FORMAL-PARAMETER

See ROUTINE LIBRARY. A routine is characterized by its formal parameters which will be substituted by entities of the proper type when the routine is invoked during an application. Furthermore, the routine has as attribute a reference to the routine library in which it is to be searched for, and it carries the type identification of the result in order to guarantee that the result type is correct. The name of the routine inside the library is stored as a user defined name in an indexL entry referring to this entity. Results of the routines may be of type real or geometric. 

See MACRO and ROUTINE. Formal parameters are characterized by a user-defined name and a type to facilitate proper binding of actual entities to these formal parameters when the MACRO or ROUTINE is invoked in an application. 

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Q, the procedure body, is any nonempty list of assignment instructions, test instructions and CALL instructions, involving as variables only the formal parameters and local variables of the procedure, such that START Q STOP is a program scheme with CALLs. 

The procedure definition gives us a local value TEMP. When substituting into the main program, formal parameter u becomes actual parameter x, y becomes and TEMP becomes TEMP. In fact, TEMP was introduced so that we do not change the value of the global variable x while executing the subroutine. Notice that in 3.4, FACT calls itself, this time with actual parameters TEMP and z- as this example shows, a local variable can become an actual parameter of another CALL. 

All local variables and formal parameters are distinct new variables, and all local variables die at the end of the procedure subroutine. 

Let P = (Q,Qp,...,Q ) be a recursion augmented program scheme with n global variables (locations in Q ) x-, ..., x. For each address r of an instruction in Q, we create a new defined function letter which is n-placed. If F is a defined function letter in P for a procedure with m formal parameters and k local variables, we create a new m-placed defined function letter F- for 1 <. I < m and an defined function letter F for each address r in the procedure defining F. ... 

The new feature is that if F is a procedure symbol in P defined by a procedure with m formal parameters, a call instruction in Q... 

Observe that the new statement first stores all global values which are not actual parameters Cy, ...,ym) on the pushdown store, then puts label Lq on top of the pushdown store, and finally lets the values of the actual parameters of the call, v, ...,vn, specify the formal parameters of procedure F, x,, ...,x the x. will be used as variables in the execution of F. Then con-trol passes to the start of the procedure body of F. When F is completed, label Lq r will be retrieved from the top of the store and a GOTO will pass control to the statement labeled by Lq. Then each actual parameter of the call, v, will be respecified by the final value of the corresponding formal parameter, x, of F, the other global variables will have their proper values restored from the pushdown store and control will return to , the statement originally following . ... 

There is only one procedure, which has formal parameters, ...,xn, LABEL and TOP. The first statement in the procedure body is ... 

The labels stored in LABEL are used simply to point to the next statement to be executed while calls are stacked or unstacked. Since LABEL is always used as an actual parameter, its value is carried along when a new call is instituted or an old call is completed. On the other hand, TOP is never used as an actual parameter. When PUSH(u) is simulated, a new call is begun with u as the new value of the formal parameter and the old value is "left behind" in the previous procedure but is not destroyed. When v POP is finally simulated, this new value of TOP goes into v, the call is ended and the old procedure is reentered with the previous value of TOP still there. In simulating STOP, the value of label becomes permanently and the calls are unpeeled until the main scheme is reentered at 3. STOP and everything halts. ... 

To each procedure F we assign two inductive assertions pA and pB which are written solely in terms of the formal parameters of procedure F flat is, the only free variables in pA and pB are the formal parameters of F. ... 

Why can we make this claim The idea is simple but subtle. If the program does not terminate for a particular input, say a, we are uninterested in the outcome. If it does terminate for input a, there must be some k such that no more than k calls are executed during the entire computation (P,I,a). Now make k complete first level macroexpansions of (P,I) and call the result (P1,1). Each time a call of F is macroexpanded, put into the diagram all the critical points and inductive assertions with the appropriate substitutions of actual parameters for formal parameters. Because of the way in which we have chosen inductive assertions before and after calls, the points before and after the macroexpansion of F will have attached the same inductive assertions as before. Finally, when we are all done, replace any remaining calls by a LOOP instruction. 

Once we are assured that the CALLs obey 2) we are in business. Now for procedure F with unchanged formal parameters x = (Xp,...,xn) and other formal parameters y = (y, ...,y ) we let input criterion pA involve all the unchanged... 

Let PR be the class of recursion augmented schemes defined in Section D of Chapter VII. Constable and Gries define a slightly different class P R using an alternative method of parameter passing. A scheme in P R contains a main scheme and procedure definitions. In this case, a procedure definition Qp contains at the start, in addition to a statement of formal parameters and local variables, a statement EETURN(z) where z is a new variable, the output variable, which can also appear in the instructions and calls of Qp. A call has the form v F(Up,...,un). If procedure Qp has formal parameters Xp,...,x, and output variable z, then the scheme executes as if call v F(Up,..., un) were replaced by... 

This condition should be fulfilled, at least approximately, for a given range of the smearing width 7 = 70 and a given order M of the correction polynomial, in order to obtain an independent of the averaging procedure and of the formal parameter 7 smooth energy. 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

At the heart of molecular mechanics is a force field [89] and the ultimate force field should be fully transferable between all types of molecule. However, progress towards comprehensive force fields, such as the Universal Force Field of Casewit and Rappe [90], is invariably accompanied by an almost exponential increase in the number of parameters. The effort to reformulate molecular mechanics in terms of valence-bond concepts [91] reduces the number of formal parameters, but at the expense of almost the same number of hybridization parameters, which the authors [92] describe as follows ... 

The definition of the concept ab initio is somewhat fluid, but usually means essentially free of empirical parameters. Being ab initio is generally considered a quality stamp, but one should be aware that some approaches, which ru e formally parameter-free, e.g. Thomas-Fermi density functional theory or ab initio tight binding, fail miserably outside limited application ranges. 

Constraints Limits on the changes that may occur in parameters in a least squares refinement. This may be done by reducing the number of formal parameters in the least squares equations. For example, individual atomic coordinates may be transformed to other parameters, fewer in number, that describe the position and orientation of a whole group of atoms. A benzene ring is an example. It can be defined as a hexagon with fixed geometry and only orientational flexibility. 

A more detailed study for these formal parameters can be done by introducing the expressions for, oe and in rel. (15) and (16). With these substitutions H will have the following formula ... 

The formal parameters in this predicate are exactly those values that make a difference for the future behaviour of the system, i.e., that have to be known in the requirements. 

Finally, the requirement can be assembled. The recipient and the court, i.e., the interest group, are formal parameters. The requirement says that whenever a recipient has accepted a message, he can from then on convince the court in the sense defined above, provided that both transactions occur in the state Correct init use. Recall that the predicate suitable defined what parameters ids can be used. 

The abstract syntax of collaboration diagrams is defined by the graph schema shown in Fig. 5.67, which will be explained later. A formal definition of the abstract syntax, again, enables the modeling environment to guarantee (syntactical) correctness and completeness with respect to context-free as well as context-sensitive conditions, such as tjrpe conformity of actual and formal parameters to facilitate the generation of executable code. 

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