### Simple Boolean Scalar and Vector Comments

General:This frame introduces you to simple booleans in Glee. I just quickly display the truth tables here in vector form. Notice Glee's use of character strings of 0's and 1's to represent boolean values. This is used primarily just in experimenting. In real life, Glee gets its boolean values by making logical tests. In the vector section I expound more on the subject of booleans in Glee.

Boolean truth tables:This is just a simple illustration of the boolean truth tables. The examples are vector, not scalar. By now you realize there is really no such thing as a scalar in Glee. The operators are (&)And; (|)Or; (^)Exclusive or; and (~)Not. There are compound operators (~&)Nand and (~|)Nor. These are the direct boolean (logical) operators. In the vector section I cover the comparison operators that create boolean data like (>)Greater than; (<=)Less than or equal, etc.

Not/#True/#False:As described in the  Glossary  Glee simulates manifest constants as niladic functions. #TRUE, and #FALSE are just such functions. Notice, Glee is not case sensitive. You can use #True, #true, or even #TruE just as freely. Because these are niladic functions and not variables or constants, it is recommended that you assign them to the name of your choice before use.

No No/Gotcha:If you do try to use #true or #false as manifest constants, this is the kind of rude behavior Glee exhibits. In detailed explanation, the first #true indeed produces a boolean vector containing the binary digit "1". Moving along to the right, the parser sees the "&" and looks to it's right for another argument. It sees a niladic function, #true. This cuts off the parsing and invokes the executor. It tries to invoke the monadic operator "&" on the left argument. This fails because "&" is not defined for that operation.

Indexing:Bit (boolean) vectors can be indexed just like other Glee vectors. Now, in this example, I can't use the convenient character vector technique of defining the bit vector being indexed. This is because, if I did, I'd just be indexing into the character vector and getting a character result. So for these examples I create the bit vectors through a testing operation (is a number equal to 1). The first example illustrates simple selection indexing. The second, simple element number indexing. The third illustrates indexing returning results for index out of range. As with other Glee indexing, if on the low side of the range, the first element is returned. On the high side, the last element is returned. The fourth example illustrates indexing with floats. The float value is floored to an integer and then used as the index.

Marking:Marking (making logical tests) is the more likely way bit vectors are used. This example illustrates creating a bit vector using relational tests. That bit vector is then used to index into the numeric vector on which the tests were made.

Selection:In this example, I show the Mark Any (*|) operator being used to mark a set of account IDs of interest among a list of all account IDs. There is a corresponding set of amounts(Amt) which are then selected using the results of this test. Notice that the ID = 30 occurs twice. This would be typical of a stream of transaction data.

Indices:. A common requirement is to test values in a vector and return elements meeting the test. Sometimes this requires finding the indices where the test is met and using them to return elements from several vectors. This example illustrates some of Glee's capability for serving this need:
<1a> creates a boolean vector and uses the ( ` ) index of operator monadically to produce the index where the test is first met. <1b> is the same but uses the ( `` ) indices of operator monadically producing all the indices where the test is met. <2> creates 5 random numbers ranging from 1 to 5 beginning with a seed of 100 (so you will see the same result as this example). <3> tests the elements of "n" to be greater than 2 returning a bit vector. <4> shows the indices where the test is met. <5> uses the indices to select elements of "n" meeting the test. And <6> shows that the bit vector can be used directly as an indexing object.

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