Abstract Syntax cs 7100 Prasad L 7 AST

Abstract Syntax cs 7100 (Prasad) L 7 AST 1

Language of l-expressions <exp> : : = <identifier> | (lambda ( <identifier> )<exp>) | (<exp>) E. g. , concrete syntax Scheme S-expressions ( lambda (x) ( f x ) ) ) cs 7100 (Prasad) L 7 AST 2

Abstract Syntax (vs Concrete Syntax) lambda-exp id body app-exp rand rator var-exp app-exp rator id rand var-exp id cs 7100 (Prasad) var-exp id L 7 AST 3

Overview Parse-expression Concrete Syntax Abstract Syntax Unparse-expression Interpreter Results cs 7100 (Prasad) L 7 AST 4

Representing Abstract Syntax with Records (define-datatype expression? (var-exp (id symbol? )) (lambda-exp (id symbol? ) (body expression? )) (app-exp (rator expression? ) (rand expression? ))) cs 7100 (Prasad) L 7 AST 5

Parse: Concrete to Abstract Syntax (define parse-expression (lambda (datum) (cond ((symbol? datum) (var-exp datum)) ((pair? datum) (if (eqv? (car datum) 'lambda) (lambda-exp (caadr datum) (parse-expression (caddr datum))) (app-exp (parse-expression (car datum)) (parse-expression (cadr datum))) ) ) (else (eopl: error 'parse-expression "Invalid concrete syntax ~s" datum)) ))) cs 7100 (Prasad) L 7 AST 6

Example (Petite Scheme) > (current-directory “I: \tkprasad\cs 784\EOPL-CODE\interps") > (load "chez-init. scm") > (load "2 -2 -2. scm") > (parse-expression 'x) (var-exp x) > (parse-expression '(lambda (x) (f x))) (lambda-exp x (app-exp (var-exp f) (var-exp x))) > (parse-expression 45) Error reported by parse-expression: Invalid concrete syntax 45 debug>e >(unparse-expression (lambda-exp 'x (app-exp (var-exp 'f) (var-exp 'x)))) (lambda (x) (f x)) cs 7100 (Prasad) L 7 AST 7

Example (PLT Scheme) cs 7100 (Prasad) L 7 AST 8

Unparse: Abstract to Concrete Syntax (define unparse-expression (lambda (exp) (cases expression exp (var-exp (id) id (lambda-exp (id body) (list 'lambda (list id) (unparse-expression body)) ) (app-exp (rator rand) (list (unparse-expression rator) (unparse-expression rand)) ) ))) cs 7100 (Prasad) L 7 AST 9

Role of Induction and Recursion • Define data structures (infinite values) by induction. • Seed elements. • Closure operations. • Define functions (operations) by recursion. • Boundary/Basis case. • Composite/Recursive case. • Prove properties using structural induction. • Basis case. • Inductive step. cs 7100 (Prasad) L 7 AST 10

Representing Environment cs 7100 (Prasad) L 7 AST 11

Alternative 1 (define empty-env (lambda () '())) (define extend-env (lambda (syms vals env) (cons (list syms vals) env) )) (define apply-env (lambda (env sym) (if (null? env) (eopl: error 'apply-env "No binding for ~s" sym) (let ((syms (car env))) (vals (cadr (car env))) (env (cdr env))) (let ((pos (list-find-position syms))) (if (number? pos) (list-ref vals pos) (apply-env sym))))) )) cs 7100 (Prasad) L 7 AST 12

Alternative 2 (define empty-env (lambda () (lambda (sym) (eopl: error 'apply-env "No binding for ~s" sym)) ) ) (define extend-env (lambda (syms vals env) (lambda (sym) (let ((pos (list-find-position syms))) (if (number? pos) (list-ref vals pos) (apply-env sym)))) ) ) (define apply-env (lambda (env sym) ) ) cs 7100 (Prasad) L 7 AST 13

Alternative 3 (define-datatype environment? (empty-env-record) (extended-env-record (syms (list-of symbol? )) (vals (list-of scheme-value? )) (env environment? ))) (define scheme-value? (lambda (v) #t)) cs 7100 (Prasad) L 7 AST 14

(cont’d) (define empty-env (lambda () (empty-env-record) )) (define extend-env (lambda (syms vals env) (extended-env-record syms vals env))) (define apply-env (lambda (env sym) (cases environment env (empty-env-record () (eopl: error 'apply-env "No binding for ~s" sym)) (extended-env-record (syms vals env) (let ((pos (list-find-position syms))) (if (number? pos) (list-ref vals pos) (apply-env sym)))) ) )) cs 7100 (Prasad) L 7 AST 15

Queue (define reset (lambda (q) (vector-ref q 0))) empty? (lambda (q) (vector-ref q 1))) enqueue (lambda (q) (vector-ref q 2))) dequeue (lambda (q) (vector-ref q 3))) (define Q (create-queue)) ((enqueue Q) 55) ((empty? Q)) ((dequeue Q)) ((empty? Q)) ((reset Q)) ((dequeue Q)) cs 7100 (Prasad) L 7 AST 16

(define create-queue (lambda () (let ((q-in '()) (q-out '())) (letrec ((reset-queue (lambda () (set! q-in '()) (set! q-out '())) ) (empty-queue? (lambda () (and (null? q-in) (null? q-out))) ) (enqueue (lambda (x) (set! q-in (cons x q-in))) ) (dequeue (lambda () (if (empty-queue? ) (eopl: error 'dequeue "On an empty queue") (begin (if (null? q-out) (begin (set! q-out (reverse q-in)) (set! q-in '())) (begin '())) (let ((ans (car q-out))) (set! q-out (cdr q-out)) ans) ) ))) ) (vector reset-queue empty-queue? enqueue dequeue)) ))) cs 7100 (Prasad) L 7 AST 17