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+;; The first three lines of this file were inserted by DrRacket. They record metadata
+;; about the language level of this file in a form that our tools can easily process.
+#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname AA-interp+defs) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
+;; Prog 2 Asg #17: Interpreters, Part 2
+; Andrew Amis
+; Started: 4.25.12
+; Ended: 4.26.12
+; http://fellowhuman.com/gbk/2012/04/17/prog-2-asg-interpreter-with-defs/
+; 17.7.1 through 17.7.4.
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 17.7.1 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+;; An expression is one of...
+;       number
+;       symbol representing a variable
+;       (make-add expression expression)
+;       (make-sub expression expression)
+;       (make-mul expression expression)
+;       (make-div expression expression)
+;       (make-fun symbol expression)
+
+(define-struct add (left right))
+(define-struct sub (left right))
+(define-struct mul (left right))
+(define-struct div (left right))
+(define-struct fun (name expr))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 17.7.2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+
+;; a function (fun) is a struct...
+(define-struct function (name argument body))
+;; where
+; name is a symbol representing the name of the function
+; argument is the name of the argument being passed
+; and body is an expression
+
+; (define (f x) (+ 3 x))
+(define f (make-function 'f 'x (make-add 3 'x)))
+
+; (define (g x) (* 3 x))
+(define g (make-function 'g 'x (make-mul 3 'x)))
+
+; (define (h u) (f (* 2 u)))
+(define h (make-function 'h 'u (make-mul 2 'u)))
+
+; (define (i v) (+ (* v v) (* v v)))
+(define y (make-function 'y 'v (make-mul 'v 'v)))
+
+; (define (k w) (* (h w) (i w)))
+(define k (make-function 'k 'w (make-fun 'y 'w)))
+
+; (define (ident x) x)
+(define ident (make-function 'ident 'x 'x))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 17.7.3 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+;; expr-left : expr -> expr
+; Returns the left hand of an expression
+(define (expr-left expr)
+  (cond
+    [(add? expr) (add-left expr)]
+    [(sub? expr) (sub-left expr)]
+    [(mul? expr) (mul-left expr)]
+    [(div? expr) (div-left expr)]))
+
+(check-expect (expr-left (make-add 1 10)) 1)
+(check-expect (expr-left (make-sub 2 9)) 2)
+(check-expect (expr-left (make-mul 3 8)) 3)
+(check-expect (expr-left (make-div 4 7)) 4)
+
+
+;; expr-right : expr -> expr
+; Returns the right hand of an expression
+(define (expr-right expr)
+  (cond
+    [(add? expr) (add-right expr)]
+    [(sub? expr) (sub-right expr)]
+    [(mul? expr) (mul-right expr)]
+    [(div? expr) (div-right expr)]))
+
+(check-expect (expr-right (make-add 1 10)) 10)
+(check-expect (expr-right (make-sub 2 9)) 9)
+(check-expect (expr-right (make-mul 3 8)) 8)
+(check-expect (expr-right (make-div 4 7)) 7)
+
+(define expr1 (make-add 10 -10))
+(define expr2 (make-add (make-mul 20 3) 33))
+(define expr3 (make-mul 3.14 (make-mul 'r 'r)))
+(define expr4 (make-add (make-mul 9/5 'c) 32))
+(define expr5 (make-add (make-mul 3.14 (make-mul 'o 'o))
+                        (make-mul 3.14 (make-mul 'i 'i))))
+
+;; apply-expr : {expr -> expr} expr -> expr
+; Applies the given function to each side of the expression, returning a new
+; expression
+(define (apply-expr fxn expr)
+  (cond
+    [(number? expr) (fxn expr)]
+    [(symbol? expr) (fxn expr)]
+    [(add? expr) (make-add (fxn (expr-left expr))
+                           (fxn (expr-right expr)))]
+    [(sub? expr) (make-sub (fxn (expr-left expr))
+                           (fxn (expr-right expr)))]
+    [(mul? expr) (make-mul (fxn (expr-left expr))
+                           (fxn (expr-right expr)))]
+    [(div? expr) (make-div (fxn (expr-left expr))
+                           (fxn (expr-right expr)))]
+    [(fun? expr) (make-fun (fun-name expr)
+                           (fxn (fun-expr expr)))]))
+(check-expect (apply-expr add1 1) 2)
+(check-expect (apply-expr symbol? 'a) true) ; Tricksy hobbits
+(check-expect (apply-expr add1 (make-add 1 10)) (make-add 2 11))
+(check-expect (apply-expr add1 (make-sub 2 9)) (make-sub 3 10))
+(check-expect (apply-expr add1 (make-mul 3 8)) (make-mul 4 9))
+(check-expect (apply-expr add1 (make-div 4 7)) (make-div 5 8))
+
+;; subst : symbol number expression -> expression
+; Replaces the given symbol with the given number in the given expression
+(define (subst sym num expr)
+  (cond
+    [(number? expr) expr]
+    [(symbol? expr) (if (symbol=? sym expr)
+                        num
+                        expr)]
+    [(expr? expr) (apply-expr (lambda (expr) (subst sym num expr)) expr)]))
+
+(check-expect (subst 'r 3 expr3) (make-mul 3.14 (make-mul 3 3)))
+(check-expect (subst 'c 10 expr4) (make-add (make-mul 9/5 10) 32))
+(check-expect (subst 'o 5 expr5) (make-add (make-mul 3.14 (make-mul 5 5))
+                                           (make-mul 3.14 (make-mul 'i 'i))))
+(check-expect (subst 'i 2 (subst 'o 5 expr5))
+              (make-add (make-mul 3.14 (make-mul 5 5))
+                        (make-mul 3.14 (make-mul 2 2))))
+
+;; expr? : any -> boolean
+; Determines whether this thing is an expression
+(define (expr? x)
+  (or (number? x)
+      (symbol? x)
+      (add? x)
+      (sub? x)
+      (mul? x)
+      (div? x)
+      (fun? x)))
+(check-expect (expr? 1) true)
+(check-expect (expr? false) false)
+(check-expect (expr? (make-add 1 10)) true)
+(check-expect (expr? (make-sub 2 9)) true)
+(check-expect (expr? (make-mul 3 8)) true)
+(check-expect (expr? (make-div 4 7)) true)
+(check-expect (expr? "test") false)
+(check-expect (expr? 'test) true)
+
+;; evaluate-with-one-def : numeric-expression function -> number
+; Evaluates the given numeric expression.
+(define (evaluate-with-one-def expr fun)
+  (cond
+    [(number? expr) expr]
+    [(symbol? expr) (error "Not a numeric expression")]
+    [(add? expr) (+ (evaluate-with-one-def (expr-left expr) fun)
+                    (evaluate-with-one-def (expr-right expr) fun))]
+    [(sub? expr) (- (evaluate-with-one-def (expr-left expr) fun)
+                    (evaluate-with-one-def (expr-right expr) fun))]
+    [(mul? expr) (* (evaluate-with-one-def (expr-left expr) fun)
+                    (evaluate-with-one-def (expr-right expr) fun))]
+    [(div? expr) (/ (evaluate-with-one-def (expr-left expr) fun)
+                    (evaluate-with-one-def (expr-right expr) fun))]
+    [(fun? expr) (if (symbol=? (function-name fun) (fun-name expr))
+                     (evaluate-with-one-def
+                      (subst (function-argument fun)
+                             (evaluate-with-one-def (fun-expr expr) fun)
+                             (function-body fun))
+                      fun)
+                     (error "Undefined function"))]))
+
+(check-expect (evaluate-with-one-def expr1 ident) 0)
+(check-expect (evaluate-with-one-def expr2 ident) 93)
+(check-expect (evaluate-with-one-def (make-sub 4 1) ident) 3)
+(check-expect (evaluate-with-one-def (make-div 4 2) ident) 2)
+(check-error (evaluate-with-one-def expr3 ident) "Not a numeric expression")
+(check-expect (evaluate-with-one-def (make-fun 'f 3) f) 6)
+(check-error (evaluate-with-one-def (make-fun 'g 3) f) "Undefined function")
+(check-expect (evaluate-with-one-def (make-fun 'y 3) y) 9)
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 17.7.4 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+;; find-first : {X -> boolean} listof[X] -> X
+; Finds the first item in the list for which the function returns true.
+(define (find-first fxn list)
+  (cond
+    [(empty? list) (error "Not found")]
+    [(cons? list)
+     (if (fxn (car list))
+         (car list)
+         (find-first fxn (cdr list)))]))
+
+(check-expect (find-first even? '(5 7 9 3 4)) 4) 
+(check-expect (find-first odd? '(5 7 9 3 4)) 5)
+(check-error (find-first boolean? '(5 7 9 3 4)) "Not found")
+
+;; evaluate-with-defs : expression listof[functions] -> number
+; Evaluates the expression with all the definitions.
+(define (evaluate-with-defs expr functions)
+  (cond
+    [(number? expr) expr]
+    [(symbol? expr) (error "Not a numeric expression")]
+    [(add? expr) (+ (evaluate-with-defs (expr-left expr) fun)
+                    (evaluate-with-defs (expr-right expr) fun))]
+    [(sub? expr) (- (evaluate-with-defs (expr-left expr) fun)
+                    (evaluate-with-defs (expr-right expr) fun))]
+    [(mul? expr) (* (evaluate-with-defs (expr-left expr) fun)
+                    (evaluate-with-defs (expr-right expr) fun))]
+    [(div? expr) (/ (evaluate-with-defs (expr-left expr) fun)
+                    (evaluate-with-defs (expr-right expr) fun))]
+    [(fun? expr) 
+     (let [(fun
+            (find-first {λ (x) (symbol=? (function-name x)
+                                         (fun-name expr))}
+                        functions))]
+       (evaluate-with-defs
+        (subst (function-argument fun)
+               (evaluate-with-defs (fun-expr expr) functions)
+               (function-body fun))
+        functions))]))
+
+(define functions (list f g h y k ident))
+
+(check-expect (evaluate-with-defs expr1 functions) 0)
+(check-expect (evaluate-with-defs expr2 functions) 93)
+(check-expect (evaluate-with-defs (make-sub 4 1) functions) 3)
+(check-expect (evaluate-with-defs (make-div 4 2) functions) 2)
+(check-error (evaluate-with-defs expr3 ident) "Not a numeric expression")
+(check-expect (evaluate-with-defs (make-fun 'f 3) functions) 6)
+(check-expect (evaluate-with-defs (make-fun 'g 3) functions) 9)
+(check-expect (evaluate-with-defs (make-fun 'y 3) functions) 9)
+(check-expect (evaluate-with-defs (make-fun 'k 3) functions) 9)
+(check-error (evaluate-with-defs (make-fun 'does-not-exist 3)
+                                 functions) "Not found")
\ No newline at end of file