1. CS 330 Programming Languages 09 / 19 / 2006 Instructor: Michael Eckmann

2. Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Today’s Topics Homework from Chapter 3 to be assigned this afternoon - -- check your email. Describing Syntax & Semantics (Chapter 3) –Short review –Mini pascal grammar –Attribute grammars to allow for specifying static semantics –Semantics Operational Axiomatics Denotational

3. Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Chapter 3 so far Generator / recognizer Is a grammar a generator or recognizer, do you think? CFG and BNF are what? CFG and BNF are used for what? Derivation for a sentence (program) Parse tree for a sentence (program) What is ambiguity and why is it bad? What is EBNF and what can you say about the languages it can generate vs. BNF (or CFG)?

4. Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Chapter 3 and 4 Just as an aside, I think it is important in this course at Skidmore to spend a good deal of time and effort on chapters 3 and 4 because there is no seperate Compiler Design course taught at Skidmore. I think this material is interesting and informative and I hope you feel the same.

5. A more complex grammar Let's take a look at the handout for the mini-pascal language. Let's today try to generate a very short valid sentence (program) given this description. Then let's in our mind sort of create a parser from this EBNF description and use that to determine if a program is syntactically correct. Notice how closely related grammars (aka generators) are to parsers (aka recognizers.) Michael Eckmann - Skidmore College - CS 330 - Fall 2006

6. Limitations of CFG and EBNF Do you think that the EBNF for mini-pascal is the complete description for the syntax of the language? Is anything missing? --- think of some syntax errors that you are used to seeing in your favorite language. Michael Eckmann - Skidmore College - CS 330 - Fall 2006

7. Attribute Grammars Hence the creation of attribute grammars. An attribute grammar is an extension to a CFG. There are some rules of programming languages that cannot be specified in BNF (or by a CFG for that matter.) e.g. All variables must be declared before they are used. Also, there are things that are possible, but just too hairy to specify using CFG's, (e.g. Type compatibility) so Attribute Grammars are used. These kinds of things that cannot be specified using CFGs are termed “static semantics.” This is a bit of a misnomer because we still consider them to be syntax rules not semantics. Michael Eckmann - Skidmore College - CS 330 - Fall 2006

8. Attribute Grammars Michael Eckmann - Skidmore College - CS 330 - Fall 2006 An attribute grammar is a CFG (S, N, T, P) with the following additions: –For each grammar symbol x there is a set A(x) of attribute values –Each production (rule) has a set of functions that define certain attributes of the nonterminals in the rule –Each rule has a (possibly empty) set of predicates to check for attribute consistency (answers “does it have valid static semantics?”) Proposed by Knuth in 1968.

9. Attribute Grammars Michael Eckmann - Skidmore College - CS 330 - Fall 2006 The example on page 145 shows the use of an attribute grammar to enhance the BNF of an assignment statement with rules that specify the allowable types that can be assigned to each other. e.g. A float (real) cannot be assigned to a variable whose type is int. But the opposite is allowed. Also, the example shows how one can determine the resulting type of an expression.

10. Attribute Grammars Michael Eckmann - Skidmore College - CS 330 - Fall 2006 I'm not concerned with us knowing all the ins and outs of attribute grammars, but what I feel is important is the general concepts involved and the intended purpose of them. Attribute grammars are generally not used in practice for a few reasons. Can you guess them?

11. Attribute Grammars Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Attribute grammars are generally not used in practice for a few reasons. Can you guess them? –Size and complexity of the grammar will be high for a typical modern programming language –The many attributes and rules that need to be added cause the grammar to be difficult to read and write, formally –The attribute values during parsing would be costly to evaluate (the way it is described in the text.) So, in practice less formal ways are used to check for “static semantics” at compile-time but the ideas are the same.

12. Practice Problems Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Before moving on to our discussion of formally describing the Semantics of a language, let's take a look at problem 8, 10 and 11 on page 171.

13. Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Now that we know how to specify the syntax of a language, we move to specifying the semantics of a language. The text uses the phrase “dynamic semantics” and semantics interchangably. Semantics is harder to describe than syntax. Programmers need to know the sematics of the syntax and so do compiler writers.

14. Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Both programmers and compiler writers often rely on English descriptions of the language. Why might you think? Are there any problems with this?

15. Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Our text describes 3 different ways to formally describe the semantics of a programming language. –Operational semantics –Axiomatic semantics –Denotational semantics

16. Operational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 First create a converter from the language you wish to describe semantically to some lower level language (e.g. assembly). Then, execute the statements of the lower level language on a real or simulated machine. Examine the behavior of the statements by looking at the state of the machine before and after. The state of a machine includes the values of CPU registers, values of memory locations, etc. The changes of the state determine the meaning of the language statements.

17. Operational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 The conversions that the converter from the language to a lower level language uses can be used to describe the semantics of the different language constructs to a programmer as is often done in manuals. This way is good if used informally as for programming manuals but extremely complex formally.

18. Operational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Example: –To describe a while loop in Java using operational semantics one might do the following: while (expr) { // statements } So, assuming the programmer can understand all the code in the “lower level” language in the operational semantics description of the code, then he/she can understand how the while loop construct works. Operational semantics for a while loop: label: if (expr) { // statements goto label; }

19. Operational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Operational semantics can be summed up as: The statements in one language (the one you're trying to describe semantically) are described in terms of a lower-level programming language. (page 150 in Sebesta). Operational semantics uses lower level programming languages not mathematics. The other two methods (which are about to be described) are more formal and based on logic and mathematics.

20. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Based on formal logic (predicate calculus) –Original purpose was for formal program verification --- that is, to prove the correctness of programs –We define axioms or inference rules for each statement type in the language (to allow transformations of expressions to other expressions) –The expressions are called assertions or predicates

21. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 An assertion before a statement is a precondition and states the relationships and constraints among variables that are true at that point in execution An assertion following a statement is a postcondition A weakest precondition is the least restrictive precondition that will guarantee the postcondition

22. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Notation for specifying the Axiomatic semantics of a statement: {P} statement {Q} {P} is precondition, {Q} is postcondition Example: a = b + 1 {a > 1} –Read this as a must be greater than one after this statement executes. So, –One possible precondition: {b > 4} –What's the weakest precondition here?

23. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 For: a = b + 1 {a > 1} –The weakest precondition is: {b > 0} –Because a > 1 implies that b + 1 has to be > 1 which implies that b must be > 0.

24. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Jumping ahead to the big picture, we might be able to gleam from the example that to prove program correctness, one might have a post condition for the entire program and then work backwards through the program until we get to the beginning and generate a weakest precondition for the entire program. If that is within the program specs, then it is correct. What does that mean? What would we do as we went backwards through the program?

25. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 When multiple statements or more complex structures are involved, we need what are called inference rules. For a sequence of statements S1;S2: {P1} S1 {P2} {P2} S2 {P3} The inference rule is: And it is read like: If {P1}S1 {P2} is true and {P2} S2 {P3} is true, then we infer that {P1} S1,S2 {P3} is true.

26. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 It gets more complex to determine the precondition for while loops and other structures that might iterate different numbers of times depending on values of variables.

27. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Developing axioms or inference rules for all of the statements in a language is difficult It is a good tool for correctness proofs but proving that an arbitrary program is correct is incomputable, so obviously there are limits to this (or any) approach that tries to prove correctness. It is an excellent framework for reasoning about programs It is not very useful for language users and compiler writers

28. Axiomatic Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Before moving on to Denotational Semantics let's try problem 20 a) on page 173

29. Denotational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 This is the most widely known and rigorous method for describing the semantics (meaning) of programs. The book only touches on how it works and we will do the same.

30. Denotational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 The process of building a denotational spec for a language (not necessarily easy): –Define a mathematical object for each language entity –Define a function that maps instances of the language entities onto instances of the corresponding mathematical objects

31. Denotational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006 Example: –The following (next slide) denotational semantics description maps decimal numbers as strings of symbols into numeric values –M dec is the semantic function and it is used to map the syntactic objects to the decimal numbers

32. Denotational Semantics Michael Eckmann - Skidmore College - CS 330 - Fall 2006  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | (0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9) M dec - a function that maps from the syntactic elements to their meaning M dec ('0') = 0, M dec ('1') = 1, …, M dec ('9') = 9 M dec ( '0') = 10 * M dec ( ) M dec ( '1’) = 10 * M dec ( ) + 1 … M dec ( '9') = 10 * M dec ( ) + 9