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4.2 Type Checking. Recall type of if statement:. (type-of-expression << test-exp >> tenv ) = bool (type-of-expression << true-exp >> tenv ) = x (type-of-expression << false-exp >> tenv ) = x. ( type-of-expression if << test-exp then true-exp else false-exp >>

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4 2 type checking
4.2 Type Checking
  • Recall type of if statement:

(type-of-expression <> tenv) = bool

(type-of-expression <> tenv) = x

(type-of-expression <> tenv) = x

(type-of-expression

if <>

tenv) = x

4 2 type checking1
4.2 Type Checking
  • Will want to check the type of all expressions.
  • Some expressions (proc, let/letrec) will need to declare types.
  • Others (if, application) will know about types from sub-expressions.
  • Language of this chapter is functional, not OO.
slide3
Recall grammar for type declarations:

::= int

int-type-exp ()

::= bool

bool-type-exp ()

::= ({}*(*)-> )

proc-type-exp (arg-texps result-texp)

e.g.,(int*int) -> bool

  • Now can write grammar for typed language:
grammar for typed language
Grammar for Typed Language

::= true

true-exp

::= false

false-exp

::= proc ({ }*(,))

proc-exp (arg-texps ids body)

grammar for typed language1
Grammar for Typed Language

::= letrec

{

({ }*(,))= }*

in

letrec-exp

(result-texps proc-names

arg-texpss idss bodies

letrec-body)

grammar for typed language2
Grammar for Typed Language
  • Examples:

(1) proc (int x) add1(x)

(2) letrec

int fact (int x) =

if zero?(x) then 1

else *(x, (fact sub1(x)))

in (fact 3)

  • Q: Why don't we need to say int proc in (1) ?
data structures for typed language
Data Structures for Typed Language
  • Need a data structure for types.
  • Recall that types are either primitives (int, bool)
  • or procedures/functions over types: int->bool

(define-datatype type type?

(atomic-type

(name symbol?)) ; int, bool, ...

(proc-type

(arg-types (list-of type?))

(result-type type?)))

slide8
Now can define as many primitive types as we like:

(define int-type (atomic-type 'int))

(define bool-type (atomic-type 'bool))

  • Checking type equality can be done using equal?

(define check-equal-type!

(lambda (t1 t2)

(if (not (equal? t1 t2))

(eopl:error ...))))

  • Q: why ! in check-equal-type!
  • Now can write type-of-expression :
slide9
(define type-of-expression

(lambda (exp tenv)

(cases expression exp

(lit-exp (number) int-type)

(true-exp () bool-type)

(false-exp () bool-type)

(var-exp (id) (apply-tenv tenv id))

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