Programming Language Semantics

1. Programming Language Semantics Mooly Sagiv Eran Yahav msagiv@post yahave@post Schrirber 317 Open space 03-640-7606 03-640-5358 html://www.cs.tau.ac.il/~msagiv/courses/sem03.html Textbook:Winskel The Formal Semantics of Programming Languages CS 0368-4348-01@listserv.tau.ac.il

2. Outline • Course requirements • What is semantics • Who needs semantics • Forms of semantics • Tentative Plan • Introduction to operational semantics

3. Course Requirements • Prerequisites • Compiler Course • Basic set theory and logic • A theoretical course • Forms of induction • Domain theory • No algorithms • Grade • Course Notes 10% • Assignments 60% • Mostly theoretical with some programming • Home exam 30%

4. Modern Programming Languages • Imperative • PL/1 • Pascal • C • Object Oriented • C++ • Java • C# • Functional • Scheme • ML • Logic • Prolog

5. Programming Languages • Syntax • Which string is a legal program? • Usually defined using context free grammar+ contextual constraints • Semantics • What does a program mean? • What is the output of the program on a given run? • When does a runtime error occur? • A formal definition

6. Benefits of Formal Semantics • Programming language design • hard- to-define= hard-to-implement=hard-to-use • Avoid design mistakes • Programming language implementation • Compiler Correctness • Correctness of program optimizations • Design of Static Analysis • Programming language understanding • Program correctness • Program equivalence • Automatic generation of interpreter • Techniques used in software engineering

7. Desired Features of PL Semantics • Tractable • as simple as possible without losing the ability to express behavior accurately • Abstract • uncluttered by irrelevant detail • Computational • an accurate abstraction from runtime behavior • Compositional • The meaning of compound language construct is defined using the meaning of subconstructs • Supports modular reasoning

8. Alternative Formal Semantics • Operational Semantics [Plotkin] • The meaning of the program is described “operationally” • Structural Operational Semantics • Denotational Semantics [Strachey, Scott] • The meaning of the program is an input/output relation • Axiomatic Semantics [Floyd, Hoare] • The meaning of the program is observed properties • Proof rules to show that the program is correct • Complement each other

9. Tentative Plan • A simple programming language IMP • Structural operational Semantics of IMP • Denotational Semantics of IMP • [Axiomatic Semantics of IMP] • Non-Determinism and Parallelism • Advanced programming languages • Java byte code

10. Chapter 2 Introduction to Operational Semantics

11. IMP: A Simple Imperative Language • numbers N • Positive and negative numbers • n, m  N • truth values T={true, false} • locations Loc • X, Y  Loc • arithmetic Aexp • a  Aexp • boolean expressions Bexp • b  Bexp • commands Com • c  Com

12. (3+5)  3 + 5 3 + 5  5+ 3 Abstract Syntax for IMP • Aexp • a ::= n | X | a0 + a1 | a0 – a1 | a0 a1 • Bexp • b ::= true | false | a0 = a1 | a0 a1 | b | b0 b1 | b0  b1 • Com • c ::= skip | X := a | c0 ; c1 | if b then c0elsec1| while b do c 2+34-5 (2+(34))-5 ((2+3)4))-5

13. Example Program Y := 1; while (X=1) do Y := Y * X; X := X - 1

14. But what about semantics

15. Expression Evaluation • States • Mapping locations to values •  - The set of states •  : Loc  N • (X)= X=value of X in  •  = [ X  5, Y  7] • The value of X is 5 • The value of Y is 7 • The value of Z is undefined • For a Exp, , n N, • <a, >  n • a is evaluated in  to n

16. Evaluating (a0 + a1) at  • Evaluate a0 to get a number n0 at  • Evaluate a1 to get a number n1 at  • Add n0 and n1

17. Expression Evaluation Rules • Numbers • <n, >  n • Locations • <X, > (X) • Sums • Subtractions • Products Axioms

18. Derivations • Arule instance • Instantiating meta variables with corresponding values

19. Derivation (Tree) • Axioms in the leafs • Rule instances at internal nodes

20. Computing a derivation • We write <a, >  n when there exists a derivation tree whose root is<a, >  n • Can be computed in a top-down manner • At every node try all derivations “in parallel” 5 16 21

21. Recap • Operational Semantics • The rules can be implemented easily • Define interpreter • Structural Operational Semantics • Syntax directed • Natural semantics

22. Equivalence of IMP expressions iff a0 a1

23. Boolean Expression Evaluation Rules • <true, >  true • <false, >  false

24. Boolean Expression Evaluation Rules(cont)

25. Equivalence of Boolean expressions iff b0b1

26. Extensions • Shortcut evaluation of Boolean expressions • “Parallell” evaluation of Boolean expressions • Other data types

27. The execution of commands • <c, >  ’ • c terminates on  in a final state ’ • Initial state 0 • 0(X)=0 for all X • Handling assignments <X:=5, >  ’ • <X:=5, >  [5/X]

28. Rules for commands Atomic • <skip, >   • Sequencing: • Conditionals:

29. Rules for commands (while)

30. Example Program Y := 1; while (X=1) do Y := Y * X; X := X - 1

31. Equivalence of commands iff c0c1

32. Proposition 2.8 while b do c  if then (c; while b do c) else skip

33. Small Step Operational Semantics • The natural semantics define evaluation in large steps • Abstracts “computation time” • It is possible to define a small step operational semantics • <a, > 1 <a’, ’> • “one” step of executing a in a state  yields a’ in a state ’

34. Small Step Semantics for Additions

35. Summary • Operational semantics enables to naturally express program behavior • Can handle • Non determinism • Concurrency • Procedures • Object oriented • Pointers and dynamically allocated structures • But remains very closed to the implementation • Two programs which compute the same functions are not necessarily equivalent