3%="Calc(A * (1 - B) * (1 - C))"
              ^!InsertText Method 1 is ^%Meth1%^%NL%Method 2 is ^%Meth2%^%NL%Method 3 is ^%Meth3%^%NL%^%NL%

              :AGAIN
              ^!Set %M1%=^$Calc(MIN(^%A%;(1 - MAX(^%B%;^%C%))))$
              ^!Set %M2%=^$Calc(^%A% * (1 - MAX(^%B%;^%C%)))$
              ^!Set %M3%=^$Calc(^%A% * (1 - ^%B%) * (1 - ^%C%))$
              ^!InsertText A B C D E = ^%A% ^%B% ^%C% ^%D% ^%E%  Method1,2,3 gives ^%M1%  ^%M2%  ^%M3%^%NL%

              ; Note the test of If A=1 AND B=1 AND C=1 AND D=1 AND E=1
              ^!IfTrue ^$Calc(^%A%*^%B%*^%C%*^%D%*^%E%)$ ^!Goto DONE
              ^!Inc %A%
              ^!If ^%A%=1 AGAIN
              ^!Set %A%=0
              ^!Inc %B%
              ^!If ^%B%=1 AGAIN
              ^!Set %B%=0
              ^!Inc %C%
              ^!If ^%C%=1 AGAIN
              ^!Set %C%=0
              ^!Inc %D%
              ^!If ^%D%=1 AGAIN
              ^!Set %D%=0
              ^!Inc %E%
              ^!If ^%E%=1 AGAIN

              :DONE
              ^!Jump TEXT_START
              ^!ClearVariable %A%
              ^!ClearVariable %B%
              ^!ClearVariable %C%
              ^!ClearVariable %D%
              ^!ClearVariable %E%
              ^!ClearVariable %M1%
              ^!ClearVariable %M2%
              ^!ClearVariable %M3%
              ^!ClearVariable %METH1%
              ^!ClearVariable %METH2%
              ^!ClearVariable %METH3%


              <--->

              Testing A AND NOT(B OR C)

              Method 1 is Calc(MIN(A;(1 - MAX(B;C))))
              Method 2 is Calc(A * (1 - MAX(B;C)))
              Method 3 is Calc(A * (1 - B) * (1 - C))

              A B C D E = 0 0 0 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 0 0 0  Method1,2,3 gives 1  1  1
              A B C D E = 0 1 0 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 0 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 1 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 1 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 1 1 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 1 0 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 0 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 0 1 0  Method1,2,3 gives 1  1  1
              A B C D E = 0 1 0 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 0 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 1 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 1 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 1 1 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 1 1 0  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 0 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 0 0 1  Method1,2,3 gives 1  1  1
              A B C D E = 0 1 0 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 0 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 1 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 1 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 0 1 1 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 1 0 1  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 0 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 0 1 1  Method1,2,3 gives 1  1  1
              A B C D E = 0 1 0 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 0 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 0 0 1 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 0 1 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 0 1 1 1 1  Method1,2,3 gives 0  0  0
              A B C D E = 1 1 1 1 1  Method1,2,3 gives 0  0  0

              Joy


              --- In ntb-clips@yahoogroups.com, <artkns@...> wrote:

              Sorry, another long post. But there's a lot to cover.

              On Wed 11 Sep 2013 08:10:08 -0700 Flo said:
              "...what matters here is this specific approach which - as Wayne explained -
              could apply to much more complex queries (with AND, OR, XOR, NOT etc). In
              cases like that, it would be difficult to use RegEx, and compound loops
              would end in extremely long "IF, ELSE IF, ELSE IF Chains" (Wayne)."

              On Thu, 19 Sep 2013 03:52:04 -0000 Flo said:
              "Nevertheless, for me the question remains: Is there any way to enlarge Wayne's
              concept to conditions like 'A AND B AND NOT (E OR D)', for example? Or is there
              no way to get beyond the borders of those five conditions?"

              BTW Five???  I only see four: NOT, OR, AND, XOR. And those are operators,
              not conditions. What am I missing>
              #############################################

              Flo, I think what you are asking is: given the absence of logical operators
              in Notetab Clip Code, how can I generalize the use of arithmetic operators
              to apply them to complex logical expressions without obtuse and lengthy
              If - Then - Else trees.

              The answer has two parts:
                1: The mapping of the logical operations to arithmetical operations
                2: The transformation of complex logical expressions into canonical form

              Regarding #1, there are a number of different mapping of logical to arithmetical
              operations as Wayne and I have discussed and with no major standouts among them.
              They all suffer from the inherent limitation of being strictly binary operations
              in Notetab, (i.e., MAX (A,B,C,D...) is not allowed). To recap two mappings:

              Operation             Addition only            Allowing Subtraction
              ============          ======================   =====================
                NOT A        <==>   (A + 1) MOD 2             (1 - A)
              A AND B        <==>   A * B                     MIN (A, B)
              A OR  B        <==>   MAX (A, B)                MAX (A, B)
              A XOR B        <==>   (A + B) MOD 2             ABS (A-B)
              NOT A AND B    <==>   (MIN (A, B) + 1) MOD 2    1 - MIN (A,B)
              NOT A OR  B    <==>   (MAX (A, B) + 1) MOD 2    1 - MAX (A,B)
              NOT A XOR B    <==>   (A + B + 1) MOD 2         1 - ABS (A-B)

              Regarding #2 as Joy and I discussed, any logical expression can be transformed
              into an equivalent DNF (an OR of ANDs), or CNF (an AND of ORs), expression. These
              canonical expressions use only the three logical operators: NOT, AND and OR.

              You can do that transform either by a series of transformations using
              DeMorgan's laws or - easier for very complicated expressions - by using truth tables. Each row in a truth table is a conjunction (AND) of the state of the columns (conditions). The disjunction (OR) of all the rows resulting in a true (=1) state is the DNF (Disjunctive Normal Form) of the system. For example:

                  ##  A B C D E   X     Y1  Y2  Y3    Y     DNF Term
                  ==  = = = = =   =     ==  ==  ==    =     ======================
                  01  0 0 x 0 0   0     0   0   0     0    
                  02  0 0 x 0 1   0     0   0   0     0    
                  03  0 0 x 1 0   0     0   0   1     1     ¬A AND ¬B AND D AND ¬E
                  04  0 0 x 1 1   0     0   0   0     0
                  05  0 1 x 0 0   0     0   0   1     1     ¬A AND B AND ¬D AND ¬E
                  06  0 1 x 0 1   0     0   1   0     1     ¬A AND B AND ¬D AND E
                  07  0 1 x 1 0   0     0   1   1     1     ¬A AND B AND D AND ¬E
                  08  0 1 x 1 1   0     0   0   0     0    
                  09  1 0 x 0 0   0     0   0   0     0    
                  10  1 0 x 0 1   0     0   0   0     0    
                  11  1 0 x 1 0   0     0   0   0     0    
                  12  1 0 x 1 1   0     0   0   0     0    
                  13  1 1 x 0 0   1     1   0   0     1     A AND B AND ¬D AND ¬E
                  14  1 1 x 0 1   0     0   0   0     0    
                  15  1 1 x 1 0   0     0   0   0     0    
                  16  1 1 x 1 1   0     0   0   0     0    

              For instance, taking your example, A AND B AND NOT (E OR D), (Col X),
              the DNF form for X is simply row 13: X = A AND B AND ¬D AND ¬E
              (where ¬ is the NOT operator). That seems like a lot of work compared
              to the trivial DeMorgan transformation but this is meant to illustrate
              a process so let's add some complication:

              Let Y = [A AND B AND NOT (E OR D)]
                         OR {¬A AND [B AND (¬D OR E) OR B AND (D OR ¬E)]}
                         OR [(¬A AND ¬E AND (B OR D)]
                    = Y1 OR Y2 OR Y3

              Where Y1 = A AND B AND NOT (E OR D)
                    Y2 = ¬A AND [B AND (¬D OR E) OR B AND (D OR ¬E)]
                    Y3 = (¬A AND ¬E AND (B OR D)

              The Y column is the conjunction of the Y1, Y2 and Y3 columns and the final DNF
              expression is just the OR (Sum), of the Y rows with true values:

              Y = R3 OR R5 OR R6 OR R7 OR R13
                = (¬A AND ¬B AND D AND ¬E) OR (¬A AND B AND ¬D AND ¬E) OR (¬A AND B AND ¬D AND E)
                       OR (¬A AND B AND D AND ¬E) OR (A AND B AND ¬D AND ¬E)

              This logical expression can now be evaluated in six clear and easily followed steps,
              none of which involve an If test:
                 Evaluate each of the five row expressions using the canonical AND operations
                 Evaluate the final result using the canonical OR operation on those five results.

              Alternatively, the expression could be coded directly using my functions. I did find
              it necessary to first transform the expression from embedded binary notation to prefix
              notation. Even then I had to be very careful not to introduce an error. I could then
              use NTB's replace dialog to convert to Clip syntax. Without a parser to analyze and
              convert an arbitrary expression with nested parentheses to Notetab format it still is
              a bit tricky. The functions work well for short or medium complexity expressions but
              a truth table is easier and more reliable for anything more complex.

              Y1 = and(A,B,¬or(E,D))
              Y2 = and(¬A,¬E,or(B,D))
              Y3 = and(¬A,or(and(B,or(¬D,E)),and(B,or(D,¬E))))

              ^!Set %Y1%^$AND(^%A%,^%B%,^$NOR(^%E%,^%D%)$)$
              ^!Set %Y2%^$AND(^$NOT(^%A%)$$,^$NOT(^%E%)$$,^$OR(^%B%,^%D%)$)$
              ^!Set %Y3%^$AND(^$NOT(^%A%)$$,^$OR(^$AND(^%B%,^$OR(^$NOT(^%D%)$$,^%E%)$)$,^$AND(^%B%,^$OR(^%D%,^$NOT(^%E%)$$)$)$
              ^!Set %Y%=^$OR(^%Y1%;^%Y2%;^%Y3%)$


              Some things to notice/consider:
              • The astute reader will notice that Y2 is equivalent to ¬A AND B AND (D XOR E)
                   However, remember we are limiting ourselves to NOT, AND and OR operators.
              • Separating the terms into partial result columns makes it easier and less
                   error prone to generate the truth table.
              • There can be some overlap in the partial results (e.g., row 7, col Y2 and Y3)
              • The growth of terms (and complexity) is linear, not exponential
              • Changes to the system criteria (truth table), are easily and fairly reliably
                   propagated to the DNF expression terms (this is much, much less error prone
                   than If - Then - Else logic trees.
              • Additional columns can easily be added to record the results of alternate
                   logical expressions using the same worksheet and input parameters states.
              • The truth table is independent and external to any program language or code.
                   It is simply prep work prior to program implementation.
              • A truth table is easy to generate, easy to understand and concise in execution
              • Most important, using a truth table to analyze and code logic expressions is
                   the most reliable and least error prone method available.

              OTOH, Trying to implement complex expressions by means of If - Then - Else
              trees is a recipe for frustration and errors. Clear computation and  program
              flow is a basic requirement for generating error free code as well for
              downstream maintainability. The VanWeerthuizenian Expressions get very messy
              very, very quickly once you go beyond the trivial two parameter, binary
              condition unless you restrict yourself to canonical forms. This is primarily
              due to the restriction of the MAX and MIN functions to two operands. That is
              why I removed that restriction from my AND and OR functions. However, in
              canonical form the benefit of my functions is much less dramatic than I expected.

              For example for R3 = ¬A AND ¬B AND D AND ¬E

              ^!Set %R3%=^$Calc(min((1-^%A%),min((1-^%B%),min(^%D%,(1-^%E%))));0)$
              vs
              ^!Set %R3%=^$AND(^$NOT(^%A%)$;^$NOT(^%B%)$;^%D%;^$NOT(^%E%)$)$

              I think the functions are clearer and less error prone than all the nested
              parentheses and remembering the correct mappings but not earth shakingly so.

              However, the major point and lesson here is the transformation to DNF
              form. Whether you use the VanWeerthuizenian constructs or my functions,
              the best path to error free coding and ease of maintenance is to transform
              your test criteria into canonical form using a single variable for each
              criteria, generate the DNF expression (by either Boolean transformations
              or via a truth table), and then evaluate the resulting products and sums.
              Do not use an If test until the final result.


              Applying this paradigm to your example:

              {A AND B|A OR B|A NOT B|A XOR B|NOT A}

              Let Y1 = A AND B; Y2 = A OR B; Y3 = A NOT B; Y4 = A XOR B; Y5 = NOT A

              The truth table is:

              #  A  B  Y1  Y2  Y3  Y4  Y5
              =  =  =  ==  ==  ==  ==  ==
              1  0  0  0   0   0   0   1
              2  0  1  0   1   0   1   1
              3  1  0  0   1   1   1   0
              4  1  1  1   1   0   0   0

              And the DNFs for the five cases are:

              Y1 = A AND B
              Y2 = A OR B
              Y3 = A AND ¬B
              Y4 = ¬A AND B OR A AND ¬B
              Y5 = ¬A

              It doesn't seem like we gained much but yours is a fairly trivial test and
              remember, I am illustrating a generalized process, not content.
              Implementing this in a clip:
              ;######################### Start of Clip Code ###############################
              ;^!SetDebug On
              ^!Set %Lines%=^$GetTextLineCount$
              ^!Set %Row%=1; %Hits%=^%Empty%
              ^!Set %Case%=^?{(H=5)Find lines matching...==_A AND B|A OR B|A NOT B|A XOR B|NOT A}

              :Loop
              ^!Jump ^%Row%
              ^!Set %A%=0; %B%=0; %Y%=0
              ^!IfMatch "^.*A.*$" "^$GetLine$" ^!Set %A%=1
              ^!IfMatch ".*B.*$" "^$GetLine$" ^!Set %B%=1

              ^!Set %Y1%=^$Calc(MIN(^%A%;^%B%))$
              ^!Set %Y2%=^$Calc(MAX(^%A%;^%B%))$
              ^!Set %Y3%=^$Calc(MIN(^%A%;1-^%B%))$
              ^!Set %Y41%=^$Calc(MIN(1-^%A%;^%B%))$
              ^!Set %Y42%=^$Calc(MIN(^%A%;1-^%B%))$
              ^!Set %Y4%=^$Calc(MAX(^%Y41%;^%Y42%))$
              ^!Set %Y5%=^$Calc(1-^%A%)$

              ^!IfMatch "^%Case%" "A AND B" ^!Set %Y%=^%Y1%
              ^!IfMatch "^%Case%" "A OR B" ^!Set %Y%=^%Y2%
              ^!IfMatch "^%Case%" "A NOT B" ^!Set %Y%=^%Y3%
              ^!IfMatch "^%Case%" "A XOR B" ^!Set %Y%=^%Y4%
              ^!IfMatch "^%Case%" "NOT A" ^!Set %Y%=^%Y5%

              ^!IfTrue ^%Y% ^!Set %Hits%=^%Hits%^$GetLine$^P
              ^!Inc %Row%
              ^!If ^$GetRow$ < ^%Lines% Loop
              ^!Info [L]Expression: ^%Case%^P^PMatches:^P^%Hits%

              ^!GoTo End

              ;Alternate set of logic expression calculations
              ^!Set %Y1%=^$AND(^%A%;^%B%)$
              ^!Set %Y2%=^$OR(%A%;^%B%)$
              ^!Set %Y3%=^$AND(^%A%;^$NOT(^%B%)$)$
              ^!Set %Y41%=^$AND(^$NOT(^%A%);^%B%)$;)$
              ^!Set %Y42%=^$AND(^%A%;^$NOT(^%B%)$)$
              ^!Set %Y4%=^$OR(^%Y41%;^%Y42%)$
              ^!Set %Y5%=^$NOT(^%A%)$
              ;######################### End of Clip Code ###############################

              This, of course, could be rearranged to use your computed GoTos, the DNF
              computations could be moved to the %case% tests with only %Y41% and %Y42%
              pre-computed or other optimizations which might or might not be significant
              depending on the application but would probably be at the cost of clarity
              and generalization. Remember, the emphasis here is on clarity of program
              flow (primarily linear), to minimize coding errors and to ease maintenance.
              The various sections are segregated, similar operations are consolidated, and
              program branches are minimized. A flow chart of this clip would not have any
              crossed lines.

              I hope this answers your questions.  Art
            • flo.gehrke
              ... Art & Joy, Many thanks again for your contributions to this topic! Obviously, I ve been on the wrong track when looking for more complex expressions based
              Message 6 of 12 , Sep 20, 2013
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                > You want to find out how to do this Wayne's way and I'm saying
                > this is a big mistake except for the simplest of cases.

                Art & Joy,

                Many thanks again for your contributions to this topic!

                Obviously, I've been on the wrong track when looking for more complex expressions based on Wayne's concept. As Art put it...

                > The VanWeerthuizenian Expressions get very messy
                > very, very quickly once you go beyond the trivial
                > two parameter, ...

                Your alternatives will provide a helpful basis for creating better solutions in a this field.

                Regards,
                Flo
              • joy8388608
                What is obvious to some may not be to others so here are a few more of my 3 AM thoughts... It may simplify things to break up the logical test into parts. We
                Message 7 of 12 , Sep 21, 2013
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                  What is obvious to some may not be to others so here are a few more of my 3 AM thoughts...


                  It may simplify things to break up the logical test into parts. We have already seen that the AND operation is easy to work with so it's good to convert to all ANDs if possible. So if you are testing A AND B AND C AND (D OR E OR F), you could first create a temp variable

                  If (D+E+F) > 0 set T=1 else set T=0. Then you can do IfTrue(A*B*C*T) 


                  I see no need to limit things to 0 and 1 as long as you remember to use comparisons instead of IfTrue\IfFalse.. The above could also be done as If (A*B*C*(D+E+F)) > 0 then it is True.


                  Also, to try to avoid NOTs, you just have to plan ahead a little. Here is a very simple example.

                  If you wanted to accept lines with at least 2 letters and 0 digits, you could do:

                  If <at least 2 letters> L=1 else L=0

                  If <digits exist> D=1 else D=0

                  Then you would have to test for L AND NOT D


                  BUT if you think in terms of what you want to accept and do

                  If <at least 2 letters> L=1 else L=0

                  If <digits exist> D=0 else D=1

                  Then you would only have to test for L AND D.


                  Unless you have some reason for doing so, I still say it's better to do one test at a time and skip as soon as a test fails.


                  I'm sure you have a good grip on this now and plenty to think about.


                  Joy



                  --- In ntb-clips@yahoogroups.com, <flo.gehrke@...> wrote:

                  > You want to find out how to do this Wayne's way and I'm saying
                  > this is a big mistake except for the simplest of cases.

                  Art & Joy,

                  Many thanks again for your contributions to this topic!

                  Obviously, I've been on the wrong track when looking for more complex expressions based on Wayne's concept. As Art put it...

                  > The VanWeerthuizenian Expressions get very messy
                  > very, very quickly once you go beyond the trivial
                  > two parameter, ...

                  Your alternatives will provide a helpful basis for creating better solutions in a this field.

                  Regards,
                  Flo
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