Texas Instruments TI89 Developer Guide - Page 211

Chapter 15: Expressions and The Expression Stack 169 15.2.8. 15.2.9. An empty tail is represented by simply an END_TAG. Thus, rand( ) is represented by END_TAG RAND_TAG. Lists and Matrices Most of the functions and operators in the system will operate on lists of expressions and matrices containing expressions. A list is represented as a LIST_TAG on top of a tail of expressions. Thus, the empty list { } is represented as END_TAG LIST_TAG. The list {a, π, tan(x)} is represented by END_TAG X_VAR_TAG TAN_TAG PI_TAG A_VAR_TAG LIST_TAG. None of the elements of a list can be a list unless they all are equal length lists thus forming a matrix. A matrix is represented as a list of lists. Each of the inner lists represents a row of the matrix. For example, the matrix [a, b; c, d] is represented by END_TAG END_TAG D_VAR_TAG C_VAR_TAG LIST_TAG END_TAG B_VAR_TAG A_VAR_TAG LIST_TAG LIST_TAG. The lengths of the rows must be equal. None of the elements of a row can be a list. The system neither generates nor expects invalid list or matrix structures. They will cause unexpected system behavior. Primary, Secondary, and Command Tags The tags discussed in the preceding sections are called primary tags. In each case the single tag on top of the representation is all that is required to identify that element. However, the Operating System provides more than 256 built-in functions, operators, commands, programming constructs, and so on. Therefore, some of the primary tags are used with additional one Quantum tag values to provide additional identifiers. The tag value SECONDARY_TAG is used with secondary tag values to provide representation for additional functions and operators. For example, ORD_TAG happens to have the same Quantum value as V_VAR_TAG, but a SECONDARY_TAG on top of that Quantum value represents the ord() function rather than the variable v. Expression getKey( ) #s vPOL Representation END_TAG GETKEY_TAG SECONDARY_TAG S_VAR_TAG INDIRECTION_TAG SECONDARY_TAG V_VAR_TAG TO_POLAR_TAG SECONDARY_TAG Table 15.10: Secondary Tag Examples Similarly, the primary tag value COMMAND_TAG is used on top of command tag values to provide representation for elements of the TI-BASIC programming language. TI-89 / TI-92 Plus Developer Guide Not for Distribution Beta Version January 26, 2001