;; The first three lines of this file were inserted by DrScheme. 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 applying_functions) (read-case-sensitive #t) (teachpacks ((lib "testing.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "testing.ss" "teachpack" "htdp")))))
;; the structure represents a student
;; name is a symbol, 
;; year-birth is a positive integer,
;; GPA is a non-negative real number <= 4.0 
(define-struct ummstudent (name year-birth GPA))

;; Template:
;;(ummstudent-name student) ....
;;(ummstudent-year-birth student) ....
;;(ummstudent-GPA student) ....

(define JoeSmith
  (make-ummstudent 'JoeSmith 1990 3.45))

(ummstudent-name JoeSmith) 
(ummstudent-year-birth JoeSmith)

(define JaneBrown 
  (make-ummstudent 'JaneBrown 1991 3.25))

;; Contract: ummstudent, ummstudent -> symbol
;; Purpose: the function compares the ages
;; of two students and returns the name of 
;; the one who is older, based on the year of birth
;; If the two students were born in the same year,
;; the function returns a symbol 'BornSameYear
(define (isOlder student1 student2)
  (cond 
    [(= (ummstudent-year-birth student1) (ummstudent-year-birth student2)) 'BornSameYear]
    [(< (ummstudent-year-birth student1) (ummstudent-year-birth student2)) (ummstudent-name student1)]
    [else (ummstudent-name student2)]
  )
)

(check-expect (isOlder JoeSmith JaneBrown) 'JoeSmith)
(check-expect (isOlder JaneBrown JoeSmith) 'JoeSmith)
(check-expect (isOlder JoeSmith JoeSmith)'BornSameYear)


;; Contract: ummstudent -> boolean
;; Purpose: to check whether a given "ummstudent" structure 
;; is well-defined: the name is a symbol, the year 
;; is an integer between 1900 and 2000,
;; the GPA is a number between 0 and 4.0
(define (is-valid student)
  (and 
   (ummstudent? student)
   (symbol? (ummstudent-name student)) ; check name
   (and (integer? (ummstudent-year-birth student)) ; check year-birth
        (<= (ummstudent-year-birth student) 2000)
        (>= (ummstudent-year-birth student) 1900)) 
   (and (real? (ummstudent-GPA student))  ; check GPA
        (<= (ummstudent-GPA student) 4.0)
        (>=  (ummstudent-GPA student) 0.0)
        )
  )
)

(check-expect (is-valid JoeSmith) true)
(check-expect (is-valid (make-ummstudent 5 'TheNineties -3.5)) false)
(check-expect (is-valid (make-ummstudent 'JoeSmith 'TheNineties 3.5)) false)
(check-expect (is-valid (make-ummstudent 'JoeSmith 1990 4.5)) false)

(define students (list JoeSmith JaneBrown (make-ummstudent 'MichaelAnderson 1990 2.95)
                       (make-ummstudent 'KristinJones 1992 3.73)))

;; use predefined functions filter, map, foldl to accomplish the following tasks:

;; create a list of students names (in any order)

;; create a list of students whose GPA is 3.0 or above

;; find the average GPA of all students

;; create a list of only valid student structures of the ones given 

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; use quicksort function to sort the student list by age
;; Can we use isOlder for this? How or why not?

;; using any of the given functions, write a function that finds if any 
;; of the students have GPA below 2.0. This function returns true if there
;; is at least one such student and false otherwise

;; using any of the functions, find out how many students have GPA 
;; 3.0 or above

;; longer exercise: find the standard deviation of the GPAs as defined here:
;; http://en.wikipedia.org/wiki/Standard_deviation#Discrete_random_variable_or_data_set