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407b1a2 May 26, 2018
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#lang eopl
;; Exercise 7.7 [★] Change the code for checking an if-exp so that if the test expression is not a boolean, the other
;; expressions are not checked. Give an expression for which the new version of the checker behaves differently from the
;; old version.
;; Grammar.
(define the-lexical-spec
'([whitespace (whitespace) skip]
[comment ("%" (arbno (not #\newline))) skip]
[identifier (letter (arbno (or letter digit "_" "-" "?"))) symbol]
[number (digit (arbno digit)) number]
[number ("-" digit (arbno digit)) number]))
(define the-grammar
'([program (expression) a-program]
[expression (number) const-exp]
[expression ("-" "(" expression "," expression ")") diff-exp]
[expression ("zero?" "(" expression ")") zero?-exp]
[expression ("if" expression "then" expression "else" expression) if-exp]
[expression (identifier) var-exp]
[expression ("let" identifier "=" expression "in" expression) let-exp]
[expression ("proc" "(" identifier ":" type ")" expression) proc-exp]
[expression ("(" expression expression ")") call-exp]
[expression ("letrec" type identifier "(" identifier ":" type ")" "=" expression "in" expression) letrec-exp]
[type ("int") int-type]
[type ("bool") bool-type]
[type ("(" type "->" type ")") proc-type]))
(sllgen:make-define-datatypes the-lexical-spec the-grammar)
(define scan&parse (sllgen:make-string-parser the-lexical-spec the-grammar))
;; Data structures - expressed values.
(define-datatype proc proc?
[procedure [bvar symbol?]
[body expression?]
[env environment?]])
(define-datatype expval expval?
[num-val [value number?]]
[bool-val [boolean boolean?]]
[proc-val [proc proc?]])
(define expval-extractor-error
(lambda (variant value)
(eopl:error 'expval-extractors "Looking for a ~s, found ~s" variant value)))
(define expval->num
(lambda (v)
(cases expval v
[num-val (num) num]
[else (expval-extractor-error 'num v)])))
(define expval->bool
(lambda (v)
(cases expval v
[bool-val (bool) bool]
[else (expval-extractor-error 'bool v)])))
(define expval->proc
(lambda (v)
(cases expval v
[proc-val (proc) proc]
[else (expval-extractor-error 'proc v)])))
;; Data structures - environment.
(define-datatype environment environment?
[extend-env [bvar symbol?]
[bval expval?]
[saved-env environment?]]
[extend-env-rec [p-name symbol?]
[b-var symbol?]
[p-body expression?]
[saved-env environment?]])
(define apply-env
(lambda (env search-sym)
(cases environment env
[empty-env () (eopl:error 'apply-env "No binding for ~s" search-sym)]
[extend-env (bvar bval saved-env) (if (eqv? search-sym bvar)
(apply-env saved-env search-sym))]
[extend-env-rec (p-name b-var p-body saved-env) (if (eqv? search-sym p-name)
(proc-val (procedure b-var p-body env))
(apply-env saved-env search-sym))])))
;; Data structures - type environment.
(define-datatype type-environment type-environment?
[extended-tenv-record [sym symbol?]
[type type?]
[tenv type-environment?]])
(define apply-tenv
(lambda (tenv sym)
(cases type-environment tenv
[empty-tenv-record () (eopl:error 'apply-tenv "Unbound variable ~s" sym)]
[extended-tenv-record (sym1 val1 old-env) (if (eqv? sym sym1)
(apply-tenv old-env sym))])))
(define empty-tenv empty-tenv-record)
(define extend-tenv extended-tenv-record)
;; Checker.
(define type-to-external-form
(lambda (ty)
(cases type ty
[int-type () 'int]
[bool-type () 'bool]
[proc-type (arg-type result-type) (list (type-to-external-form arg-type)
(type-to-external-form result-type))])))
(define report-unequal-types
(lambda (ty1 ty2 exp)
(eopl:error 'check-equal-type!
"Types didn't match: ~s != ~a in~%~a"
(type-to-external-form ty1)
(type-to-external-form ty2)
(define check-equal-type!
(lambda (ty1 ty2 exp)
(when (not (equal? ty1 ty2))
(report-unequal-types ty1 ty2 exp))))
(define report-rator-not-a-proc-type
(lambda (rator-type rator)
(eopl:error 'type-of-expression
"Rator not a proc type:~%~s~%had rator type ~s"
(type-to-external-form rator-type))))
(define type-of
(lambda (exp tenv)
(cases expression exp
[const-exp (num) (int-type)]
[var-exp (var) (apply-tenv tenv var)]
[diff-exp (exp1 exp2) (let ([ty1 (type-of exp1 tenv)]
[ty2 (type-of exp2 tenv)])
(check-equal-type! ty1 (int-type) exp1)
(check-equal-type! ty2 (int-type) exp2)
[zero?-exp (exp1) (let ([ty1 (type-of exp1 tenv)])
(check-equal-type! ty1 (int-type) exp1)
[if-exp (exp1 exp2 exp3) (let ([ty1 (type-of exp1 tenv)])
(check-equal-type! ty1 (bool-type) exp1)
(let ([ty2 (type-of exp2 tenv)]
[ty3 (type-of exp3 tenv)])
(check-equal-type! ty2 ty3 exp)
[let-exp (var exp1 body) (let ([exp1-type (type-of exp1 tenv)])
(type-of body (extend-tenv var exp1-type tenv)))]
[proc-exp (var var-type body) (let ([result-type (type-of body (extend-tenv var var-type tenv))])
(proc-type var-type result-type))]
[call-exp (rator rand) (let ([rator-type (type-of rator tenv)]
[rand-type (type-of rand tenv)])
(cases type rator-type
[proc-type (arg-type result-type) (begin (check-equal-type! arg-type rand-type rand)
[else (report-rator-not-a-proc-type rator-type rator)]))]
[letrec-exp (p-result-type p-name b-var b-var-type p-body letrec-body)
(let ([tenv-for-letrec-body (extend-tenv p-name (proc-type b-var-type p-result-type) tenv)])
(let ([p-body-type (type-of p-body (extend-tenv b-var b-var-type tenv-for-letrec-body))])
(check-equal-type! p-body-type p-result-type p-body)
(type-of letrec-body tenv-for-letrec-body)))])))
(define type-of-program
(lambda (pgm)
[cases program pgm (a-program (exp1) (type-of exp1 (empty-tenv)))]))
;; Interpreter.
(define apply-procedure
(lambda (proc1 arg)
(cases proc proc1
[procedure (var body saved-env) (value-of body (extend-env var arg saved-env))])))
(define value-of
(lambda (exp env)
(cases expression exp
[const-exp (num) (num-val num)]
[var-exp (var) (apply-env env var)]
[diff-exp (exp1 exp2) (let ([val1 (expval->num (value-of exp1 env))]
[val2 (expval->num (value-of exp2 env))])
(num-val (- val1 val2)))]
[zero?-exp (exp1) (let ([val1 (expval->num (value-of exp1 env))])
(if (zero? val1)
(bool-val #t)
(bool-val #f)))]
[if-exp (exp0 exp1 exp2) (if (expval->bool (value-of exp0 env))
(value-of exp1 env)
(value-of exp2 env))]
[let-exp (var exp1 body) (let ([val (value-of exp1 env)])
(value-of body (extend-env var val env)))]
[proc-exp (bvar ty body) (proc-val (procedure bvar body env))]
[call-exp (rator rand) (let ([proc (expval->proc (value-of rator env))]
[arg (value-of rand env)])
(apply-procedure proc arg))]
[letrec-exp (ty1 p-name b-var ty2 p-body letrec-body) (value-of letrec-body
(extend-env-rec p-name b-var p-body env))])))
(define value-of-program
(lambda (pgm)
(cases program pgm
[a-program (body) (value-of body (empty-env))])))
;; Interface.
(define check
(lambda (string)
(type-to-external-form (type-of-program (scan&parse string)))))
(define run
(lambda (string)
(value-of-program (scan&parse string))))
(provide check num-val run)