Abstract Syntax - PowerPoint Presentation

Slide1

Abstract SyntaxSlide2

Different Levels of Syntax

Lexical syntax

Basic symbols (names, values, operators, etc.)

Concrete syntaxRules for writing expressions, statements, programsInput to compilers/interpretersAbstract syntax“Internal” representationCaptures semantics

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2Slide3

3

Overview

Parse-expression

Unparse-expression

Interpreter

Concrete

Syntax

Abstract

Syntax

Results

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Concrete vs. Abstract Syntax

Expressions with common meaning (should) have the same abstract syntax

.

C: a+b*cAssumes certain operator precedence (why?)Forth: bc*a+ (reverse Polish)

This expression tree represents the

meaning

of expression

Not the same as parse tree (why?)

Does

the value depend on traversal order?

abc

*+ (or is this it?)

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4Slide5

5

Parse tree vs. AST

+

expr

1

2

+

3

expr

expr

(

)

(

)

expr

expr

1

2

+

3

+

expr

expr

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6

Abstract Syntax Tree

More useful representation of syntax tree

Less clutterActual level of detail depends on your designBasis for semantic analysisLater annotated with various informationType informationComputed values

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7

Compilation in a Nutshell

Source code

(character stream)

Lexical analysis

Parsing

Token stream

Abstract syntax tree

(AST)

Semantic Analysis

if (b == 0) a = b;

if

(

b

)

a

=

b

;

0

==

if

==

b

0

=

a

b

if

==

int

b

int

0

=

int

a

lvalue

int

b

boolean

Decorated AST

int

;

;

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λ-expressions

<exp> ::=

<identifier>

| (lambda (<identifier> ) <exp>) | (<exp> <exp>) Compare with Scheme S-expressions.

EOPL3 p52: Lc-exp

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Lc-exp ::=

Identifier

var

-exp (var)(lambda (Identifier) Lc-exp)

lambda-exp (bound-var

body)

(

Lc

-exp

Lc

-exp)app-exp (rator

rand)Abstract syntaxCS784(PM)

9Slide10

EOPL3 Scheme: define-datatype

Syntax definition:

(define-

datatype type-name type-predicate-name {(variant-name {(field

-name predicate)}* )} + )An Example:

(define-

datatype

environment

environment

?

(empty-

env-record) (extended-env-record (syms (list-of symbol?))

(vals (list-of scheme-value?)) (env environment?)))

Data types built by define-datatype may be mutually recursive.CS784(PM)

10Slide11

Syntax Driven Representation

(define-datatype expression expression?

(var-exp

(id symbol?))

(lambda-exp

(id symbol?)

(body expression?))

(app-exp

(rator expression?)

(rand expression?)))

11

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Figure 2.2: (lambda (x) (f (f x)))

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12Slide13

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)) )))CS784(PM)13Slide14

14

DrRacket

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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)) ))))

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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.

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The Environment

Environment:

table of variable-value pairs

Chronologically later var-value pair overridesConstructorsempty-env extend-env Observerapply-envCS784(PM)

17Slide18

The Environment Spec

(empty-

env

) = ∅(apply-env f

var) = f (var)

(extend-

env

var

v

 f] ) = g

,where g(var1 )= v, if var1 = var= f (var

1). otherwisefrom EOPL3 p36CS784(PM)

18Slide19

An Example Env e

(define e

(extend-

env ’d 6 (extend-env

’y 8 (extend-

env

’x 7

(extend-

env

’y 14

(empty-

env))))))e(d)=6, e(x)=7, e(y)=8

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Representing Environment

Many representations are possible

Speedy access

Memory frugalChange in the interface: Syms x Vals(define extend-env (lambda (

syms vals

env

) … ))

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Alt-1: env is a List of Ribs

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left rib: list of variables

right rib: corresponding list of values.

Exercise 2.11 EOPL3 (Ribcage)Slide22

Alt-1: List of Ribs (Ribcage)

(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)))))))

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Alt-2: env

is a Unary Function

(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)

))CS784(PM)

23Slide24

Alt-3: Tagged Records

(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))

(define empty-env

(lambda ()

(empty-env

-record) ))(define extend-

env (lambda (syms vals env) (extended-env-record

syms vals

env)

))

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Alt-3: Tagged records

(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)))))))

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26

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))

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27

(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))

)))

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