Interpreters

1
Interpreters

• Study Semantics of Programming Languages through
  interpreters
• (Executable Specifications)

2
Interpreters

• Input
• Representation of a program (AST)
• Output
• Meaning of the program
• Interpreter vs Compiler
• Interpreter carries out the meaning of a
  program, while a compiler transforms a program in
  one language into a program in a lower-level
  language preserving the meaning.

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Simple Expression Language

• ltprogramgt ltexpressiongt
• ltexpressiongt ltnumbergt
• ltidentifiergt
• ltprimitivegt ltoperandsgt
• ltoperandsgt ()
• (ltexpressiongt
• ,ltexpressiongt)
• ltprimitivegt - add1 sub1
• E.g., 5
• add1((3,j))

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Informal Semanics

• Number
• same as what Scheme associates with numerals.
• (internal to the entity)
• Symbolic names
• value bound to it in the environment
• (external to the entity)
• Application expression
• recursively evaluate operator and operands.
• primitive operators interpreted by Scheme.

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Example (Petite Scheme)

• gt (just-scan "add1((1,3))")
• ((literal-string28 "add1" 1)
• (literal-string28 "(" 1)
• (literal-string28 "" 1)
• (literal-string28 "(" 1)
• (number 1 1)
• (literal-string28 "," 1)
• (number 3 1)
• (literal-string28 ")" 1)
• (literal-string28 ")" 1))

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Example

• gt (scanparse "add1((1,3))")
• (a-program
• (primapp-exp
• (incr-prim)
• ((primapp-exp (add-prim)
• ((lit-exp 1)
• (lit-exp 3))))))
• gt (eval-program
• (scanparse "add1((1,3))"))
• 5

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The Abstract Syntax

• (define-datatype program program?
• (a-program (exp expression?)))
• (define-datatype expression expression?
• (lit-exp (datum number?))
• (var-exp (id symbol?))
• (primapp-exp
• (prim primitive?)
• (rand (list-of expression?))) )
• (define-datatype primitive primitive?
• (add-prim)
• (subtract-prim)
• (mult-prim)
• (incr-prim)
• (decr-prim))

8
The evaluator

• (define eval-program
• (lambda (pgm)
• (cases program pgm
• (a-program (body)
• (eval-expression body (init-env))))))
• (define eval-expression
• (lambda (exp env)
• (cases expression exp
• (lit-exp (datum) datum)
• (var-exp (id) (apply-env env id) )
• (primapp-exp (prim rands)
• (let ((args (eval-rands rands env)))
• (apply-primitive prim args)) ) )))

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(contd)

• (define eval-rands
• (lambda (rands env)
• (map (lambda (x)(eval-rand x env))
• rands)))
• (define eval-rand
• (lambda (rand env)
• (eval-expression rand env)))
• (define eval-rands
• (lambda (rands env)
• (map (lambda (x)
• (eval-expression x env))
• rands)))

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(contd)

• (define apply-primitive
• (lambda (prim args)
• (cases primitive prim
• (add-prim () ( (car args) (cadr args)) )
• (subtract-prim () (- (car args) (cadr
  args)) )
• (mult-prim () ( (car args) (cadr args)) )
• (incr-prim () ( (car args) 1) )
• (decr-prim () (- (car args) 1) ) )))
• (define init-env
• (lambda ()
• (extend-env
• '(i v x) '(1 5 10) (empty-env))))
• . . . Code for environment manipulation . . .

11
Scanner Specification

• (define the-lexical-spec
• '((whitespace (whitespace) skip)
• (comment ("" (arbno (not \newline)))
  skip)
• (identifier
• (letter (arbno (or letter digit "_" "-"
  "?"))) symbol)
• (integer (digit (arbno digit)) number))
• )

12
Parser Specification

• (define the-grammar
• '((program (expression) a-program)
• (expression (integer) lit-exp)
• (expression (identifier) var-exp)
• (expression
• (primitive "(" (separated-list expression
  ",") ")")
• primapp-exp)
• (primitive ("") add-prim)
• (primitive ("-") subtract-prim)
• (primitive ("") mult-prim)
• (primitive ("add1") incr-prim)
• (primitive ("sub1") decr-prim))
• )

13
Example (Dr. Racket)

• gt (scanparse "-(v,x)")
• (structa-program
• (structprimapp-exp
• (structsubtract-prim)
• ( (structvar-exp v)
• (structvar-exp x) )
• ) )
• gt (eval-program
• (scanparse "-(v,x)"))
• -5
• Recall that v 5 and x 10 in init-env.

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Adding conditional

• Concrete Syntax
• ltexpressiongt if ltexpressiongt
• then ltexpressiongt else ltexpressiongt
• Abstract Syntax
• if-exp (test-exp true-exp false-exp)
• Addl. Semantic Function
• (define (true-value? x)
• (not (zero? x)) )

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• Addl. Interpreter Clause
• (if-exp (test-exp true-exp false-exp)
• (if (true-value?
• (eval-expression test-exp env))
• (eval-expression true-exp env)
• (eval-expression false-exp env)) )
  
• Defined language vs Defining language
• Inductively defined data structure naturally
  leads to recursively defined function.

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Scanner Details

• gt (just-scan "if while -
• Abc
• Def
• pqr")
• ((literal-string45 "if" 1)
• (identifier while 1)
• (literal-string45 "-" 1)
• (identifier Abc 2)
• (identifier Def 3)
• (literal-string45 "" 4))

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Local Bindings Issues
x 5

• let x 5
• in let y 6 x
• in x y
• Sub-expressions may be evaluated in different
  contexts/environments.
• let x 5
• in let x 6 x
• in x x
• Inner x shadows outer x in nested let-body.

x 5 y11
x 5
x 11
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• let x 5
• in let x 6 x
• in x x
• x
• Introducing let requires passing relevant
  environment to the evaluator.
• Inner binding hides the outer one in case of
  redefinion. (Example Expression Value 110)

x 5
x 5 x 11
x 5
19
Adding let

• Concrete Syntax
• ltexpressiongt
• let ltidentifiergt
• ltexpressiongt
• in ltexpressiongt
• Abstract Syntax
• let-exp (ids rands body)

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Introducing if and let expressions

• (define-datatype expression expression?
• . . .
• (if-exp
• (test-exp expression?)
• (true-exp expression?)
• (false-exp expression?))
• (let-exp
• (ids (list-of symbol?))
• (rands (list-of expression?))
• (body expression?) )
• )

21
Introducing if and let into the evaluator

• (define eval-expression
• (lambda (exp env)
• (cases expression exp
• . . .
• (if-exp (test-exp true-exp false-exp)
• (if (true-value? (eval-expression
  test-exp env))
• (eval-expression true-exp env)
• (eval-expression false-exp env)) )
• (let-exp (ids rands body)
• (let ((args (eval-rands rands env)))
• (eval-expression body (extend-env ids
  args env))
• ) )
• (else (eoplerror 'eval-expression "Not
  heres" exp))
• )))

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Recapitulation
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Polynomial Calculators

• To specify/design a programmable polynomial
  calculator, the object language must contain
  syntax for creating and manipulating polynomials,
  and
• the meta-language (Scheme) must provide suitable
  semantic structure
• to map variables to polynomials (environment).
• to interpret operations on polynomials (using
  corresponding Scheme code).
• Meta-language support is analogous to hardware
  support.
• The semantics of the ADT Polynomials can be
  specified through algebraic techniques.