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#lang racket
; Do programming.rkt dodajemy instrukcje
(provide eval-while parse-while env-empty env-lookup)
;;; We współpracy z Kacprem Soleckim
; --------- ;
; Wyrazenia ;
; --------- ;
(struct const (val) #:transparent)
(struct binop (op l r) #:transparent)
(struct var-expr (id) #:transparent)
(struct let-expr (id e1 e2) #:transparent)
(struct letrec-expr (id e1 e2) #:transparent)
(struct if-expr (eb et ef) #:transparent)
(struct cons-expr (e1 e2) #:transparent)
(struct car-expr (e) #:transparent)
(struct cdr-expr (e) #:transparent)
(struct null-expr () #:transparent)
(struct null?-expr (e) #:transparent)
(struct app (f e) #:transparent)
(struct lam (id e) #:transparent)
(define (expr? e)
(match e
[(const n) (or (number? n) (boolean? n) (string? n))]
[(binop op l r) (and (symbol? op) (expr? l) (expr? r))]
[(var-expr x) (symbol? x)]
[(let-expr x e1 e2)
(and (symbol? x) (expr? e1) (expr? e2))]
[(letrec-expr x e1 e2)
(and (symbol? x) (expr? e1) (expr? e2))]
[(if-expr eb et ef)
(and (expr? eb) (expr? et) (expr? ef))]
[(cons-expr e1 e2) (and (expr? e1) (expr? e2))]
[(car-expr e) (expr? e)]
[(cdr-expr e) (expr? e)]
[(null-expr) true]
[(null?-expr e) (expr? e)]
[(app f e) (and (expr? f) (expr? e))]
[(lam id e) (and (symbol? id) (expr? e))]
[_ false]))
(define (parse q)
(cond
[(number? q) (const q)]
[(eq? q 'true) (const true)]
[(eq? q 'false) (const false)]
[(eq? q 'null) (null-expr)]
[(string? q) (const q)]
[(symbol? q) (var-expr q)]
[(and (list? q) (eq? (length q) 2) (eq? (first q) 'null?))
(null?-expr (parse (second q)))]
[(and (list? q) (eq? (length q) 3) (eq? (first q) 'cons))
(cons-expr (parse (second q))
(parse (third q)))]
[(and (list? q) (eq? (length q) 2) (eq? (first q) 'car))
(car-expr (parse (second q)))]
[(and (list? q) (eq? (length q) 2) (eq? (first q) 'cdr))
(cdr-expr (parse (second q)))]
[(and (list? q) (eq? (length q) 3) (eq? (first q) 'let))
(let-expr (first (second q))
(parse (second (second q)))
(parse (third q)))]
[(and (list? q) (eq? (length q) 3) (eq? (first q) 'letrec))
(letrec-expr (first (second q))
(parse (second (second q)))
(parse (third q)))]
[(and (list? q) (eq? (length q) 4) (eq? (first q) 'if))
(if-expr (parse (second q))
(parse (third q))
(parse (fourth q)))]
[(and (list? q) (eq? (length q) 3) (eq? (first q) 'lambda))
(parse-lam (second q) (third q))]
[(and (list? q) (pair? q) (not (op->proc (car q))))
(parse-app q)]
[(and (list? q) (eq? (length q) 3) (symbol? (first q)))
(binop (first q)
(parse (second q))
(parse (third q)))]))
(define (parse-app q)
(define (parse-app-accum q acc)
(cond [(= 1 (length q)) (app acc (parse (car q)))]
[else (parse-app-accum (cdr q) (app acc (parse (car q))))]))
(parse-app-accum (cdr q) (parse (car q))))
(define (parse-lam pat e)
(cond [(= 1 (length pat))
(lam (car pat) (parse e))]
[else
(lam (car pat) (parse-lam (cdr pat) e))]))
; ---------- ;
; Srodowiska ;
; ---------- ;
(struct blackhole () #:transparent)
(struct environ (xs) #:transparent)
(define env-empty (environ null))
(define (env-add x v env)
(environ (cons (mcons x v) (environ-xs env))))
(define (env-lookup x env)
(define (assoc-lookup xs)
(cond [(null? xs) (error "Unknown identifier" x)]
[(eq? x (mcar (car xs)))
(match (mcdr (car xs))
[(blackhole) (error "Stuck forever in a black hole!")]
[x x])]
[else (assoc-lookup (cdr xs))]))
(assoc-lookup (environ-xs env)))
(define (env-update! x v xs)
(define (assoc-update! xs)
(cond [(null? xs) (error "Unknown identifier" x)]
[(eq? x (mcar (car xs))) (set-mcdr! (car xs) v)]
[else (env-update! x v (cdr xs))]))
(assoc-update! (environ-xs xs)))
(define (env-update x v xs) ; <---------------------------------- !!!
(define (assoc-update xs)
(cond [(null? xs) (list (mcons x v))]
[(eq? x (mcar (car xs))) (cons (mcons x v) (cdr xs))]
[else (cons (car xs) (assoc-update (cdr xs)))]))
(environ (assoc-update (environ-xs xs))))
; --------- ;
; Ewaluacja ;
; --------- ;
(struct clo (id e env) #:transparent)
(struct let-var (v) #:transparent)
(define (value? v)
(or (number? v)
(boolean? v)
(string? v)
(and (pair? v) (value? (car v)) (value? (cdr v)))
(null? v)
(clo? v)
(blackhole? v)))
(define (op->proc op)
(match op ['+ +] ['- -] ['* *] ['/ /] ['% modulo]
['= =] ['> >] ['>= >=] ['< <] ['<= <=]
['and (lambda (x y) (and x y))]
['or (lambda (x y) (or x y))]
['eq? eq?]
[_ false]))
(define (eval-env e env)
(match e
[(const n) n]
[(binop op l r) ((op->proc op) (eval-env l env)
(eval-env r env))]
[(let-expr x e1 e2)
(eval-env e2 (env-add x (let-var (eval-env e1 env)) env))]
[(letrec-expr x e1 e2)
(let* ([new-env (env-add x (blackhole) env)]
[v (eval-env e1 new-env)])
(begin
(env-update! x v new-env)
(eval-env e2 new-env)))]
[(var-expr x) (let ((f (env-lookup x env)))
(if (let-var? f) (let-var-v f) f))]
[(if-expr eb et ef) (if (eval-env eb env)
(eval-env et env)
(eval-env ef env))]
[(cons-expr e1 e2) (cons (eval-env e1 env)
(eval-env e2 env))]
[(car-expr e) (car (eval-env e env))]
[(cdr-expr e) (cdr (eval-env e env))]
[(null-expr) null]
[(null?-expr e) (null? (eval-env e env))]
[(lam x e) (clo x e env)]
[(app f e)
(let ([vf (eval-env f env)]
[ve (eval-env e env)])
(match vf [(clo x body fun-env)
(eval-env body (env-add x ve (merge-let-vars env fun-env)))]))]))
(define (merge-let-vars env1 env2)
(define (iter xs env)
(if (null? xs)
env
(let ((cur-var (car xs)))
(if (let-var? (mcdr cur-var))
(iter (cdr xs) (env-add (mcar cur-var) (mcdr cur-var) env))
(iter (cdr xs) env)))))
(iter (reverse (environ-xs env2)) env1))
(define (eval e) (eval-env e env-empty))
; ---------------------------------------------------------------- !!!
(struct skip () #:transparent)
(struct assign (x e) #:transparent)
(struct if-cmd (eb ct cf) #:transparent)
(struct while (eb cb) #:transparent)
(struct comp (c1 c2) #:transparent)
(define (cmd? c)
(match c
[(skip) true]
[(assign x e) (and (symbol? x) (expr? e))]
[(if-cmd eb ct cf) (and (expr? eb) (cmd? ct) (cmd? cf))]
[(while eb ct) (and (expr? eb) (cmd? ct))]
[else false]))
(define (parse-while q)
(cond
[(eq? q 'skip) (skip)]
[(null? q) (skip)]
[(and (list? q) (= (length q) 3) (eq? (second q) ':=))
(assign (first q)
(parse (third q)))]
[(and (list? q) (= (length q) 4) (eq? (car q) 'if))
(if-cmd (parse (second q))
(parse-while (third q))
(parse-while (fourth q)))]
[(and (list? q) (= (length q) 3) (eq? (car q) 'while))
(while (parse (second q))
(parse-while (third q)))]
[(and (list? q) (= (length q) 2))
(comp (parse-while (first q))
(parse-while (second q)))]
[(and (list? q) (> (length q) 2))
(comp (parse-while (first q))
(parse-while (cdr q)))]
[else (error "while parse error")]))
(define (eval-while e env)
(match e
[(skip) env]
[(assign x e)
(env-update x (eval-env e env) env)]
[(if-cmd eb ct cf)
(if (eval-env eb env)
(eval-while ct env)
(eval-while cf env))]
[(while eb cb)
(if (eval-env eb env)
(eval-while e (eval-while cb env))
env)]
[(comp c1 c2) (eval-while c2 (eval-while c1 env))]))
; zakladamy, ze program startuje z pamiecia w ktorej
; aktwna jest zmienna t
(define WHILE_FACT
'{(i := 1)
(while (> t 0)
{(i := (* i t))
(t := (- t 1))})})
(define (fact n)
(let* ([init-env (env-add 't n env-empty)]
[final-env
(eval-while (parse-while WHILE_FACT) init-env)])
(env-lookup 'i final-env)))
(define prog1 '{(x := 5)
(f := (let [x 50] (lambda (y) (+ x y))))
(x := 10)
(z := (f 0))})
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