Static and Dynamic Programming Structures: A Comprehensive Study

1. Part IIProcedural, block structured, languages Procedural: • Function(*) as main programming construct • variables to denote values Block-structured: • Blocks to control visibility of variables (local definitions) (*)In this part, function is used for both function, procedure block structure

2. Main requirements: • Precisely defined, conceptually simple static structure for programs addressed by universally accepted scope rules • Static structure should provide good understanding of dynamic behavior addressed by correct use of scope in semantics & implementation Program structure should enable programmer to predict its behavior block structure

3. Contents: • Semi-formal description of static structure • The substitution model: operational semantics for asimple functional language • Introduction to type systems • Definitions, comparison of dynamic/static typing • A simple monomorphictype system – specification, type-checking, correctness • Extensions of the language with additional constructs recursion, cells with assignment, data structures,… including both semantics and types The environment model: an alternative operational semantics block structure

4. Block structure • Literals, identifiers, variables • Variable declarations, definitions, uses • Blocks, regions, scope • Common kinds of blocks block structure

5. Literals, identifiers & variables • literals: numbers, booleans, strings, … • identifiers --- used by programmers to name entities Two categories distinguished by syntax conventions Identifier name spaces : • Variables: denotevalues (numbers, booleans, cells, functions, lists, …) • Type names(simply: types) • Constructors (in ML) • . . . . . block structure

6. An identifier collision: when same identifier used for different purposes in a program Collisions between different name spaces – often resolved by position: type bing = Bing of int;; let bing= Bing(5);; (* a value of type bing *) But, within a space, rules must be used. We deal with variable space block structure

7. Variable declarations, definitions, uses Variableoccurrence: a variable in a specific position Occurrences divided into: • declaration -- introduces a variable often carries additional information: type,lifetime,… • use: an occurrence that is not a declaration • definition:occurrence in expression whose elaboration at run-time associates the variable with a value may be a use, or a declaration(most often the latter) block structure

8. Programming languages offer a variety of • declaration constructs • definition constructs These often group several declarations/definitions together block structure

9. Examples in C: int x; a declaration & (implicit) definition (why?) real foo(real x){, int z; … return x+y+z;} declares &defines foo, declares x, declares & defines z, uses x, y, z int goo(int x); (a function prototype) declares goo, x int goo(int x){return x+1;} given the declaration, a definition & a use of goo block structure

10. Scheme, OCAML: • (define foo (lambda (x) (+ x y))) declares & defines foo, declares x, uses x, y 2. (let ((x 3) (y (+ z 1))) (+ x z))(a definition construct) declares & defines x, y; uses x, z • let x = 5;; declares & defines x 4. let foo = function x  x+1; declares & defines foo, declares x 5. let x = 4 and y = z+1 in x+z;; declares & defines x, y; uses x, z block structure

11. Block, region , scope Block: any program construct that restricts visibility of variables declared in it variable declared at most once in a block • Functions/procedures are abstractions  restrict visibility of formal parameters are blocks • Other common blocks: let, let rec, let* (scheme), program, function body, compound statement (in some pl’s) block structure

12. A program may contain several declarations of variables with same name (in different blocks) – these are different variables • Blocks may be nested Q:To which variable (declaration) does a give use refer (is statically bound to)? block structure

13. Examples: int x; real y = 0.0; real foo(real x){int z; … return x+y+z;} (define foo (lambda (x) (+ x y))) The use of x is statically bound, that of y is free block structure

14. Q: Why is it important to associate uses with declarations? A: This defines their meaning, their run-time values • At run-time, declared variables are dynamically bound to values Each binding is associated with a declaration • Many bindings for a given identifier may exist • Static binding of a use to a declaration allows to select for it only the dynamic binding(s) associated with that declaration Static structure determines dynamic behavior block structure

15. zoo 5: zoo 5: zoo 5: Example: int n = 43; ………… int x = 3; int zoo(int n){if n =0 then return 1 else x+zoo(n-1) block structure

16. Terminology: d(x) – a declaration of x, u(x) – a use of x decl(u(x)) – the declaration to which u(x) is statically bound The rules that determine decl(u(x)): • Block specific rules • A universal rule block structure

17. Block specific: Each variable declared in a block has an associated region (ofvisibility)in the block ( a component of the block) Each block-kind has specific rules that determine the region for each variable declared in it block structure

18. Examples: 1. let x = E1 in E2;; the region of d(x) here is E2 2. let rec f = E1 in E2;; the region of d(f) here is both E1, E2 3. int x = 5; int y = x+5; the region of a declared variable in a C block : from after the declaration to end of block block structure

19. Blocks and regions may be nested Partial overlap not allowed  hierarchies The important one: theregion hierarchy The universal rule: The scopeof a declaration of x: its region, excluding allnested regions of other declarations of x block structure

20. Region --- associated with block kinds Scope --- determines actual visibility in given program, based on actual nesting Region – איזור , scope – תחום The discipline is called static/lexical) scoping: תיחום סטטי Static--- determined by program structure block structure

21. Example: int n = 43; ………… int x = 3; int zoo(int n){if n =0 then return 1 else x+zoo(n-1) The region of 1st declaration of n: down to end of program Its scope: the function expression for zoo is excluded block structure

22. A bit more terminology: A declaration d(x) binds each u(x) in its scope ‘use bound todecl.’ --- a binary, functional relation A use u(x) is bound/free in a program phrase E: decl(u(x)) is/is not defined in E (two unary predicates) ( local, globalhave similar meanings) Variable x is free/bound in E, if it has a free/bound use in E (can have both) For all: add statically- block structure

23. Common kinds of blocks • Function • Non-recursive, (possibly) parallel(collateral) • Regions do not contain defining expressions • independent definitions • Sequential – definitions elaboratedone by one, • each may use previously defined variables • regions do not contain defining expressions • Recursive – the regions do contain the defining expressions Comment: In all kinds except function, each declaration may be viewed as a definition (possibly to null) block structure

24. region region dec dec (pseudo-code) (pseudo-code) Graphic illustration: P Non-recursive, parallel block: let x = 3, y = x + 5 in x + y Sequential block: let* x = 3, y = x + 5 in x + y (Scheme let*) block structure

25. A recursive block: let rec factorial = function n => if n=0 then 1 else n*factorial (n-1) in factorial 3 Another recursive block(mutual recursion) letrec even = function n  if n = 0 then true else odd (n-1) and odd = function n  if n=0 then false else even (n-1) in even 3;; block structure

26. Comment on recursion in C • Recursion of a single function – by default (in C) a recursive block • For mutual recursion – use a sequential block, separate declaration from definition int foo(int x); // function declaration … int goo(int y){…foo(y-1)…} int foo(int x){….goo(x+1)…} // function definition block structure

27. Every block is (up syntactic variation) one of the four kinds Example: for (int i = 1, i++, i<k){ …} This loop construct is a block Could separate the definition from the uses: {int t; (implicit definition) for (i=1…… } • It is convenient to make blocks of various constructs (here a loop) • But, they typically fall into one of the kinds above block structure

28. A sequential block may interleave defintions and expressions A sequential block can be converted to nested parallel blocks (let* ((x 3) (y (+ x 4)) (+ x y))  (let ((x 3)) (let ((Y (+ x 4)) (+ x y)))  It can be ignored in general semantic discussion block structure

29. Conclusions: • Languages are very similar in terms of their block structure • It suffices to define semantics for a toy language with the three main kinds of blocks block structure