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project.rkt
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project.rkt
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;; PL Project - Fall 2020
;; NUMEX interpreter
#lang racket
(provide (all-defined-out)) ;; so we can put tests in a second file
;; definition of structures for NUMEX programs
(struct var (string) #:transparent) ;; a variable, e.g., (var "foo")
(struct num (int) #:transparent) ;; a constant number, e.g., (num 17)
(struct bool (boolean) #:transparent) ;; a boolean variable, e.g, (#t or #f)
(struct minus (e1 e2) #:transparent) ;; subtract two numex num
(struct mult (e1 e2) #:transparent) ;; multiply two numex num
(struct div (e1 e2) #:transparent) ;; divide two numex num
(struct plus (e1 e2) #:transparent) ;; add two numex num
(struct neg (e1) #:transparent) ;; negate a numex num or bool
(struct andalso (e1 e2) #:transparent) ;; logical and two numex bool
(struct orelse (e1 e2) #:transparent) ;; logical or two numex bool
(struct cnd (e1 e2 e3) #:transparent) ;; condition, if e1 then e2 else e3
(struct iseq (e1 e2) #:transparent) ;; check equality
(struct ifnzero (e1 e2 e3) #:transparent) ;; if e1 is zero then e2 else e3
(struct ifleq (e1 e2 e3 e4) #:transparent) ;; if e1 < e2 then e3 else e4
(struct lam (s1 s2 e) #:transparent) ;; a recursive(?) 1-argument function
(struct lam2 (s1 s2 s3 e)#:transparent) ;; a 2-argument function
(struct apply (e1 e2) #:transparent) ;; function application
(struct with (s e1 e2) #:transparent) ;; let e1 be s in e2
(struct apair (e1 e2) #:transparent) ;; a pair of two expressions
(struct 1st (e1) #:transparent) ;; first element of pair
(struct 2nd (e1) #:transparent) ;; second element of pair
(struct munit () #:transparent) ;; unit value -- good for ending a list
(struct ismunit (e) #:transparent) ;; if e1 is unit then true else false
(struct key (s e) #:transparent) ;; key holds corresponding value of s which is e
(struct record (k r) #:transparent) ;; record/munit holds several keys
(struct value (s r) #:transparent) ;; value returns corresponding value of s in r
;; a closure is not in "source" programs; it is what functions evaluate to
(struct closure (env f) #:transparent)
(struct letrec (s1 e1 s2 e2 s3 e3 s4 e4 e5) #:transparent) ;; a letrec expression for recursive definitions
;; Problem 1
(define (racketlist->numexlist xs) (cond [(null? xs) (munit)]
[#t (apair (car xs) (racketlist->numexlist (cdr xs)))]
)
)
(define (numexlist->racketlist xs) (cond [(munit? xs) null]
[#t (cons (apair-e1 xs) (numexlist->racketlist (apair-e2 xs)))]
)
)
;; Problem 2
;; lookup a variable in an environment
;; an environment is a racket list of racket pairs
;; Complete this function
(define (envlookup env str)
(cond [(null? env) (error "unbound variable during evaluation" str)]
[(equal? (car (car env)) str) (cdr (car env))]
[#t (envlookup (cdr env) str)]
)
)
;; Complete more cases for other kinds of NUMEX expressions.
;; We will test eval-under-env by calling it directly even though
;; "in real life" it would be a helper function of eval-exp.
(define (eval-under-env e env)
(cond
;; DATA TYPES
[(var? e)
(if (string? (var-string e))
(envlookup env (var-string e))
(error "NUMEX var should be string")
)
]
[(num? e)
(if (integer? (num-int e))
(num (num-int e))
(error "NUMEX num should be an integer")
)
]
[(bool? e)
(if (boolean? (bool-boolean e))
(bool (bool-boolean e))
(error "NUMEX bool should be a boolean")
)
]
[(apair? e)
(let (
[v1 (eval-under-env (apair-e1 e) env)]
[v2 (eval-under-env (apair-e2 e) env)]
)
(apair v1 v2)
)]
[(key? e)
(let (
[v1 (eval-under-env (key-e e) env)]
)
(if (string? (key-s e))
(key (key-s e) v1)
(error "NUMEX first arg should be a string")
)
)]
[(record? e)
(let (
[v1 (eval-under-env (record-k e) env)]
[v2 (eval-under-env (record-r e) env)]
)
(cond
[(and (key? v1) (munit? v2)) (record v1 v2)]
[(and (key? v1) (record? v2)) (record v1 v2)]
[#t (error "NUMEX first arg should be key second munit or record")]
)
)]
[(lam? e) (closure env e)]
[(lam2? e) (lam2 (lam2-s1 e) (lam2-s2 e) (lam2-s3 e) (lam2-e e))]
[(closure? e)
(closure (closure-env e) (closure-f e))
]
[(munit? e) (munit)]
;; LOGICAL, ARITHMETIC AND LIST OPERATIONS
[(plus? e)
(let (
[v1 (eval-under-env (plus-e1 e) env)]
[v2 (eval-under-env (plus-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (+ (num-int v1) (num-int v2)))
(error "NUMEX addition applied to non-number")
)
)
]
[(minus? e)
(let (
[v1 (eval-under-env (minus-e1 e) env)]
[v2 (eval-under-env (minus-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (- (num-int v1) (num-int v2)))
(error "NUMEX subtraction applied to non-number")
)
)
]
[(mult? e)
(let (
[v1 (eval-under-env (mult-e1 e) env)]
[v2 (eval-under-env (mult-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (* (num-int v1) (num-int v2)))
(error "NUMEX multiplication applied to non-number")
)
)
]
[(div? e)
(let (
[v1 (eval-under-env (div-e1 e) env)]
[v2 (eval-under-env (div-e2 e) env)]
)
(if (and (num? v1) (num? v2) (ifnzero v2 #t #f))
(num (quotient (num-int v1) (num-int v2)))
(error "NUMEX division applied to non-number or e2 is zero")
)
)
]
[(andalso? e)
(let (
[v1 (eval-under-env (andalso-e1 e) env)]
)
(cond [(bool? v1) (if (eq? (bool-boolean v1) #f)
(bool #f)
(eval-under-env (andalso-e2 e) env)
)
]
[#t (error "NUMEX andalso applied to non-bool")]
)
)
]
[(orelse? e)
(let (
[v1 (eval-under-env (orelse-e1 e) env)]
)
(cond [(bool? v1) (if (eq? (bool-boolean v1) #t) (bool #t) (eval-under-env (orelse-e2 e) env))]
[#t (error "NUMEX orelse applied to non-bool")]
)
)
]
[(neg? e)
(let (
[v1 (eval-under-env (neg-e1 e) env)]
)
(cond
[(num? v1) (num (- (num-int v1)))]
[(bool? v1) (bool (not (bool-boolean v1)))]
[#t (error "NUMEX neg applied to non-num and non-bool")]
)
)
]
[(1st? e)
(let (
[v1 (eval-under-env (1st-e1 e) env)]
)
(cond
[(apair? v1) (eval-under-env (apair-e1 v1) env)]
[#t (error "NUMEX first arg should be apair")]
)
)]
[(2nd? e)
(let (
[v1 (eval-under-env (2nd-e1 e) env)]
)
(cond
[(apair? v1) (eval-under-env (apair-e2 v1) env)]
[#t (error "NUMEX second arg should be apair")]
)
)]
;; CONDITIONS
[(cnd? e)
(let (
[v1 (eval-under-env (cnd-e1 e) env)]
)
(if (bool? v1)
(cond
[(bool-boolean v1) (eval-under-env (cnd-e2 e) env)]
[#t (eval-under-env (cnd-e3 e) env)]
)
(error "NUMEX cnd should have bool for first arg")
)
)
]
[(iseq? e)
(let (
[v1 (eval-under-env (iseq-e1 e) env)]
[v2 (eval-under-env (iseq-e2 e) env)]
)
(cond [(and (num? v1) (num? v2))
(cond
[(equal? (num-int v1) (num-int v2)) (bool #t)]
[#t (bool #f)]
)
]
[(and (bool? v1) (bool? v2))
(cond
[(equal? (bool-boolean v1) (bool-boolean v2)) (bool #t)]
[#t (bool #f)]
)
]
[(or (and (bool? v1) (num? v2)) (and (num? v1) (bool? v2))) (bool #f)]
[#t (error "NUMEX iseq args should be bool or num")]
)
)
]
[(ifnzero? e)
(let (
[v1 (eval-under-env (ifnzero-e1 e) env)]
)
(if (num? v1)
(cond
[(eq? (num-int v1) 0) (eval-under-env (ifnzero-e3 e) env)]
[#t (eval-under-env (ifnzero-e2 e) env)]
)
(error "NUMEX ifnzero first arg should be num")
)
)
]
[(ifleq? e)
(let (
[v1 (eval-under-env (ifleq-e1 e) env)]
[v2 (eval-under-env (ifleq-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(cond
[ (or (eq? (num-int v1) (num-int v2)) (< (num-int v1) (num-int v2)))
(eval-under-env (ifleq-e3 e) env)
]
[#t (eval-under-env (ifleq-e4 e) env)]
)
(error "NUMEX e1 and e2 should be numbers")
)
)
]
;; FUNCTIONS
[(with? e)
(let (
[v1 (eval-under-env (with-e1 e) env)]
)
(eval-under-env (with-e2 e) (cons (cons (with-s e) v1) env))
)
]
[(apply? e)
(let ([v (eval-under-env (apply-e2 e) env)]
[v1 (eval-under-env (apply-e1 e) env)])
(if (closure? v1)
(let ([v2 (closure-f v1)])
(if (null? (lam-s1 v2))
(eval-under-env (lam-e v2) (cons (cons (lam-s2 v2) v) (closure-env v1)))
(eval-under-env (lam-e v2) (cons (cons (lam-s1 v2) v1) (cons (cons (lam-s2 v2) v) (closure-env v1))))))
(if (lam? v1)
(eval-under-env (apply v1 (apply-e2 e)) env)
(if (lam2? v1)
(let (
[var1 (eval-under-env (1st v) env)]
[var2 (eval-under-env (2nd v) env)]
)
(eval-under-env (lam2-e v1) (append (list (cons (lam2-s2 v1) var1)
(cons (lam2-s3 v1) var2)
)
env
)
)
)
(error "NUMEX apply must be applied to closure or lam")
)
)
)
)
]
[(letrec? e)
(if (and (string? (letrec-s1 e))
(string? (letrec-s2 e))
(string? (letrec-s3 e))
(string? (letrec-s4 e)))
(eval-under-env (letrec-e5 e) (append (list (cons (letrec-s1 e) (letrec-e1 e))
(cons (letrec-s2 e) (letrec-e2 e))
(cons (letrec-s3 e) (letrec-e3 e))
(cons (letrec-s4 e) (letrec-e4 e))) env))
(error "NUMEX letrec s must be string")
)
]
[(ismunit? e)
(let (
[v1 (eval-under-env (ismunit-e e) env)]
)
(cond
[(munit? v1) (bool #t)]
[#t (bool #f)]
)
)]
[(value? e)
(let (
[v1 (eval-under-env (value-r e) env)]
)
(if (and (string? (value-s e)) (record? v1))
(cond
[(equal? (value-s e) (key-s (record-k v1))) (eval-under-env (key-e (record-k v1)) env)]
[(munit? (record-r v1)) (munit)]
[#t (eval-under-env (value (value-s e) (record-r v1)) env)]
)
(error "NUMEX first arg should be string and second record")
)
)]
[#t (error (format "bad NUMEX expression: ~v" e))]))
;; Do NOT change
(define (eval-exp e)
(eval-under-env e null))
;; Problem 3
(define (ifmunit e1 e2 e3)
(cnd
(ismunit e1) e2 e3
)
)
(define (with* bs e2)
(cond
[(null? bs) e2]
[#t (with (car (car bs))
(cdr (car bs))
(with* (cdr bs) e2)
)
]
)
)
(define (ifneq e1 e2 e3 e4) (cnd (iseq e1 e2) e4 e3))
;; Problem 4
(define numex-filter
(lam null "func" (lam "filter" "list" (cnd (ismunit (var "list"))
(munit)
(cnd
(iseq (apply (var "func") (1st (var "list"))) (num 0) )
(apply (var "filter") (2nd (var "list")))
(apair (apply (var "func") (1st (var "list"))) (apply (var "filter") (2nd (var "list"))))
)
)
)
)
)
(define numex-all-gt
(lam null "i"
(lam "allgt" "list"
(apply
(apply numex-filter (lam "getgt" "x"
(cnd (iseq (var "x") (var "i"))
(num 0)
(ifleq (var "i") (var "x") (var "x") (num 0))
)
)
)
(var "list")
)
)
)
)
;; Challenge Problem
(struct fun-challenge (nameopt formal body freevars) #:transparent) ;; a recursive(?) 1-argument function
;; We will test this function directly, so it must do
;; as described in the assignment
(define (compute-free-vars e)
(car (compute-free-vars-rec e))
)
(define (compute-free-vars-rec e)
(cond
[(var? e) (cons e (set (var-string e)))]
[(bool? e) (cons e (set))]
[(num? e) (cons e (set))]
[(munit? e) (cons e (set))]
[(closure? e) (cons e (set))]
[(munit? e) (cons e (set))]
[(neg? e) (let ([v1 (compute-free-vars-rec (neg-e1 e))])
(cons (neg (car v1)) (cdr v1)))
]
[(1st? e) (let ([v1 (compute-free-vars-rec (1st-e1 e))])
(cons (1st (car v1)) (cdr v1)))
]
[(2nd? e) (let ([v1 (compute-free-vars-rec (2nd-e1 e))])
(cons (2nd (car v1)) (cdr v1)))
]
[(ismunit? e) (let ([v1 (compute-free-vars-rec (ismunit-e e))])
(cons (ismunit (car v1)) (cdr v1)))
]
[(apair? e) (let ([v1 (compute-free-vars-rec (apair-e1 e))]
[v2 (compute-free-vars-rec (apair-e2 e))]
)
(cons (apair (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(plus? e) (let ([v1 (compute-free-vars-rec (plus-e1 e))]
[v2 (compute-free-vars-rec (plus-e2 e))]
)
(cons (plus (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(minus? e) (let ([v1 (compute-free-vars-rec (minus-e1 e))]
[v2 (compute-free-vars-rec (minus-e2 e))]
)
(cons (minus (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(mult? e) (let ([v1 (compute-free-vars-rec (mult-e1 e))]
[v2 (compute-free-vars-rec (mult-e2 e))]
)
(cons (mult (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(div? e) (let ([v1 (compute-free-vars-rec (div-e1 e))]
[v2 (compute-free-vars-rec (div-e2 e))]
)
(cons (div (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(andalso? e) (let ([v1 (compute-free-vars-rec (andalso-e1 e))]
[v2 (compute-free-vars-rec (andalso-e2 e))]
)
(cons (andalso (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(orelse? e) (let ([v1 (compute-free-vars-rec (orelse-e1 e))]
[v2 (compute-free-vars-rec (orelse-e2 e))]
)
(cons (orelse (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(iseq? e) (let ([v1 (compute-free-vars-rec (iseq-e1 e))]
[v2 (compute-free-vars-rec (iseq-e2 e))]
)
(cons (iseq (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(apply? e) (let ([v1 (compute-free-vars-rec (apply-e1 e))]
[v2 (compute-free-vars-rec (apply-e2 e))]
)
(cons (apply (car v1) (car v2))
(set-union (cdr v1) (cdr v2))
))
]
[(cnd? e) (let
([v1 (compute-free-vars-rec (cnd-e1 e))]
[v2 (compute-free-vars-rec (cnd-e2 e))]
[v3 (compute-free-vars-rec (cnd-e3 e))]
)
(cons (cnd (car v1) (car v2) (car v3))
(set-union (cdr v1) (set-union (cdr v2) (cdr v3)))
))
]
[(ifnzero? e) (let
([v1 (compute-free-vars-rec (ifnzero-e1 e))]
[v2 (compute-free-vars-rec (ifnzero-e2 e))]
[v3 (compute-free-vars-rec (ifnzero-e3 e))]
)
(cons (ifnzero (car v1) (car v2) (car v3))
(set-union (cdr v1) (set-union (cdr v2) (cdr v3)))
))
]
[(ifleq? e) (let
([v1 (compute-free-vars-rec (ifleq-e1 e))]
[v2 (compute-free-vars-rec (ifleq-e2 e))]
[v3 (compute-free-vars-rec (ifleq-e3 e))]
[v4 (compute-free-vars-rec (ifleq-e4 e))]
)
(cons (ifleq (car v1) (car v2) (car v3) (car v4))
(set-union (cdr v1) (set-union (cdr v2) (set-union (cdr v3) (cdr v4))))
))
]
[(lam? e) (let
([v1 (compute-free-vars-rec (lam-e e))])
(let
([v2 (set-remove (set-remove (cdr v1) (lam-s2 e)) (lam-s1 e))])
(cons (fun-challenge (lam-s1 e) (lam-s2 e) (lam-e e) v2) v2)
)
)
]
[(with? e)
(let (
[v1 (compute-free-vars-rec (with-e1 e))]
[v2 (compute-free-vars-rec (with-e2 e))]
)
(cons (with (with-s e) (car v1) (car v2))
(set-remove (set-union (cdr v1) (cdr v2)) (with-s e))
)
)
]
[(letrec? e)
(let (
[v1 (compute-free-vars-rec (letrec-e1 e))]
[v2 (compute-free-vars-rec (letrec-e2 e))]
[v3 (compute-free-vars-rec (letrec-e3 e))]
[v4 (compute-free-vars-rec (letrec-e4 e))]
[v5 (compute-free-vars-rec (letrec-e4 e))]
)
(cons (letrec (letrec-s1 e) (car v1) (letrec-s2 e) (car v2) (letrec-s3 e) (car v3) (letrec-s4 e) (car v4) (car v5))
(set-remove
(set-union (cdr v1)
(set-union (cdr v2)
(set-union (cdr v3)
(set-union (cdr v4) (cdr v5))
)
)
)
(set-union (letrec-s1 e)
(set-union (letrec-s2 e)
(set-union (letrec-s3 e)
(letrec-s4 e)
)
)
)
)
)
)
]
[#t error("something bad happened")]
)
)
(define (freevarEnv env freevars)
(cond [(null? env) '()]
[#t (cond
[(set-member? freevars (car (car env))) (cons (car env) (freevarEnv (cdr env) freevars))]
[#t (freevarEnv (cdr env) freevars)]
)
]
)
)
;; Do NOT share code with eval-under-env because that will make grading
;; more difficult, so copy most of your interpreter here and make minor changes
(define (eval-under-env-c e env)
(cond
[(var? e)
(if (string? (var-string e))
(envlookup env (var-string e))
(error "NUMEX var should be string")
)
]
[(num? e)
(if (integer? (num-int e))
(num (num-int e))
(error "NUMEX num should be an integer")
)
]
[(bool? e)
(if (boolean? (bool-boolean e))
(bool (bool-boolean e))
(error "NUMEX bool should be a boolean")
)
]
[(plus? e)
(let (
[v1 (eval-under-env-c (plus-e1 e) env)]
[v2 (eval-under-env-c (plus-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (+ (num-int v1) (num-int v2)))
(error "NUMEX addition applied to non-number")
)
)
]
[(minus? e)
(let (
[v1 (eval-under-env-c (minus-e1 e) env)]
[v2 (eval-under-env-c (minus-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (- (num-int v1) (num-int v2)))
(error "NUMEX subtraction applied to non-number")
)
)
]
[(mult? e)
(let (
[v1 (eval-under-env-c (mult-e1 e) env)]
[v2 (eval-under-env-c (mult-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(num (* (num-int v1) (num-int v2)))
(error "NUMEX multiplication applied to non-number")
)
)
]
[(div? e)
(let (
[v1 (eval-under-env-c (div-e1 e) env)]
[v2 (eval-under-env-c (div-e2 e) env)]
)
(if (and (num? v1) (num? v2) (ifnzero v2 #t #f))
(num (quotient (num-int v1) (num-int v2)))
(error "NUMEX division applied to non-number or e2 is zero")
)
)
]
[(andalso? e)
(let (
[v1 (eval-under-env-c (andalso-e1 e) env)]
[v2 (eval-under-env-c (andalso-e2 e) env)]
)
(if (and (bool? v1) (bool? v2))
(bool (and (bool-boolean v1) (bool-boolean v2)))
(error "NUMEX and also applied to non-bool")
)
)
]
[(orelse? e)
(let (
[v1 (eval-under-env-c (orelse-e1 e) env)]
[v2 (eval-under-env-c (orelse-e2 e) env)]
)
(if (and (bool? v1) (bool? v2))
(bool (or (bool-boolean v1) (bool-boolean v2)))
(error "NUMEX or else applied to non-bool")
)
)
]
[(neg? e)
(let (
[v1 (eval-under-env-c (neg-e1 e) env)]
)
(cond
[(num? v1) (num (- (num-int v1)))]
[(bool? v1) (bool (not (bool-boolean v1)))]
[#t (error "NUMEX neg applied to non-num and non-bool")]
)
)
]
[(cnd? e)
(let (
[v1 (eval-under-env-c (cnd-e1 e) env)]
)
(if (bool? v1)
(cond
[(bool-boolean v1) (eval-under-env-c (cnd-e2 e) env)]
[#t (eval-under-env-c (cnd-e3 e) env)]
)
(error "NUMEX cnd should have bool for first arg")
)
)
]
[(iseq? e)
(let (
[v1 (eval-under-env-c (iseq-e1 e) env)]
[v2 (eval-under-env-c (iseq-e2 e) env)]
)
(cond [(and (num? v1) (num? v2))
(cond
[(equal? (num-int v1) (num-int v2)) (bool #t)]
[#t (bool #f)]
)
]
[(and (bool? v1) (bool? v2))
(cond
[(equal? (bool-boolean v1) (bool-boolean v2)) (bool #t)]
[#t (bool #f)]
)
]
[(or (and (bool? v1) (num? v2)) (and (num? v1) (bool? v2))) (bool #f)]
[#t (error "NUMEX iseq args should be num")]
)
)
]
[(ifnzero? e)
(let (
[v1 (eval-under-env-c (ifnzero-e1 e) env)]
)
(if (num? v1)
(cond
[(eq? (num-int v1) 0) (eval-under-env-c (ifnzero-e3 e) env)]
[#t (eval-under-env-c (ifnzero-e2 e) env)]
)
(error "NUMEX ifnzero first arg should be num")
)
)
]
[(ifleq? e)
(let (
[v1 (eval-under-env-c (ifleq-e1 e) env)]
[v2 (eval-under-env-c (ifleq-e2 e) env)]
)
(if (and (num? v1) (num? v2))
(cond
[ (or (eq? (num-int v1) (num-int v2)) (< (num-int v1) (num-int v2)))
(eval-under-env-c (ifleq-e3 e) env)
]
[#t (eval-under-env-c (ifleq-e4 e) env)]
)
(error "NUMEX e1 and e2 should be numbers")
)
)
]
[(with? e)
(let (
[v1 (eval-under-env-c (with-e1 e) env)]
)
(eval-under-env-c (with-e2 e) (cons (cons (with-s e) v1) env))
)
]
[(fun-challenge? e)
(closure (freevarEnv env (set-remove (fun-challenge-freevars e) (fun-challenge-nameopt e))) e)
]
[(closure? e)
(closure (closure-env e) (closure-f e))
]
[(apply? e)
(let (
[v1 (eval-under-env-c (apply-e1 e) env)]
)
(cond
[(closure? v1) (let (
[v2 (closure-f v1)]
)
(let (
[v3 (eval-under-env-c (apply-e2 e) env)]
)
(eval-under-env-c (lam-e v2)
(cons
(cons (lam-s2 v2) v3)
(cons (cons (lam-s1 v2) v1) (closure-env v1))
)
)
)
)
]
[#t (error "NUMEX aply first arg should be closure")]
)
)
]
[(apair? e)
(let (
[v1 (eval-under-env-c (apair-e1 e) env)]
[v2 (eval-under-env-c (apair-e2 e) env)]
)
(apair v1 v2)
)
]
[(1st? e)
(let (
[v1 (eval-under-env-c (1st-e1 e) env)]
)
(cond
[(apair? v1) (eval-under-env-c (apair-e1 v1) env)]
[#t (error "NUMEX first arg should be apair")]
)
)]
[(2nd? e)
(let (
[v1 (eval-under-env-c (2nd-e1 e) env)]
)
(cond
[(apair? v1) (eval-under-env-c (apair-e2 v1) env)]
[#t (error "NUMEX second arg should be apair")]
)
)]
[(ismunit? e)
(let (
[v1 (eval-under-env-c (ismunit-e e) env)]
)
(cond
[(munit? v1) (bool #t)]
[#t (bool #f)]
)
)]
[(letrec? e)
(if (and (string? (letrec-s1 e))
(string? (letrec-s2 e))
(string? (letrec-s3 e))
(string? (letrec-s4 e)))
(eval-under-env-c (letrec-e5 e) (append (list (cons (letrec-s1 e) (letrec-e1 e))
(cons (letrec-s2 e) (letrec-e2 e))
(cons (letrec-s3 e) (letrec-e3 e))
(cons (letrec-s4 e) (letrec-e4 e))) env))
(error "NUMEX letrec s must be string")
)
]
[(key? e)
(let (
[v1 (eval-under-env-c (key-e e) env)]
)
(if (string? (key-s e))
(key (key-s e) v1)
(error "NUMEX first arg should be a string")
)
)]
[(record? e)
(let (
[v1 (eval-under-env-c (record-k e) env)]
[v2 (eval-under-env-c (record-r e) env)]
)
(cond
[(and (key? v1) (munit? v2)) (record v1 v2)]
[(and (key? v1) (record? v2)) (record v1 v2)]
[#t (error "NUMEX first arg should be key second munit or record")]
)
)]
[(value? e)
(let (
[v1 (eval-under-env-c (value-r e) env)]
)
(if (and (string? (value-s e)) (record? v1))
(cond
[(equal? (value-s e) (key-s (record-k v1))) (eval-under-env-c (key-e (record-k v1)) env)]
[(munit? (record-r v1)) (munit)]
[#t (eval-under-env-c (value (value-s e) (record-r v1)) env)]
)
(error "NUMEX first arg should be string and second record")
)
)]
[(munit? e) (munit)]
[#t (error (format "bad NUMEX expression: ~v" e))])
)
;; Do NOT change this
(define (eval-exp-c e)
(eval-under-env-c (compute-free-vars e) null))
;; SAT with two parameters; checks if a numex expression is satisfiable
(define (sat e)
(if (lam2? e)
(cnd
(iseq (apply e (apair (bool #t) (bool #t))) (bool #t) )
(bool #t)
(cnd
(iseq (apply e (apair (bool #t) (bool #f))) (bool #t) )
(bool #t)
(cnd
(iseq (apply e (apair (bool #f) (bool #t))) (bool #t) )
(bool #t)
(cnd
(iseq (apply e (apair (bool #f) (bool #f))) (bool #t) )
(bool #t)
(bool #f)
)
)
)
)
(error "NUMEX sat should take a lam2")
)
)
(define (pureSat e)
(cnd
(iseq (with "x1" (bool #t) (with "x2" (bool #t) e)) (bool #t) )
(bool #t)
(cnd
(iseq (with "x1" (bool #t) (with "x2" (bool #f) e)) (bool #t) )
(bool #t)
(cnd
(iseq (with "x1" (bool #f) (with "x2" (bool #t) e)) (bool #t) )
(bool #t)
(cnd
(iseq (with "x1" (bool #f) (with "x2" (bool #f) e)) (bool #t) )
(bool #t)
(bool #f)
)
)
)
)
)
(define (listLen e)
(if (apair? e)
(apply (lam "len" "list" (cnd (ismunit (var "list")) (num 0) (plus (num 1) (apply (var "len") (2nd (var "list"))))))
(eval-exp e)
)
(error "NUMEX listLen should take apair")
)
)
(define (listSum e)
(if (apair? e)
(apply (lam "sum" "list" (cnd (ismunit (var "list")) (num 0) (plus (1st(var "list")) (apply (var "sum") (2nd (var "list"))))))
(eval-exp e)
)
(error "NUMEX listSum should take apair")
)
)
;; Averages items of a numex list
(define (listAvg e)
(if (apair? e)
(div (listSum e)
(listLen e)
)
(error "listAvg should take apair")
)
)