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a12.rkt
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a12.rkt
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#lang racket
;; Peter Fogg
(require C311/pmatch)
(require C311/monads)
;; 1
(define assv-maybe
(lambda (x l)
(cond
((null? l) (fail))
((eqv? x (car (car l))) `(Just ,(cdr (car l))))
(else (assv-maybe x (cdr l))))))
;; 2
(define partition-writer
(lambda (f l)
(cond
((null? l) (return-writer '()))
((f (car l)) (bind-writer
(tell-writer (car l))
(lambda (_)
(partition-writer f (cdr l)))))
(else (bind-writer
(partition-writer f (cdr l))
(lambda (l^)
(return-writer (cons (car l) l^))))))))
;; 3
(define powerXpartials
(lambda (x n)
(cond
((zero? n) (return-writer 1))
((= n 1) (return-writer x))
((odd? n) (do bind-writer
(res <- (powerXpartials x (sub1 n)))
(tell-writer res)
(return-writer (* x res))))
(else (do bind-writer
(res <- (powerXpartials x (/ n 2)))
(tell-writer res)
(return-writer (* res res)))))))
;; 4
(define abc-game
(lambda (l)
(if (null? l)
(return-state '__)
(do bind-state
(score <- get-state)
(put-state (+ score
(cond
((eqv? 'a (car l)) 1)
((eqv? 'b (car l)) -1)
(else 0))))
(abc-game (cdr l))))))
;; 5
(define traverse
(lambda (return bind f)
(letrec ((trav (lambda (tree)
(cond
((pair? tree)
(do bind
(a <- (trav (car tree)))
(b <- (trav (cdr tree)))
(return (cons a b))))
(else (f tree))))))
trav)))
(define reciprocal
(lambda (n)
(if (zero? n)
'(Nothing)
(return-maybe (/ 1 n)))))
(define traverse-reciprocal
(traverse return-maybe bind-maybe reciprocal))
;; 6
(define halve
(lambda (n)
(if (even? n)
(return-writer (/ n 2))
(bind-writer (tell-writer n)
(lambda (_) (return-writer n))))))
(define traverse-halve
(traverse return-writer bind-writer halve))
;; 7
(define state/sum
(lambda (n)
(do bind-state
(x <- get-state)
(put-state (+ x n))
(return-state x))))
(define traverse-state/sum
(traverse return-state bind-state state/sum))
;; 8
(define apply-env
(lambda (env x)
(env x)))
(define extend-env
(lambda (x a env)
(lambda (y)
(if (eqv? x y)
a
(apply-env env y)))))
(define empty-env
(lambda ()
(lambda (x)
(error "unbound variable" x))))
(define closure
(lambda (x body env)
(lambda (a)
(value-of-cps body (extend-env x a env)))))
(define apply-proc
(lambda (c a)
(c a)))
(define value-of-cps
(lambda (expr env)
(pmatch expr
[`,n (guard (or (number? n) (boolean? n))) (return-cont n)]
[`,x (guard (symbol? x)) (return-cont (apply-env env x))]
[`(* ,x1 ,x2) (do bind-cont
(c1 <- (value-of-cps x1 env))
(c2 <- (value-of-cps x2 env))
(return-cont (* c1 c2)))]
[`(sub1 ,x) (bind-cont (value-of-cps x env)
(lambda (n)
(return-cont (sub1 n))))]
[`(zero? ,x) (bind-cont (value-of-cps x env)
(lambda (n)
(return-cont (zero? n))))]
[`(if ,test ,conseq ,alt) (bind-cont (value-of-cps test env)
(lambda (b)
(if b
(value-of-cps conseq env)
(value-of-cps alt env))))]
[`(capture ,k-id ,body) (callcc (lambda (k)
(value-of-cps body (extend-env k-id k env))))]
[`(return ,v-exp ,k-exp) (do bind-cont
(k <- (value-of-cps k-exp env))
(v <- (value-of-cps v-exp env))
(k v))]
[`(lambda (,id) ,body) (return-cont (closure id body env))]
[`(,rator ,rand) (do bind-cont
(t <- (value-of-cps rator env))
(n <- (value-of-cps rand env))
(apply-proc t n))])))
(define fact-5
'((lambda (f)
((f f) 5))
(lambda (f)
(lambda (n)
(if (zero? n)
1
(* n ((f f) (sub1 n))))))))
(define capture-fun
'(* 3 (capture q (* 2 (return 4 q)))))