1. ISBN 0-321-49362-1 Chapter 9 Subprograms

2. Copyright © 2009 Addison-Wesley. All rights reserved.1-2 Chapter 9 Topics Introduction Fundamentals of Subprograms Design Issues for Subprograms Local Referencing Environments Parameter-Passing Methods Parameters That Are Subprograms Overloaded Subprograms Generic Subprograms Design Issues for Functions User-Defined Overloaded Operators Coroutines

3. Copyright © 2009 Addison-Wesley. All rights reserved.1-3 Introduction Two fundamental abstraction facilities –Process abstraction Emphasized from early days –Data abstraction Emphasized in the1980s

4. Copyright © 2009 Addison-Wesley. All rights reserved.1-4 Fundamentals of Subprograms Each subprogram has a single entry point The calling program is suspended during execution of the called subprogram Control always returns to the caller when the called subprogram’s execution terminates

5. Copyright © 2009 Addison-Wesley. All rights reserved.1-5 Basic Definitions A subprogram definition describes the interface to and the actions of the subprogram abstraction - In Python, function definitions are executable; in all other languages, they are non-executable A subprogram call is an explicit request that the subprogram be executed A subprogram header is the first part of the definition, including the name, the kind of subprogram, and the formal parameters The parameter profile (aka signature) of a subprogram is the number, order, and types of its parameters The protocol is a subprogram’s parameter profile and, if it is a function, its return type

6. Copyright © 2009 Addison-Wesley. All rights reserved.1-6 Basic Definitions (continued) Function declarations in C and C++ are often called prototypes A subprogram declaration provides the protocol, but not the body, of the subprogram A formal parameter is a dummy variable listed in the subprogram header and used in the subprogram An actual parameter represents a value or address used in the subprogram call statement

7. Copyright © 2009 Addison-Wesley. All rights reserved.1-7 Actual/Formal Parameter Correspondence Positional –The binding of actual parameters to formal parameters is by position: the first actual parameter is bound to the first formal parameter and so forth –Safe and effective xyz(a, b, c);... public static void xyz (int x, int y, int z) {... }

8. Copyright © 2009 Addison-Wesley. All rights reserved.1-8 Actual/Formal Parameter Correspondence Keyword –The name of the formal parameter to which an actual parameter is to be bound is specified with the actual parameter –Advantage: Parameters can appear in any order, thereby avoiding parameter correspondence errors –Disadvantage: User must know the formal parameter’s names xyz (x = b, z = a, y = c);

9. Copyright © 2009 Addison-Wesley. All rights reserved.1-9 Formal Parameter Default Values In certain languages (e.g., C++, Python, Ruby, Ada, PHP), formal parameters can have default values (if no actual parameter is passed) –In C++, default parameters must appear last because parameters are positionally associated Variable numbers of parameters –C# methods can accept a variable number of parameters as long as they are of the same type—the corresponding formal parameter is an array preceded by params –In Ruby, the actual parameters are sent as elements of a hash literal and the corresponding formal parameter is preceded by an asterisk. –In Python, the actual is a list of values and the corresponding formal parameter is a name with an asterisk –In Lua, a variable number of parameters is represented as a formal parameter with three periods; they are accessed with a for statement or with a multiple assignment from the three periods

10. C# Example public void DisplayList(params int[ ] list) { foreach (int next in list) { Console.WriteLine(“Next value {0}”, next); } ----------------- Myclass myobject = new myclass; int[ ] myList = new int[6] {2, 4, 6, 8, 10, 12}; ----------------- myObject.DisplayList(myList); myObject.DisplayList(2, 4, 3 * x – 1, 17); Copyright © 2009 Addison-Wesley. All rights reserved.1-10

11. Copyright © 2009 Addison-Wesley. All rights reserved.1-11 Ruby Blocks Ruby includes a number of iterator functions, which are often used to process the elements of arrays Iterators are implemented with blocks, which can also be defined by applications Blocks are attached methods calls; they can have parameters (in vertical bars); they are executed when the method executes a yield statement def fibonacci(last) first, second = 1, 1 while first <= last yield first first, second = second, first + second end puts "Fibonacci numbers less than 100 are:" fibonacci(100) {|num| print num, " "} puts

12. Copyright © 2009 Addison-Wesley. All rights reserved.1-12 Procedures and Functions There are two categories of subprograms –Procedures are collection of statements that define parameterized computations –Functions structurally resemble procedures but are semantically modeled on mathematical functions They are expected to produce no side effects In practice, program functions may have side effects

13. Copyright © 2009 Addison-Wesley. All rights reserved.1-13 Design Issues for Subprograms Are local variables static or dynamic? Can subprogram definitions appear in other subprogram definitions? What parameter passing methods are provided? Are parameter types checked? If subprograms can be passed as parameters and subprograms can be nested, what is the referencing environment of a passed subprogram? Can subprograms be overloaded? Can subprograms be generic?

14. Copyright © 2009 Addison-Wesley. All rights reserved.1-14 Local Referencing Environments Local variables can be stack-dynamic - Advantages Support for recursion Storage for locals is shared among some subprograms –Disadvantages Allocation/de-allocation, initialization time Indirect addressing Subprograms cannot be history sensitive Local variables can be static –Advantages and disadvantages are the opposite of those for stack-dynamic local variables

15. Local Referencing Environments: Examples In most contemporary languages, locals are stack dynamic In C-based languages, locals are by default stack dynamic, but can be declared static The methods of C++, Java, Python, and C# only have stack dynamic locals In Lua, all implicitly declared variables are global; local variables are declared with local and are stack dynamic Copyright © 2012 Addison-Wesley. All rights reserved.1-15

16. C/C++ Example int adder(int list[ ], int listlen) { static int sum = 0; int count; for (count = 0; count < listlen; count++) sum += list [count]; return sum; } Copyright © 2009 Addison-Wesley. All rights reserved.1-16

17. Copyright © 2009 Addison-Wesley. All rights reserved.1-17 Semantic Models of Parameter Passing In mode Out mode Inout mode

18. Copyright © 2009 Addison-Wesley. All rights reserved.1-18 Models of Parameter Passing

19. Copyright © 2009 Addison-Wesley. All rights reserved.1-19 Conceptual Models of Transfer Copy a value Provide an access path to a value

20. Copyright © 2009 Addison-Wesley. All rights reserved.1-20 Pass-by-Value (In Mode) The value of the actual parameter is used to initialize the corresponding formal parameter –Normally implemented by copying –Can be implemented by transmitting an access path but not recommended (enforcing write protection is not easy) –Disadvantages (if by physical move): additional storage is required (stored twice) and the actual move can be costly (for large parameters) –Disadvantages (if by access path method): must write- protect in the called subprogram and accesses cost more (indirect addressing)

21. Copyright © 2009 Addison-Wesley. All rights reserved.1-21 Pass-by-Result (Out Mode) When a parameter is passed by result, no value is transmitted to the subprogram; the corresponding formal parameter acts as a local variable; its value is transmitted to caller’s actual parameter when control is returned to the caller, by physical move –Require extra storage location and copy operation Potential problem: sub(p1, p1); whichever formal parameter is copied back last will represent the current value of p1

22. C# Example void Fixer (out int x, out int y) { x = 17; y = 35; }... f.Fixer(out a, out a); Copyright © 2009 Addison-Wesley. All rights reserved.1-22

23. C# Example void DoIt (out int x, int index) { x = 17; index = 42; }... sub = 21; f.DoIt(list[sub], sub); Copyright © 2009 Addison-Wesley. All rights reserved.1-23

24. Copyright © 2009 Addison-Wesley. All rights reserved.1-24 Pass-by-Value-Result (inout Mode) A combination of pass-by-value and pass-by-result Sometimes called pass-by-copy Formal parameters have local storage Disadvantages: –Those of pass-by-result –Those of pass-by-value

25. Copyright © 2009 Addison-Wesley. All rights reserved.1-25 Pass-by-Reference (Inout Mode) Pass an access path Also called pass-by-sharing Advantage: Passing process is efficient (no copying and no duplicated storage) Disadvantages –Slower accesses (compared to pass-by-value) to formal parameters –Potentials for unwanted side effects (collisions) –Unwanted aliases (access broadened)

26. C++ Aliasing void fun (int &first, int &second)...... fun (total, total);... fun (list[i], list[j]);... fun1 (list[i], list); Copyright © 2009 Addison-Wesley. All rights reserved.1-26

27. C++ Aliasing int * global; void main ( ) {... sub(global);... } void sub (int * param) {... } Copyright © 2009 Addison-Wesley. All rights reserved.1-27

28. Copyright © 2009 Addison-Wesley. All rights reserved.1-28 Pass-by-Name (Inout Mode) By textual substitution Formals are bound to an access method at the time of the call, but actual binding to a value or address takes place at the time of a reference or assignment Allows flexibility in late binding Implementation requires that the referencing environment of the caller is passed with the parameter, so the actual parameter address can be calculated Originally defined in Algol…required thunk to implement

29. PZ09B Programming Language design and Implementation -4th Edition Copyright©Prentice Hall, 200029 Pass by name Substitute argument for parameter at each occurrence of parameter: Invocation: P(A, B+2, 27+3) Definition: procedure P(X,Y,Z) {int I; I=7; X = I + (7/Y)*Z;} Meaning: P(X,Y,Z) {int I; I=7; A=I+(7/(B+2))*(27+3);} This is a true macro expansion. Simple semantics, BUT: 1. Implementation. How to do it? 2. Aliases. What if statement of P were: I = A? 3. Expressions versus statements: If we had D=P(1,2,3) and a return(42) in P, what do semantics mean? 4. Error conditions: P(A+B, B+2, 27+3)

30. PZ09B Programming Language design and Implementation -4th Edition Copyright©Prentice Hall, 200030 Implementation of Pass by name A thunk is the code which computes the L-value and R- value of an argument. For each argument, pass code address that computes both L-values and R-values of arguments. P(A, B+2, 27+3) generates: jump to subroutine P address of thunk to return L-value(A) address of thunk to return R-value(A) address of thunk to return L-value(B+2) address of thunk to return R-value(B+2) address of thunk to return L-value(27+3) address of thunk to return R-value(27+3) To assign to X, call thunk 1, To access X, call thunk 2 To assign to Y, call thunk 3, To access Y, call thunk 4 To assign to Z, call thunk 5, To access Z, call thunk 6 Issue: Assignment to (B+2): How? Call by name is conceptually convenient, but inefficient.

31. PZ09B Programming Language design and Implementation -4th Edition Copyright©Prentice Hall, 200031 Examples of Pass by Name 1. P(x) {x = x + x;} Seems simple enough … Y = 2;P(Y); write(Y)  means Y = Y+Y write(Y)  prints 4 2. int A[10]; for(I=0; I<10; I++) {A[I]=I;}; I=1; P(A[I])  A[1] = A[1] + A[1]  A[1] set to 2 3. But: F {I = I + 1; return I;} What is: P(A[F])? P(A[F])  A[F] = A[F]+A[F]  A[++I] = A[++I] + A[++I]  A[2] = A[3] + A[4]

32. Copyright © 2009 Addison-Wesley. All rights reserved.1-32 Implementing Parameter-Passing Methods In most languages parameter communication takes place thru the run- time stack Pass-by-reference is the simplest to implement; only an address is placed in the stack A subtle but fatal error can occur with pass-by-reference and pass-by-value- result: a formal parameter corresponding to a constant can mistakenly be changed

33. Implementing Parameter-Passing Methods Copyright © 2012 Addison-Wesley. All rights reserved.1-33 Function header: void sub(int a, int b, int c, int d) Function call in main: sub(w, x, y, z) (pass w by value, x by result, y by value-result, z by reference)

34. Copyright © 2009 Addison-Wesley. All rights reserved.1-34 Parameter Passing Methods of Major Languages C –Pass-by-value –Pass-by-reference is achieved by using pointers as parameters C++ –A special pointer type (called a reference type) for pass-by- reference –constant reference Java –All parameters are passed by value –Object parameters are passed by reference Ada –Three semantic modes of parameter transmission: in, out, in out; in is the default mode –Formal parameters declared out can be assigned but not referenced; those declared in can be referenced but not assigned; in out parameters can be referenced and assigned

35. Copyright © 2009 Addison-Wesley. All rights reserved.1-35 Parameter Passing Methods of Major Languages (continued) Fortran 95+ - Parameters can be declared to be in, out, or inout mode C# - Default method: pass-by-value –Pass-by-reference is specified by preceding both a formal parameter and its actual parameter with ref PHP: very similar to C# Perl: all actual parameters are implicitly placed in a predefined array named @_ Python and Ruby use pass-by-assignment (all data values are objects)

36. Copyright © 2009 Addison-Wesley. All rights reserved.1-36 Type Checking Parameters Considered very important for reliability FORTRAN 77 and original C: none Pascal, FORTRAN 90, Java, and Ada: it is always required ANSI C and C++: choice is made by the user –Prototypes Relatively new languages Perl, JavaScript, and PHP do not require type checking In Python and Ruby, variables do not have types (objects do), so parameter type checking is not possible

37. Copyright © 2009 Addison-Wesley. All rights reserved.1-37 Multidimensional Arrays as Parameters If a multidimensional array is passed to a subprogram and the subprogram is separately compiled, the compiler needs to know the declared size of that array to build the storage mapping function

38. Copyright © 2009 Addison-Wesley. All rights reserved.1-38 Multidimensional Arrays as Parameters: C and C++ Programmer is required to include the declared sizes of all but the first subscript in the actual parameter Disallows writing flexible subprograms Solution: pass a pointer to the array and the sizes of the dimensions as other parameters; the user must include the storage mapping function in terms of the size parameters

39. Copyright © 2009 Addison-Wesley. All rights reserved.1-39 Multidimensional Arrays as Parameters: Ada Ada – not a problem –Constrained arrays – size is part of the array’s type –Unconstrained arrays - declared size is part of the object declaration

40. Copyright © 2009 Addison-Wesley. All rights reserved.1-40 Multidimensional Arrays as Parameters: Fortran Formal parameters that are arrays have a declaration after the header –For single-dimension arrays, the subscript is irrelevant –For multidimensional arrays, the sizes are sent as parameters and used in the declaration of the formal parameter, so those variables are used in the storage mapping function

41. Copyright © 2009 Addison-Wesley. All rights reserved.1-41 Multidimensional Arrays as Parameters: Java and C# Similar to Ada Arrays are objects; they are all single- dimensioned, but the elements can be arrays Each array inherits a named constant ( length in Java, Length in C#) that is set to the length of the array when the array object is created

42. Copyright © 2009 Addison-Wesley. All rights reserved.1-42 Design Considerations for Parameter Passing Two important considerations –Efficiency –One-way or two-way data transfer But the above considerations are in conflict –Good programming suggest limited access to variables, which means one-way whenever possible –But pass-by-reference is more efficient to pass structures of significant size

43. Copyright © 2009 Addison-Wesley. All rights reserved.1-43 Parameters that are Subprogram Names It is sometimes convenient to pass subprogram names as parameters Issues: 1.Are parameter types checked? 2.What is the correct referencing environment for a subprogram that was sent as a parameter?

44. Copyright © 2009 Addison-Wesley. All rights reserved.1-44 Parameters that are Subprogram Names: Parameter Type Checking C and C++: functions cannot be passed as parameters but pointers to functions can be passed and their types include the types of the parameters, so parameters can be type checked FORTRAN 95 type checks Ada does not allow subprogram parameters; an alternative is provided via Ada’s generic facility Java does not allow method names to be passed as parameters

45. Copyright © 2009 Addison-Wesley. All rights reserved.1-45 Parameters that are Subprogram Names: Referencing Environment Shallow binding: The environment of the call statement that enacts the passed subprogram - Most natural for dynamic-scoped languages Deep binding: The environment of the definition of the passed subprogram - Most natural for static-scoped languages Ad hoc binding: The environment of the call statement that passed the subprogram

46. Example Copyright © 2009 Addison-Wesley. All rights reserved.1-46 function sub1( ) { var x;// it’s this one for deep binding function sub2( ) { alert(x);// creates dialog box }; function sub3( ) { var x;// it’s this one for ad hoc binding x = 3; sub4(sub2); }; function sub4(subx) { var x;// it’s this one for shallow binding x = 4; subx( ); }; x = 1; sub3( ); };

47. Calling Subprograms Indirectly Usually when there are several possible subprograms to be called and the correct one on a particular run of the program is not know until execution (e.g., event handling and GUIs) In C and C++, such calls are made through function pointers Copyright © 2012 Addison-Wesley. All rights reserved.1-47

48. Calling Subprograms Indirectly (continued) In C#, method pointers are implemented as objects called delegates –A delegate declaration: public delegate int Change(int x); - This delegate type, named Change, can be instantiated with any method that takes an int parameter and returns an int value A method: static int fun1(int x) { … } Instantiate: Change chgfun1 = new Change(fun1); Can be called with: chgfun1(12); - A delegate can store more than one address, which is called a multicast delegate Copyright © 2012 Addison-Wesley. All rights reserved.1-48

49. Copyright © 2009 Addison-Wesley. All rights reserved.1-49 Overloaded Subprograms An overloaded subprogram is one that has the same name as another subprogram in the same referencing environment –Every version of an overloaded subprogram has a unique protocol C++, Java, C#, and Ada include predefined overloaded subprograms In Ada, the return type of an overloaded function can be used to disambiguate calls (thus two overloaded functions can have the same parameters) Ada, Java, C++, and C# allow users to write multiple versions of subprograms with the same name

50. Copyright © 2009 Addison-Wesley. All rights reserved.1-50 Generic Subprograms A generic or polymorphic subprogram takes parameters of different types on different activations Overloaded subprograms provide ad hoc polymorphism Subtype polymorphism means that a variable of type T can access any object of type T or any type derived from T (OOP languages) A subprogram that takes a generic parameter that is used in a type expression that describes the type of the parameters of the subprogram provides parametric polymorphism - A cheap compile-time substitute for dynamic binding

51. Generic Subprograms (continued) Ada –Versions of a generic subprogram are created by the compiler when explicitly instantiated by a declaration statement –Generic subprograms are preceded by a generic clause that lists the generic variables, which can be types or other subprograms Copyright © 2009 Addison-Wesley. All rights reserved.1-51

52. Generic Subprograms (continued) C++ –Versions of a generic subprogram are created implicitly when the subprogram is named in a call or when its address is taken with the & operator –Generic subprograms are preceded by a template clause that lists the generic variables, which can be type names or class names Copyright © 2009 Addison-Wesley. All rights reserved.1-52

53. Copyright © 2009 Addison-Wesley. All rights reserved.1-53 Examples of parametric polymorphism: C++ template Type max(Type first, Type second) { return first > second ? first : second; } The above template can be instantiated for any type for which operator > is defined int x,y; int z = GetMax (x,y); Generates int max (int first, int second) { return first > second? first : second; }

54. // function template #include using namespace std; template T GetMax (T a, T b) { T result; result = (a>b)? a : b; return (result); } int main ( ) { int i=5, j=6, k; long l=10, m=5, n; k = GetMax (i, j); n = GetMax (l, m); cout << k << endl; cout << n << endl; return 0; } Copyright © 2009 Addison-Wesley. All rights reserved.1-54

55. Copyright © 2009 Addison-Wesley. All rights reserved.1-55 Generic Subprograms (continued) Java - Differences between generics in Java and those of C++ and Ada: 1. Generic parameters in Java must be classes 2. Java generic methods are instantiated just once as truly generic methods 3. Restrictions can be specified on the range of classes that can be passed to the generic method as generic parameters 4. Wildcard types of generic parameters

56. Generic Subprograms (continued) Java 5.0 (continued) public static T doIt(T[] list) { … } - The parameter is an array of generic elements ( T is the name of the type) - A call: doIt (myList); Generic parameters can have bounds: public static T doIt(T[] list) { … } The generic type must be of a class that implements the Comparable interface Copyright © 2012 Addison-Wesley. All rights reserved.1-56

57. Generic Subprograms (continued) Java 5.0 (continued) –Wildcard types Collection is a wildcard type for collection classes void printCollection(Collection c) { for (Object e: c) { System.out.println(e); } - Works for any collection class Copyright © 2012 Addison-Wesley. All rights reserved.1-57

58. Copyright © 2009 Addison-Wesley. All rights reserved.1-58 Generic Subprograms (continued) C# 2005 - Supports generic methods that are similar to those of Java 5.0 - One difference: actual type parameters in a call can be omitted if the compiler can infer the unspecified type

59. Generic Subprograms (continued) F# –Infers a generic type if it cannot determine the type of a parameter or the return type of a function – automatic generalization –Such types are denoted with an apostrophe and a single letter, e.g., ′a –Functions can be defined to have generic parameters let printPair (x: ′a) (y: ′a) = printfn ″%A %A″ x y - %A is a format code for any type - These parameters are not type constrained Copyright © 2012 Addison-Wesley. All rights reserved.1-59

60. Generic Subprograms (continued) F# (continued) –If the parameters of a function are used with arithmetic operators, they are type constrained, even if the parameters are specified to be generic –Because of type inferencing and the lack of type coercions, F# generic functions are far less useful than those of C++, Java 5.0+, and C# 2005+ Copyright © 2012 Addison-Wesley. All rights reserved.1-60

61. Copyright © 2009 Addison-Wesley. All rights reserved.1-61 Design Issues for Functions Are side effects allowed? –Parameters should always be in-mode to reduce side effect (like Ada) What types of return values are allowed? –Most imperative languages restrict the return types –C allows any type except arrays and functions –C++ is like C but also allows user-defined types –Ada subprograms can return any type (but Ada subprograms are not types, so they cannot be returned) –Java and C# methods can return any type (but because methods are not types, they cannot be returned) –Python and Ruby treat methods as first-class objects, so they can be returned, as well as any other class –Lua allows functions to return multiple values

62. Copyright © 2009 Addison-Wesley. All rights reserved.1-62 User-Defined Overloaded Operators Operators can be overloaded in Ada, C++, Python, and Ruby An Ada example function "*" (A,B: in Vec_Type): return Integer is Sum: Integer := 0; begin for Index in A'range loop Sum := Sum + A(Index) * B(Index) end loop return sum; end "*"; … c = a * b; -- a, b, and c are of type Vec_Type

63. Copyright © 2012 Addison-Wesley. All rights reserved.1-63 User-Defined Overloaded Operators A Python example def __add__ (self, second) : return Complex(self.real + second.real, self.imag + second.imag) Use: To compute x + y, x.__add__(y)

64. Closures A closure is a subprogram and the referencing environment where it was defined –The referencing environment is needed if the subprogram can be called from any arbitrary place in the program –A static-scoped language that does not permit nested subprograms doesn’t need closures –Closures are only needed if a subprogram can access variables in nesting scopes and it can be called from anywhere –To support closures, an implementation may need to provide unlimited extent to some variables (because a subprogram may access a nonlocal variable that is normally no longer alive) Copyright © 2012 Addison-Wesley. All rights reserved.1-64

65. Closures (continued) A JavaScript closure: function makeAdder(x) { return function(y) {return x + y;} }... var add10 = makeAdder(10); var add5 = makeAdder(5); document.write(″add 10 to 20: ″ + add10(20) + ″ ″); document.write(″add 5 to 20: ″ + add5(20) + ″ ″); - The closure is the anonymous function returned by makeAdder Copyright © 2012 Addison-Wesley. All rights reserved.1-65

66. Closures (continued) C# -We can write the same closure in C# using a nested anonymous delegate -Func (the return type) specifies a delegate that takes an int as a parameter and returns and int static Func makeAdder(int x) { return delegate(int y) {return x + y;}; }... Func Add10 = makeAdder(10); Func Add5 = makeAdder(5); Console.WriteLine(″Add 10 to 20: {0}″, Add10(20)); Console.WriteLine(″Add 5 to 20: {0}″, Add5(20)); Copyright © 2012 Addison-Wesley. All rights reserved.1-66

67. Copyright © 2009 Addison-Wesley. All rights reserved.1-67 Coroutines A coroutine is a subprogram that has multiple entries and controls them itself – supported directly in Lua Also called symmetric control: caller and called coroutines are on a more equal basis A coroutine call is named a resume The first resume of a coroutine is to its beginning, but subsequent calls enter at the point just after the last executed statement in the coroutine Coroutines repeatedly resume each other, possibly forever Coroutines provide quasi-concurrent execution of program units (the coroutines); their execution is interleaved, but not overlapped

68. Example sub co1( ) {... resume co2( );... resume co3( );... } Copyright © 2009 Addison-Wesley. All rights reserved.1-68

69. Copyright © 2009 Addison-Wesley. All rights reserved.1-69 Coroutines Illustrated: Possible Execution Controls

70. Copyright © 2009 Addison-Wesley. All rights reserved.1-70 Coroutines Illustrated: Possible Execution Controls

71. Copyright © 2009 Addison-Wesley. All rights reserved.1-71 Coroutines Illustrated: Possible Execution Controls with Loops

72. Copyright © 2009 Addison-Wesley. All rights reserved.1-72 Summary A subprogram definition describes the actions represented by the subprogram Subprograms can be either functions or procedures Local variables in subprograms can be stack- dynamic or static Three models of parameter passing: in mode, out mode, and inout mode Some languages allow operator overloading Subprograms can be generic A coroutine is a special subprogram with multiple entries