Why do we need an interpreter? SICP Interpretation part 1. Role of each part of the interpreter. 1. Arithmetic calculator.

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1 .00 SICP Interpretation part Parts of an interpreter Arithmetic calculator Names Conditionals and if Store procedures in the environment Environment as explicit parameter Defining new procedures Why do we need an interpreter? Abstractions let us bury details and focus on use of modules to solve large systems Need to unwind abstractions at execution time to deduce meaning Have seen such a process Environment Model Now want to describe that process as a procedure Stages of an interpreter input to each stage Lexical analyzer "(average (+ ))" Parser Evaluator Environment Printer ( average ( average + ) ) "" + Role of each part of the interpreter Lexical analyzer break up input string into "words" called tokens Parser convert linear sequence of tokens to a tree like diagramming sentences in elementary school also convert self-evaluating tokens to their internal values #f is converted to the internal false value Evaluator follow language rules to convert parse tree to a value read and modify the environment as needed Printer convert value to human-readable output string Goal of lecture Implement an interpreter for a programming language Only write evaluator and environment use scheme's reader for lexical analysis and parsing use scheme's printer for output to do this, our language must look like scheme. Arithmetic calculator Want to evaluate arithmetic expressions of two arguments, like: ( ( )) Call the language scheme* All names end with a star Start with a simple calculator for arithmetic Progressively add scheme* features only get halfway there today

2 . Arithmetic calculator We are just walking through a tree (define (tag-check e sym) (and (pair? e) (eq? (car e) sym))) (define (sum? e) (tag-check e ')) ((sum? exp) (eval-sum exp)) (eval ) (define (eval-sum exp) (+ (eval (cadr exp)) (eval (caddr exp)))) (eval '( ( ))) sum? checks the tag We are just walking through a tree (eval-sum ). Arithmetic calculator ( ( )) What are the argument and return values of eval each time it is called in the evaluation of line? (+ (eval ) (eval )) (eval ) (eval ) (eval ) (eval-sum '( )) (eval '( )) (eval-sum '( ( ))) (eval '( ( ))) (+ (eval ) (eval )) 0. Things to observe cond determines the expression type no work to do on numbers scheme's reader has already done the work it converts a sequence of characters like "" to an internal binary representation of the number eval-sum recursively calls eval on both argument expressions. Names Extend the calculator to store intermediate results as named values (define* x* ( )) store result as x* ( x* ) use that result Store bindings between names and values in a table What are the argument and return values of eval each time it is called in lines and? Show the environment each time it changes during evaluation of these two lines.

3 . Names (define (define? exp) (tag-check exp 'define*)) ((sum? exp) (eval-sum exp)) ((? exp) (lookup exp)) ((define? exp) (eval-define exp)) ; table ADT from prior lecture: ; make-table void -> table ; table-get table, -> (binding null) ; table-put! table,, anytype -> undef ; binding-value binding -> anytype (define environment (make-table)). Names (define (lookup name) (let ((binding (table-get environment name))) (if (null? binding) (error "unbound variable: " name) (binding-value binding)))) (define (eval-define exp) (let ((name (cadr exp)) (defined-to-be (caddr exp))) (table-put! environment name (eval defined-to-be)) 'undefined)) (eval '(define* x* ( ))) (eval '( x* )) How many times is eval called in these two evaluations? Evaluation of page lines and (eval '(define* x* ( ))) (eval '( )) (eval ) ==> (eval ) ==> ==> names values ==> undefined x* (eval '( x* )) (eval 'x*) ==> (eval ) ==> ==>. Things to observe Use scheme function? to check for a name the reader converts sequences of characters like "x*" to s in the parse tree Can use any implementation of the table ADT eval-define recursively calls eval on the second subtree but not on the first one eval-define returns a special undefined value. Conditionals and if Extend the calculator to handle conditionals and if: (if* (greater* y* ) ( y* ) ) greater* if* an operation that returns a boolean an operation that evaluates the first subexp, checks if value is true or false What are the argument and return values of eval each time it is called in line? (define (greater? exp) (tag-check exp 'greater*)) (define (if? exp) (tag-check exp 'if*))... ((greater? exp) (eval-greater exp)) ((if? exp) (eval-if exp)) (define (eval-greater exp) (> (eval (cadr exp)) (eval (caddr exp)))). Conditionals and If (define (eval-if exp) (let ((predicate (cadr exp)) Note: if* is stricter (consequent (caddr exp)) (alternative (cadddr exp))) than Scheme s if (let ((test (eval predicate))) ((eq? test #t) (eval consequent)) ((eq? test #f) (eval alternative)) (error "predicate not boolean: " predicate)))))) (eval '(define* y* )) (eval '(if* (greater* y* ) ( y* ) ))

4 We are just walking through a tree if* greater* y* y* (eval ) greater* y* Then (eval ) or (eval ) Evaluation of page line (eval '(if* (greater* y* ) ( y* ) )) (eval '(greater* y* )) (eval 'y*) ==> (eval ) ==> ==> #t (eval '( y* )) (eval 'y*) ==> (eval ) ==> ==> ==> y* 0. Things to observe eval-greater is just like eval-sum from page recursively call eval on both argument expressions call scheme > to compute value eval-if does not call eval on all argument expressions: call eval on the predicate call eval on the consequent or on the alternative but not both. Store operators in the environment Want to add lots of operators but keep eval short Operations like and greater* are similar evaluate all the argument subexpressions perform the operation on the resulting values Call this standard pattern an application Implement a single case in eval for all applications Approach: eval the first subexpression of an application put a name in the environment for each operation value of that name is a procedure apply the procedure to the operands (define (application? e) (pair? e)) ((? exp) (lookup exp)) ((define? exp) (eval-define exp)) ((if? exp) (eval-if exp)) ((application? exp) (apply (eval (car exp)) (map eval (cdr exp)))). Store operators in the environment (define scheme-apply apply) ;; rename scheme s apply so we can reuse the name (define (apply operator operands) (if (primitive? operator) (scheme-apply (get-scheme-procedure operator) operands) (error "operator not a procedure: " operator))) ;; primitive: an ADT that stores scheme procedures (define prim-tag 'primitive) (define (make-primitive scheme-proc)(list prim-tag scheme-proc)) (define (primitive? e) (tag-check e prim-tag)) (define (get-scheme-procedure prim) (cadr prim)) (define environment (make-table)) (table-put! environment ' (make-primitive +)) (table-put! environment 'greater* (make-primitive >)) (table-put! environment 'true* #t) Environment after eval line names values z* true* #t greater* primitive scheme procedure + (eval '(define* z* )) (eval '( )) (eval '(if* true* 0 )) primitive scheme procedure >

6 (define (lambda? e) (tag-check e 'lambda*)) (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (eval-define exp env)) ((if? exp) (eval-if exp env)) ((lambda? exp) (eval-lambda exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (eval-lambda exp env) (let ((args (cadr exp)) (body (caddr exp))) (make-compound args body env))). Defining new procedures Implementation of lambda* (eval '(lambda* (x*) ( x* x*)) GE) (eval-lambda '(lambda* (x*) ( x* x*)) GE) (make-compound '(x*) '( x* x*) GE) (list 'compound '(x*) '( x* x*) GE) (define (apply operator operands) ((primitive? operator) (scheme-apply (get-scheme-procedure operator) operands)) ((compound? operator) (eval (body operator) (extend-env-with-new-frame (parameters operator) operands (env operator)))) (error "operator not a procedure: " operator)))) ;; ADT that implements the double bubble (define compound-tag 'compound) (define (make-compound parameters body env) (list compound-tag parameters body env)) (define (compound? exp) (tag-check exp compound-tag)) (define (parameters compound) (cadr compound)) (define (body compound) (caddr compound)) (define (env compound) (cadddr compound)) compound x* GE This data structure is a procedure! Defining a named procedure (eval '(define* twice* (lambda* (x*) ( x* x*))) GE) names values z* true* #t twice* primitive scheme procedure + Implementation of apply () (eval '(twice* ) GE) some-other-environment) (apply (eval 'twice* GE) (map (lambda (e) (eval e GE)) '())) (apply (list 'compound '(x*) '( x* x*) GE) '()) (eval '( x* x*) (extend-env-with-new-frame '(x*) '() GE)) (eval '( x* x*) E) compound A name value E x* x* GE Implementation of apply () (eval '( x* x*) E) (apply (eval ' E) (map (lambda (e) (eval e E)) '(x* x*))) (apply '(primitive #[add]) (list (eval 'x* E) (eval 'x* E))) (apply '(primitive #[add]) '( )) (scheme-apply #[add] '( )) After is returned by (eval '( x* x*) E), where is frame A stored? GE A E name value x* Implementation of environment model Environment = list<table> E E name value x* GE A name value x* GE name value (primitive #[add]) greater* (primitive #[grt])...

7 ; Environment model code (part of eval ) ; Environment = list<table> (define (extend-env-with-new-frame names values env) (let ((new-frame (make-table))) (make-bindings! names values new-frame) (cons new-frame env))) (define (make-bindings! names values table) (for-each (lambda (name value) (table-put! table name value)) names values)) ; the initial global environment (define GE (extend-env-with-new-frame (list ' 'greater*) (list (make-primitive +) (make-primitive >)) nil)) ; lookup searches the list of frames for the first match (define (lookup name env) (if (null? env) (error "unbound variable: " name) (let ((binding (table-get (car env) name))) (if (null? binding) (lookup name (cdr env)) (binding-value binding))))) 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 no pending operations on either call an iterative algorithm if the expression is iterative What is still missing from scheme*? ability to evaluate a sequence of expressions data types other than numbers and booleans ; define changes the first frame in the environment (define (eval-define exp env) (let ((name (cadr exp)) (defined-to-be (caddr exp))) (table-put! (car env) name (eval defined-to-be env)) 'undefined)) (eval '(define* twice* (lambda* (x*) ( x* x*))) GE) (eval '(twice* ) GE) Everything in these lectures would still work if you deleted the stars from the names!

8 0. Arithmetic calculator (define (tag-check e sym) (and (pair? e) (eq? (car e) sym))) (define (sum? e) (tag-check e ')) ((sum? exp) (eval-sum exp)) (define (eval-sum exp) (+ (eval (cadr exp)) (eval (caddr exp)))) (eval '( ( )))

9 Names (define (define? exp) (tag-check exp 'define*)) ((sum? exp) (eval-sum exp)) ((? exp) (lookup exp)) ((define? exp) (eval-define exp)) ; variation on table ADT from March lecture (only difference is ; that table-get returns a binding, while original version ; returned a value): ; make-table void -> table ; table-get table, -> (binding null) ; table-put! table,, anytype -> undef ; binding-value binding -> anytype (define environment (make-table)) (define (lookup name) (let ((binding (table-get environment name))) (if (null? binding) (error "unbound variable: " name) (binding-value binding)))) (define (eval-define exp) (let ((name (cadr exp)) (defined-to-be (caddr exp))) (table-put! environment name (eval defined-to-be)) 'undefined)) (eval '(define* x* ( ))) (eval '( x* )) ; Index to procedures that have not changed: ; procedure page line ; sum? ; eval-sum

10 Conditionals and if (define (greater? exp) (tag-check exp 'greater*)) (define (if? exp) (tag-check exp 'if*)) ((sum? exp) (eval-sum exp)) ((? exp) (lookup exp)) ((define? exp) (eval-define exp)) ((greater? exp) (eval-greater exp)) ((if? exp) (eval-if exp)) (define (eval-greater exp) (> (eval (cadr exp)) (eval (caddr exp)))) (define (eval-if exp) (let ((predicate (cadr exp)) (consequent (caddr exp)) (alternative (cadddr exp))) (let ((test (eval predicate))) ((eq? test #t) (eval consequent)) ((eq? test #f) (eval alternative)) (error "predicate not boolean: " predicate)))))) (eval '(define* y* )) (eval '(if* (greater* y* ) ( y* ) )) ; Index to procedures that have not changed: ; procedure page line ; sum? ; eval-sum ; lookup ; define? ; eval-define

11 Store operators in the environment (define (application? e) (pair? e)) ((? exp) (lookup exp)) ((define? exp) (eval-define exp)) ((if? exp) (eval-if exp)) ((application? exp) (apply (eval (car exp)) (map eval (cdr exp)))) ;; rename scheme s apply so we can reuse the name (define scheme-apply apply) (define (apply operator operands) (if (primitive? operator) (scheme-apply (get-scheme-procedure operator) operands) (error "operator not a procedure: " operator))) ;; primitive: an ADT that stores scheme procedures (define prim-tag 'primitive) (define (make-primitive scheme-proc)(list prim-tag scheme-proc)) (define (primitive? e) (tag-check e prim-tag)) (define (get-scheme-procedure prim) (cadr prim)) (define environment (make-table)) (table-put! environment ' (make-primitive +)) (table-put! environment 'greater* (make-primitive >)) (table-put! environment 'true* #t) (eval '(define* z* )) (eval '( )) (eval '(if* true* 0 )) ; Index to procedures that have not changed: ; procedure evaluator line ; lookup ; define? ; eval-define ; if? ; eval-if 0

12 Environment as explicit parameter ;This change is boring! Exactly the same functionality as #. (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (eval-define exp env)) ((if? exp) (eval-if exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (lookup name env) (let ((binding (table-get env name))) (if (null? binding) (error "unbound variable: " name) (binding-value binding)))) (define (eval-define exp env) (let ((name (cadr exp)) (defined-to-be (caddr exp))) (table-put! env name (eval defined-to-be env)) 'undefined)) (define (eval-if exp env) (let ((predicate (cadr exp)) (consequent (caddr exp)) (alternative (cadddr exp))) (let ((test (eval predicate env))) ((eq? test #t) (eval consequent env)) ((eq? test #f) (eval alternative env)) (error "predicate not boolean: " predicate)))))) (eval '(define* z* ( )) environment) (eval '(if* (greater* z* ) 0 ) environment) Index to procedures that have not changed: procedure evaluator line define? if? application? apply

13 Defining new procedures (define (lambda? e) (tag-check e 'lambda*)) (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (eval-define exp env)) ((if? exp) (eval-if exp env)) ((lambda? exp) (eval-lambda exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (eval-lambda exp env) (let ((args (cadr exp)) (body (caddr exp))) (make-compound args body env))) (define (apply operator operands) ((primitive? operator) (scheme-apply (get-scheme-procedure operator) operands)) ((compound? operator) (eval (body operator) (extend-env-with-new-frame (parameters operator) operands (env operator)))) (error "operator not a procedure: " operator)))) ;; ADT that implements the double bubble (define compound-tag 'compound) (define (make-compound parameters body env) (list compound-tag parameters body env)) (define (compound? exp) (tag-check exp compound-tag)) (define (parameters compound) (cadr compound)) (define (body compound) (caddr compound)) (define (env compound) (cadddr compound))

14 ; Environment model code (part of eval ) ; Environment = list<table> (define (extend-env-with-new-frame names values env) (let ((new-frame (make-table))) (make-bindings! names values new-frame) (cons new-frame env))) (define (make-bindings! names values table) (for-each (lambda (name value) (table-put! table name value)) names values)) ; the initial global environment (define GE (extend-env-with-new-frame (list ' 'greater*) (list (make-primitive +) (make-primitive >)) nil)) ; lookup searches the list of frames for the first match (define (lookup name env) (if (null? env) (error "unbound variable: " name) (let ((binding (table-get (car env) name))) (if (null? binding) (lookup name (cdr env)) (binding-value binding))))) ; define changes the first frame in the environment (define (eval-define exp env) (let ((name (cadr exp)) (defined-to-be (caddr exp))) (table-put! (car env) name (eval defined-to-be env)) 'undefined)) (eval '(define* twice* (lambda* (x*) ( x* x*))) GE) (eval '(twice* ) GE) Index to procedures that have not changed: procedure evaluator line define? if? application? eval-i

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