1. cs7100(Prasad)L8Interp1 Interpreters Study Semantics of Programming Languages through interpreters (Executable Specifications)

2. cs7100(Prasad)L8Interp2 Interpreters Input: –Representation of a program (AST) Output: –“Meaning” of the program ; Interpreter vs Compiler Interpreter carries out the meaning of a program, while a compiler transforms a program in one language into a program in a lower-level language preserving the meaning.

3. cs7100(Prasad)L8Interp3 Simple Expression Language ::= | ::= () | ( {, }*) ::= + | - | * | add1 | sub1 E.g., 5 add1(+(3,j))

4. cs7100(Prasad)L8Interp4 Informal Semanics Number same as what Scheme associates with numerals. (internal to the entity) Symbolic names value bound to it in the environment (external to the entity) Application expression recursively evaluate operator and operands. primitive operators interpreted by Scheme.

5. cs7100(Prasad)L8Interp5 Example (Petite Scheme) > (just-scan "add1(+(1,3))") ((literal-string28 "add1" 1) (literal-string28 "(" 1) (literal-string28 "+" 1) (literal-string28 "(" 1) (number 1 1) (literal-string28 "," 1) (number 3 1) (literal-string28 ")" 1) (literal-string28 ")" 1))

6. cs7100(Prasad)L8Interp6 Example > (scan&parse "add1(+(1,3))") (a-program (primapp-exp (incr-prim) ((primapp-exp (add-prim) ((lit-exp 1) (lit-exp 3)))))) > (eval-program (scan&parse "add1(+(1,3))")) 5

7. cs7100(Prasad)L8Interp7 The Abstract Syntax (define-datatype program program? (a-program (exp expression?))) (define-datatype expression expression? (lit-exp (datum number?)) (var-exp (id symbol?)) (primapp-exp (prim primitive?) (rand (list-of expression?))) ) (define-datatype primitive primitive? (add-prim) (subtract-prim) (mult-prim) (incr-prim) (decr-prim))

8. cs7100(Prasad)L8Interp8 The evaluator (define eval-program (lambda (pgm) (cases program pgm (a-program (body) (eval-expression body (init-env)))))) (define eval-expression (lambda (exp env) (cases expression exp (lit-exp (datum) datum) (var-exp (id) (apply-env env id) ) (primapp-exp (prim rands) (let ((args (eval-rands rands env))) (apply-primitive prim args)) ) )))

9. cs7100(Prasad)L8Interp9 (cont’d) (define eval-rands (lambda (rands env) (map (lambda (x)(eval-rand x env)) rands))) (define eval-rand (lambda (rand env) (eval-expression rand env))) (define eval-rands (lambda (rands env) (map (lambda (x) (eval-expression x env)) rands)))

10. cs7100(Prasad)L8Interp10 (cont’d) (define apply-primitive (lambda (prim args) (cases primitive prim (add-prim () (+ (car args) (cadr args)) ) (subtract-prim () (- (car args) (cadr args)) ) (mult-prim () (* (car args) (cadr args)) ) (incr-prim () (+ (car args) 1) ) (decr-prim () (- (car args) 1) ) ))) (define init-env (lambda () (extend-env '(i v x) '(1 5 10) (empty-env))))... Code for environment manipulation...

11. cs7100(Prasad)L8Interp11 Scanner Specification (define the-lexical-spec '((whitespace (whitespace) skip) (comment ("%" (arbno (not #\newline))) skip) (identifier (letter (arbno (or letter digit "_" "-" "?"))) symbol) (integer (digit (arbno digit)) number)) )

12. cs7100(Prasad)L8Interp12 Parser Specification (define the-grammar '((program (expression) a-program) (expression (integer) lit-exp) (expression (identifier) var-exp) (expression (primitive "(" (separated-list expression ",") ")") primapp-exp) (primitive ("+") add-prim) (primitive ("-") subtract-prim) (primitive ("*") mult-prim) (primitive ("add1") incr-prim) (primitive ("sub1") decr-prim)) )

13. cs7100(Prasad)L8Interp13 Example (Dr. Racket) > (scan&parse "-(v,x)") #(struct:a-program #(struct:primapp-exp #(struct:subtract-prim) ( #(struct:var-exp v) #(struct:var-exp x) ) ) ) > (eval-program (scan&parse "-(v,x)")) -5 Recall that v = 5 and x = 10 in init-env.

14. cs7100(Prasad)L8Interp14 Adding conditional Concrete Syntax ::= if then else Abstract Syntax if-exp (test-exp true-exp false-exp) Addl. Semantic Function (define (true-value? x) (not (zero? x)) )

15. cs7100(Prasad)L8Interp15 Addl. Interpreter Clause (if-exp (test-exp true-exp false-exp) ( (if (true-value? (eval-expression test-exp env)) (eval-expression true-exp env) ) (eval-expression false-exp env)) ) Defined language vs Defining language Inductively defined data structure naturally leads to recursively defined function.

16. cs7100(Prasad)L8Interp16 Scanner Details > (just-scan " if while - Abc Def + # pqr") ((literal-string45 "if" 1) (identifier while 1) (literal-string45 "-" 1) (identifier Abc 2) (identifier Def 3) (literal-string45 "+" 4))

17. cs7100(Prasad)L8Interp17 let x = 5 in let y = 6 + x in x + y; Sub-expressions may be evaluated in different contexts/environments. let x = 5 in let x = 6 + x in x + x; Inner x shadows outer x in nested let -body. x = 11 x = 5 y=11 x = 5 Local Bindings : Issues

18. cs7100(Prasad)L8Interp18 let x = 5 x in let x = 6 + x xx in x + x * x; Introducing let requires passing relevant environment to the evaluator. 110Inner binding overrides the outer one in case of conflict. (Example Expression Value: 110) x = 5 x = 11 x = 5

19. cs7100(Prasad)L8Interp19 Adding let Concrete Syntax ::= let { = } * in Abstract Syntax let-exp (ids rands body)

20. cs7100(Prasad)L8Interp20 Introducing if and let expressions ( define-datatype expression expression?... (if-exp (test-exp expression?) (true-exp expression?) (false-exp expression?)) (let-exp (ids (list-of symbol?)) (rands (list-of expression?)) (body expression?) ) )

21. cs7100(Prasad)L8Interp21 Introducing if and let into the evaluator (define eval-expression (lambda (exp env) (cases expression exp... (if-exp (test-exp true-exp false-exp) (if (true-value? (eval-expression test-exp env)) (eval-expression true-exp env) (eval-expression false-exp env)) ) (let-exp (ids rands body) (let ((args (eval-rands rands env))) ( eval-expression body (extend-env ids args env)) ) ) (else (eopl:error 'eval-expression "Not here:~s" exp)) )))

22. cs7100(Prasad)L8Interp22 Recapitulation Evaluator Variable-free Arithmetic Expressions (Integers, +, *,…) Integer syntax (program) semantics structure (Scheme) Semantics (meaning) CALCULATOR

23. cs7100(Prasad)L8Interp23 Evaluator Arithmetic Expressions Environment; (Integers, +, *,…) Integer syntax (program) semantic structure (Scheme) Semantics (meaning) CALCULATOR WITH MEMORY

24. cs7100(Prasad)L8Interp24 Evaluator Arithmetic Expressions; Procedure Definitions and Calls Environment; (Integers, +, *,…); Addl. Scheme Support Integer; Procedures syntax (program) semantic structure (Scheme) Semantics (meaning) PROGRAMMABLE CALCULATOR

25. cs7100(Prasad)L8Interp25 Polynomial Calculators 9 To specify/design a programmable polynomial calculator, the object language must contain syntax for creating and manipulating polynomials, and 9 the meta-language (Scheme) must provide suitable semantic structure to map variables to polynomials (environment). to interpret operations on polynomials (using corresponding Scheme code). –Meta-language support is analogous to hardware support. ; The semantics of the ADT Polynomials can be specified through algebraic techniques.