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


 Clementine Gregory
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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 selfevaluating 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 humanreadable 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 (tagcheck e sym) (and (pair? e) (eq? (car e) sym))) (define (sum? e) (tagcheck e ')) ((sum? exp) (evalsum exp)) (eval ) (define (evalsum exp) (+ (eval (cadr exp)) (eval (caddr exp)))) (eval '( ( ))) sum? checks the tag We are just walking through a tree (evalsum ). 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 ) (evalsum '( )) (eval '( )) (evalsum '( ( ))) (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 evalsum 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) (tagcheck exp 'define*)) ((sum? exp) (evalsum exp)) ((? exp) (lookup exp)) ((define? exp) (evaldefine exp)) ; table ADT from prior lecture: ; maketable void > table ; tableget table, > (binding null) ; tableput! table,, anytype > undef ; bindingvalue binding > anytype (define environment (maketable)). Names (define (lookup name) (let ((binding (tableget environment name))) (if (null? binding) (error "unbound variable: " name) (bindingvalue binding)))) (define (evaldefine exp) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! environment name (eval definedtobe)) '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 evaldefine recursively calls eval on the second subtree but not on the first one evaldefine 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) (tagcheck exp 'greater*)) (define (if? exp) (tagcheck exp 'if*))... ((greater? exp) (evalgreater exp)) ((if? exp) (evalif exp)) (define (evalgreater exp) (> (eval (cadr exp)) (eval (caddr exp)))). Conditionals and If (define (evalif 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 evalgreater is just like evalsum from page recursively call eval on both argument expressions call scheme > to compute value evalif 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) (evaldefine exp)) ((if? exp) (evalif exp)) ((application? exp) (apply (eval (car exp)) (map eval (cdr exp)))). Store operators in the environment (define schemeapply apply) ;; rename scheme s apply so we can reuse the name (define (apply operator operands) (if (primitive? operator) (schemeapply (getschemeprocedure operator) operands) (error "operator not a procedure: " operator))) ;; primitive: an ADT that stores scheme procedures (define primtag 'primitive) (define (makeprimitive schemeproc)(list primtag schemeproc)) (define (primitive? e) (tagcheck e primtag)) (define (getschemeprocedure prim) (cadr prim)) (define environment (maketable)) (tableput! environment ' (makeprimitive +)) (tableput! environment 'greater* (makeprimitive >)) (tableput! 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 >
5 Evaluation of eval line (eval '( )) (apply (eval ') (map eval '( ))) (apply '(primitive #[add]) (list (eval ) (eval )) (apply '(primitive #[add]) '( )) (schemeapply (getschemeprocedure '(primitive #[add])) '( )) (schemeapply #[add] '( )) Evaluation of eval line (eval '(if* true* 0 )) (evalif '(if* true* 0 )) (let ((test (eval 'true*)))...)) (let ((test (lookup 'true*)))...)) (let ((test #t))...)) (eval 0) 0 Apply is never called!. Things to observe applications must be last case in eval no tag check apply is never called in line applications evaluate all subexpressions expressions that need special handling, like if*, gets their own case in eval. Environment as explicit parameter change from (eval '( )) to (eval '( ) environment) all procedures that call eval have extra argument lookup and define use environment from argument No other change from evaluator Only nontrivial code: case for application? in eval (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (evaldefine exp env)) ((if? exp) (evalif exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (lookup name env) (let ((binding (tableget env name))) (if (null? binding) (error "unbound variable: " name) (bindingvalue binding)))). Environment as explicit parameter This change is boring! Exactly the same functionality as #. (define (evaldefine exp env) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! env name (eval definedtobe env)) 'undefined)) (define (evalif exp env) (let ((predicate (cadr exp)) (eval '(define* z* ( )) (consequent (caddr exp)) environment) (alternative (cadddr exp))) (eval '(if* (greater* z* ) 0 ) (let ((test (eval predicate env))) environment) ((eq? test #t) (eval consequent env)) ((eq? test #f) (eval alternative env)) (error predicate not boolean: " predicate)))))). Defining new procedures Want to add new procedures For example, a scheme* program: (define* twice* (lambda* (x*) ( x* x*))) (twice* ) Strategy: Add a case for lambda* to eval the value of lambda* is a compound procedure Extend apply to handle compound procedures Implement environment model 0
6 (define (lambda? e) (tagcheck e 'lambda*)) (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (evaldefine exp env)) ((if? exp) (evalif exp env)) ((lambda? exp) (evallambda exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (evallambda exp env) (let ((args (cadr exp)) (body (caddr exp))) (makecompound args body env))). Defining new procedures Implementation of lambda* (eval '(lambda* (x*) ( x* x*)) GE) (evallambda '(lambda* (x*) ( x* x*)) GE) (makecompound '(x*) '( x* x*) GE) (list 'compound '(x*) '( x* x*) GE) (define (apply operator operands) ((primitive? operator) (schemeapply (getschemeprocedure operator) operands)) ((compound? operator) (eval (body operator) (extendenvwithnewframe (parameters operator) operands (env operator)))) (error "operator not a procedure: " operator)))) ;; ADT that implements the double bubble (define compoundtag 'compound) (define (makecompound parameters body env) (list compoundtag parameters body env)) (define (compound? exp) (tagcheck exp compoundtag)) (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) someotherenvironment) (apply (eval 'twice* GE) (map (lambda (e) (eval e GE)) '())) (apply (list 'compound '(x*) '( x* x*) GE) '()) (eval '( x* x*) (extendenvwithnewframe '(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]) '( )) (schemeapply #[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 (extendenvwithnewframe names values env) (let ((newframe (maketable))) (makebindings! names values newframe) (cons newframe env))) (define (makebindings! names values table) (foreach (lambda (name value) (tableput! table name value)) names values)) ; the initial global environment (define GE (extendenvwithnewframe (list ' 'greater*) (list (makeprimitive +) (makeprimitive >)) nil)) ; lookup searches the list of frames for the first match (define (lookup name env) (if (null? env) (error "unbound variable: " name) (let ((binding (tableget (car env) name))) (if (null? binding) (lookup name (cdr env)) (bindingvalue 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 (evaldefine exp env) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! (car env) name (eval definedtobe 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 (tagcheck e sym) (and (pair? e) (eq? (car e) sym))) (define (sum? e) (tagcheck e ')) ((sum? exp) (evalsum exp)) (define (evalsum exp) (+ (eval (cadr exp)) (eval (caddr exp)))) (eval '( ( )))
9 Names (define (define? exp) (tagcheck exp 'define*)) ((sum? exp) (evalsum exp)) ((? exp) (lookup exp)) ((define? exp) (evaldefine exp)) ; variation on table ADT from March lecture (only difference is ; that tableget returns a binding, while original version ; returned a value): ; maketable void > table ; tableget table, > (binding null) ; tableput! table,, anytype > undef ; bindingvalue binding > anytype (define environment (maketable)) (define (lookup name) (let ((binding (tableget environment name))) (if (null? binding) (error "unbound variable: " name) (bindingvalue binding)))) (define (evaldefine exp) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! environment name (eval definedtobe)) 'undefined)) (eval '(define* x* ( ))) (eval '( x* )) ; Index to procedures that have not changed: ; procedure page line ; sum? ; evalsum
10 Conditionals and if (define (greater? exp) (tagcheck exp 'greater*)) (define (if? exp) (tagcheck exp 'if*)) ((sum? exp) (evalsum exp)) ((? exp) (lookup exp)) ((define? exp) (evaldefine exp)) ((greater? exp) (evalgreater exp)) ((if? exp) (evalif exp)) (define (evalgreater exp) (> (eval (cadr exp)) (eval (caddr exp)))) (define (evalif 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? ; evalsum ; lookup ; define? ; evaldefine
11 Store operators in the environment (define (application? e) (pair? e)) ((? exp) (lookup exp)) ((define? exp) (evaldefine exp)) ((if? exp) (evalif exp)) ((application? exp) (apply (eval (car exp)) (map eval (cdr exp)))) ;; rename scheme s apply so we can reuse the name (define schemeapply apply) (define (apply operator operands) (if (primitive? operator) (schemeapply (getschemeprocedure operator) operands) (error "operator not a procedure: " operator))) ;; primitive: an ADT that stores scheme procedures (define primtag 'primitive) (define (makeprimitive schemeproc)(list primtag schemeproc)) (define (primitive? e) (tagcheck e primtag)) (define (getschemeprocedure prim) (cadr prim)) (define environment (maketable)) (tableput! environment ' (makeprimitive +)) (tableput! environment 'greater* (makeprimitive >)) (tableput! environment 'true* #t) (eval '(define* z* )) (eval '( )) (eval '(if* true* 0 )) ; Index to procedures that have not changed: ; procedure evaluator line ; lookup ; define? ; evaldefine ; if? ; evalif 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) (evaldefine exp env)) ((if? exp) (evalif exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (lookup name env) (let ((binding (tableget env name))) (if (null? binding) (error "unbound variable: " name) (bindingvalue binding)))) (define (evaldefine exp env) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! env name (eval definedtobe env)) 'undefined)) (define (evalif 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) (tagcheck e 'lambda*)) (define (eval exp env) ((? exp) (lookup exp env)) ((define? exp) (evaldefine exp env)) ((if? exp) (evalif exp env)) ((lambda? exp) (evallambda exp env)) ((application? exp) (apply (eval (car exp) env) (map (lambda (e) (eval e env)) (cdr exp)))) (define (evallambda exp env) (let ((args (cadr exp)) (body (caddr exp))) (makecompound args body env))) (define (apply operator operands) ((primitive? operator) (schemeapply (getschemeprocedure operator) operands)) ((compound? operator) (eval (body operator) (extendenvwithnewframe (parameters operator) operands (env operator)))) (error "operator not a procedure: " operator)))) ;; ADT that implements the double bubble (define compoundtag 'compound) (define (makecompound parameters body env) (list compoundtag parameters body env)) (define (compound? exp) (tagcheck exp compoundtag)) (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 (extendenvwithnewframe names values env) (let ((newframe (maketable))) (makebindings! names values newframe) (cons newframe env))) (define (makebindings! names values table) (foreach (lambda (name value) (tableput! table name value)) names values)) ; the initial global environment (define GE (extendenvwithnewframe (list ' 'greater*) (list (makeprimitive +) (makeprimitive >)) nil)) ; lookup searches the list of frames for the first match (define (lookup name env) (if (null? env) (error "unbound variable: " name) (let ((binding (tableget (car env) name))) (if (null? binding) (lookup name (cdr env)) (bindingvalue binding))))) ; define changes the first frame in the environment (define (evaldefine exp env) (let ((name (cadr exp)) (definedtobe (caddr exp))) (tableput! (car env) name (eval definedtobe 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? evali
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