1 / 17

Abstract Syntax

Abstract Syntax. Language of l -expressions. <exp> ::= <identifier> | ( lambda ( <identifier> ) <exp> ) | ( <exp> <exp> ) E.g., concrete syntax Scheme S-expressions ( lambda (x) ( f ( f x ) ) ). Abstract Syntax ( vs Concrete Syntax ). lambda-exp. id. body.

marcus
Download Presentation

Abstract Syntax

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Abstract Syntax L7AST

  2. Language of l-expressions <exp> ::= <identifier> | (lambda( <identifier>)<exp>) | (<exp> <exp>) E.g.,concrete syntax Scheme S-expressions ( lambda (x) ( f ( f x ) ) ) L7AST

  3. Abstract Syntax (vs Concrete Syntax) lambda-exp id body app-exp rand rator var-exp app-exp rator rand id var-exp var-exp id id L7AST

  4. Overview Parse-expression Concrete Syntax Abstract Syntax Unparse-expression Interpreter Results L7AST

  5. Representing Abstract Syntax with Records (define-datatype expression expression? (var-exp (id symbol?)) (lambda-exp (id symbol?) (body expression?)) (app-exp (rator expression?) (rand expression?))) L7AST

  6. 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)) ))) L7AST

  7. Example (Petite Scheme) > (current-directory “I:\\tkprasad\\cs784\\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)) L7AST

  8. Example (PLT Scheme) L7AST

  9. 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)) ) ))) L7AST

  10. 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. L7AST

  11. Representing Environment L7AST

  12. 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 (car env))) (vals (cadr (car env))) (env (cdr env))) (let ((pos (rib-find-position sym syms))) (if (number? pos) (list-ref vals pos) (apply-env env sym))))) )) L7AST

  13. 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 sym syms))) (if (number? pos) (list-ref vals pos) (apply-env env sym)))) ) ) (define apply-env (lambda (env sym) (env sym) ) ) L7AST

  14. Alternative 3 (define-datatype environment environment? (empty-env-record) (extended-env-record (syms (list-of symbol?)) (vals (list-of scheme-value?)) (env environment?))) (define scheme-value? (lambda (v) #t)) L7AST

  15. (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 sym syms))) (if (number? pos) (list-ref vals pos) (apply-env env sym)))) ) )) L7AST

  16. Queue (define reset (lambda (q) (vector-ref q 0))) (define empty? (lambda (q) (vector-ref q 1))) (define enqueue (lambda (q) (vector-ref q 2))) (define dequeue (lambda (q) (vector-ref q 3))) (define Q (create-queue)) ((enqueue Q) 55) ((empty? Q)) ((dequeue Q)) ((empty? Q)) ((reset Q)) ((dequeue Q)) L7AST

  17. (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 "Not on an empty queue") (begin (if (null? q-out) (begin (set! q-out (reverse q-in)) (set! q-in '()))) (let ((ans (car q-out))) (set! q-out (cdr q-out)) ans))))) ) (vector reset-queue empty-queue? enqueue dequeue)) ))) L7AST

More Related