Lecture 18 Continue Evaluator 1 Representing procedures eval

Lecture 18 Continue Evaluator 1

Representing procedures (eval '(define twice (lambda (x) (+ x x))) GE) z 9 true #t + symbol primitive scheme procedure + twice symbol procedure symbol + symbol x 2

Representing the Environment Abstractly • (eval ‘(twice 4)) • (extend-environment '(x) '(4) GE E 1 Concretely x: 10 +: (primitive. . . ) twice: (procedure. . ) x: 4 GE E 1 frame list of variables list of values 10 x 4 x + twice primitive 3

Representing the Environment • (eval ‘(twice 5)) • (extend-environment '(x) '(5) GE) E 2 x 5 GE E 1 frame list of variables list of values 10 x 4 x + twice primitive 4

(define (lookup-variable-value var env) (define (env-loop env) (define (scan vars vals) (cond ((null? vars) (env-loop (enclosing-environment env))) ((eq? var (car vars)) (car vals)) (else (scan (cdr vars) (cdr vals))))) (if (eq? env the-empty-environment) (error "Unbound variable" var) (let ((frame (first-frame env))) (scan (frame-variables frame) (frame-values frame))))) (env-loop env)) (define (enclosing-environment env) (cdr env)) (define (first-frame env) (car env)) (define (frame-variables frame) (car frame)) (define (frame-values frame) (cdr frame)) 5

(define-variable! var val env) (let ((frame (first-frame env))) (define (scan vars vals) (cond ((null? vars) (add-binding-to-frame! var val frame)) ((eq? var (car vars)) (set-car! vals val)) (else (scan (cdr vars) (cdr vals))))) (scan (frame-variables frame) (frame-values frame)))) (define (eval-definition exp env) (let ((name (cadr exp)) (defined-to-be (eval (caddr exp) env))) (define-variable! name defined-to-be env) ‘undefined)) 6

Assignments )define (eval-assignment exp env( ) set-variable-value! (assignment-variable exp( ) eval (assignment-value exp) env( ' ok( )define (assignment? exp( ) tagged-list? exp 'set((! )define (assignment-variable exp) (cadr exp(( )define (assignment-value exp) (caddr exp((

set-variable-value! )define (set-variable-value! var val env( ) define (env-loop env( ) )) ) ) define (scan vars vals( cond ((null? vars( env-loop (enclosing-environment env((( eq? var (car vars(( set-car! vals val(( else (scan (cdr vars) (cdr vals((((( ) if (eq? env the-empty-environment( ) error "Unbound variable -- SET!" var( ) let ((frame (first-frame env((( ) scan (frame-variables frame( ) frame-values frame)(((( ) env-loop env((

Initialization primitives and initial env. (define the-global-environment (setup-environment)) (define (setup-environment) (let ((initial-env (extend-environment (primitive-procedure-names) (primitive-procedure-objects) the-empty-environment))) (define-variable! 'true #t initial-env) (define-variable! 'false #f initial-env)) (define the-empty-environment '()) 9

(define primitive-procedure (list 'car car) (list 'cdr cdr) (list 'cons) (list 'null? ) (list '+ +) ; ; more primitives )) (define (primitive-procedure-names) (map car primitive-procedures)) (define (primitive-procedure-objects) (map (lambda (proc) (list 'primitive (cadr proc))) primitive-procedures)) 10

Read-Eval-Print Loop (define input-prompt "; ; ; M-Eval input: ") (define output-prompt "; ; ; M-Eval value: ") (define (prompt-for-input string) (newline) (display string) (newline)) (define (announce-output string) (newline) (display string) (newline)) (define (driver-loop) (prompt-for-input-prompt) (let ((input (read))) (let ((output (eval input the-global-env))) (announce-output-prompt) (user-print output))) (driver-loop)) 11

Apply (reminder) (define (apply procedure arguments) (cond ((primitive-procedure? procedure) (apply-primitive-procedure arguments)) ((compound-procedure? procedure) (eval-sequence (procedure-body procedure) (extend-environment (procedure-parameters procedure) arguments (procedure-env procedure)))) (else (error "Unknown procedure type -- APPLY" procedure))))

Execution Examples • An iterative algorithm in scheme (eval '(define odd (lambda (n) (odd (- n 2)))) GE) • A recursive algorithm in scheme (eval '(define sum (lambda (n) (+ n (sum (- n 1))))) GE) • Base case and if check omitted from both algorithms to simplify the example 15

Summary • Cycle between eval and apply is the core of the evaluator • eval calls apply with operator and argument values • apply calls eval with expression and environment • What is still missing from scheme ? • Some special forms • data types other than numbers and booleans 18

Example – Changing Syntax • Suppose you wanted a "verbose" application syntax: (CALL <proc> ARGS <arg 1> <arg 2>. . . ) • Changes – only in the syntax routines! (define (application? exp) (tagged-list? 'CALL)) (define (operator app) (cadr app)) (define (operands app) (cdddr app)) 21

Implementing "Syntactic Sugar" • Idea: • Implement a simple fundamental "core" in the evaluator • Easy way to add alternative/convenient syntax? • "let" as sugared procedure application: (let ((<name 1> <val 1>) (<name 2> <val 2>)) <body>) ((lambda (<name 1> <name 2>) <val 1> <val 2>) <body>) 22

Detect and Transform the Alternative Syntax (define (eval exp env) (cond ((self-evaluating? exp) ((variable? exp) (lookup-variable-value exp env)) ((quoted? exp) (text-of-quotation exp)). . . ((cond? exp) (eval (cond->if exp) env)) ((let? exp) (eval (let->combination exp) env)) ((application? exp) (apply (eval (operator exp) env) (list-of-values (operands exp) env))) (else (error "Unknown expression" exp)))) 23

Implementing cond: Syntax procedures (cond ((= x 23) (+ x 1)) (else (- x 1))) (if (= x 23) (+ x 1) (- x 1)) (define (cond-clauses exp) (cdr exp)) (define (cond-else-clause? clause) (eq? (cond-predicate clause) 'else)) (define (cond-predicate clause) (car clause)) (define (cond-actions clause) (cdr clause)) 24

Cond syntax (cond ((= x 23) (+ x 1)) (else (- x 1))) cond else = x x 1 23 + x 1 25

Transforming sequence of expression to an expression (define (sequence->exp seq) (cond ((null? seq) ((last-exp? seq) (first-exp seq)) (else (make-begin seq)))) (define (make-begin seq) (cons 'begin seq)) begin * x 2 car y 26

Implementing cond (Cont. ) (cond ((= x 23) (+ x 1)) (else (- x 1))) (if (= x 23) (+ x 1) (- x 1)) 27

Implementing cond (define (cond->if exp) (expand-clauses (cond-clauses exp))) (define (expand-clauses) (if (null? clauses) 'false ; no else clause (let ((first (car clauses)) (rest (cdr clauses))) (if (cond-else-clause? first) (if (null? rest) (sequence->exp (cond-actions first)) (error "ELSE clause isn't last -- COND->IF" clauses)) (make-if (cond-predicate first) (sequence->exp (cond-actions first)) (expand-clauses rest)))))) 28

Details of cond syntax transformation (cond ((= x 23) (+ x 1)) (else (- x 1))) cond else = x x 1 23 + x 1 29

Details of cond syntax transformation (expand-clauses else = x 23 x 1 ) + x 1 30

Details of cond syntax transformation rest first else = x x 1 23 + x 1 31

Details of cond syntax transformation (make-if = x 23 + x 1 )) (expand-clauses else - x 1 32

Details of cond syntax transformation (make-if = x 23 + x 1 - x 1 ) 33

Details of cond syntax transformation if = x + 23 x - 1 x 1 34

Named Procedures Support (define (foo <parm>) <body>) (define (eval-definition exp env) (define-variable! (definition-variable exp) (eval (definition-value exp) env)) (define (definition-variable exp) (if (symbol? (cadr exp)) (cadr exp) (caadr exp))) (define (definition-value exp) (if (symbol? (cadr exp)) (caddr exp) (make-lambda (cdadr exp) (cddr exp)))) ; formal params ; body 35

Exam • 4 Questions • 3 Hours • You may bring any written or printed material (no laptops. . ) • You can use every function studied in class recitation exercise • All covered material • Good Luck and have a nice vacation!