Copyright © 2006 The McGraw-Hill Companies, Inc. Programming Languages 2nd edition Tucker and Noonan Chapter 10 Function Implementation In theory, there is no difference between theory and practice, but not in practice. Anonymous

Copyright © 2006 The McGraw-Hill Companies, Inc. Contents 10.1 Function Declaration and Call in Clite 10.2 Completing the Clite Type System 10.3 Semantics of Call and Return 10.4 Formal Treatment of Types and Semantics

Copyright © 2006 The McGraw-Hill Companies, Inc Formal Treatment of Types and Semantics The type map for a function f, tm f, is a set of pairs and triples, representing global variables (tm G ), functions (tm F ), f’s parameters, and f’s locals. E.g., for the program in Figure 10.1:

Copyright © 2006 The McGraw-Hill Companies, Inc. Typing Function The function typing creates type maps for each individual function f in a program with globals G and functions F.

Copyright © 2006 The McGraw-Hill Companies, Inc. Validity of a Clite Program A program is valid if its global variables and function declarations are valid, and each function is valid with respect to their type maps.

Copyright © 2006 The McGraw-Hill Companies, Inc. Validity of a Clite Function A function is valid if 1) its parameters and locals have unique names, 2) its statements are valid in its type map, and 3) it contains (does not contain) a return statement if it is a non-void (void) function.

Copyright © 2006 The McGraw-Hill Companies, Inc. Validity of a Clite Call and Return Validity of most Clite statements is defined in Chapter 6. Validity of a Call and a Return is defined below:

Copyright © 2006 The McGraw-Hill Companies, Inc. Formalizing the Semantics of Clite Memory (  ), Environment (  ) and State (  ): The State of a function f,  f, is a triple  f    a where a addresses the top of the run-time stack,  is a set of address-value pairs, and  f has f’s visible variables and their addresses.

Copyright © 2006 The McGraw-Hill Companies, Inc. Allocate and Deallocate Functions allocate changes the state by adding a group of variable-address pairs to it. deallocate removes such a group.

Copyright © 2006 The McGraw-Hill Companies, Inc. Calling a Void Function Meaning Rule 10.1 in functional form, skipping temporarily the returned result:

Copyright © 2006 The McGraw-Hill Companies, Inc. Call/Return for a Non-Void Function The Call returns a Value; the Return identifies it:

Copyright © 2006 The McGraw-Hill Companies, Inc. Meaning of a Block Since a block can contain a Return, it must exit as soon as the return is encountered (Meaning Rule 10.3). Here is the functional definition.