;; 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 union-type-intro) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))

(require "student-extras.rkt")
#|
;   Union Types -- intro


;
; - What is the type of (the signature of)...
;     a.  string=? : ...
;     b.  string?  : ...
;
; - What are the steps of the design recipe [complete the 3 lines]
;     ;;; Per-function:
;     4.
;     5.
;     7.
;     8. Watch your tests pass, and celebrate!












   ---- per function:
    4. write tests
    5. stub: signature, purpose-statement, header, stub
    7. complete the function-body
    8. watch your tests pass
|#


; To-model:
; A *course-result* is:
;  - grade,  OR
;  - incomplete,
;  - in-progress,
;  - a planned semester to take it in future

; We say this is a "union type, with 4 variants".

; datatype definition:
(define (course-result? x)
   (or ...          ; interpretation: letter grade
       ...          ; interpretation: Incomplete
       ...          ; interpretation: in-progress
       ...))        ; interpretation: planned-future-semester

; For this class:
; If you say "datatype definition" before a function,
; you DO NOT need purpose-statement nor signature (both clear from knowing it's a datatype-defn),
; nor even unit-tests!
; (though myself, I still include unit tests if there's anything nontrivial,
;  like in this example making sure I got the regexp correct).

; Give several examples of the data.
;









; Template for *any* course which handles a course-result:
; (have a 4-branch cond)
;
(define/contract (func-for-course-result a-cr)
  (-> course-result?  ...?)
  (cond [(real? a-cr)               ...]
        [(equal? a-cr 'incomplete)  ...]
        [(equal? a-cr 'in-progress) ...]
        [(string? a-cr)             ...]))
;
; Btw:
; You might say "shouldn't that first branch check that we have a `real?` *bewteen 0 and 4* ??"
; Or similarly, "shouldn't the last branch check that the string meets the desired pattern?".
; While that wouldn't be wrong, it's not necessary:
; Our signature is already ensuring that `a-cr` really is a valid course-result.
; Once we know that, just asking `real?` or `string?` is enough to know which variant we have.





; Task: write a function to determine if a student can register itec220 (CS2),
; given their course-result from itec120 (CS1).
; Policy: you are allowed to register for itec220 if you got a C or better (2.0),
; or if you're currently-enrolled, or if you have an unresolved-incomplete,
; but not if you're just enrolled in CS1 for *next* semester.














;  Another examples of union types:

; When querying a name in the student-database for their email address,
; the returned answer must be able to represent indicate:
;    - a match (the student's username), OR
;    - no such person is found, OR
;    - the person exists, but information is non-public.
;
; TODO: How should we represent the student-query result?
;
;   (brainstorm, then scroll)











; Datatype definition:
(define (student-query-result? x)
   (or (username? x)          
       (false? x)             ; interpretation: no such person
       (equal? x 'private)))  ; interpretation: info is to be kept private

; Datatype definition:
(define (username? x)    ; interpretation: an RU student's username
  (and (string? x)
       (<= 1 (string-length x) 17)   ; "cmartinezmurillo@"
       (regexp-match? #px"^[a-z]+[0-9]*$" x)))

(check-expect (username? "ibarland") #true)
(check-expect (username? "president") #true)
(check-expect (username? "z") #true)
(check-expect (username? "z9") #true)
(check-expect (username? "9") #false)

(check-expect (username? "bottles99") #true)  ; Ben Ottles  -- one of many
(check-expect (username? "99bottles") #false)
(check-expect (username? "cmartinezmurrillo") #true)
(check-expect (username? "TooLongcmartinezmurrillo") #false)
(check-expect (username? "hi2bye3") #false)
; non-strings
(check-expect (username? 'ibarland) #false)
(check-expect (username? 99) #false)
(check-expect (username? #true) #false)
(check-expect (username? #px"[a-z][a-z][0-9]+") #false)

; TODO: What is the template, for any function processing ...







#|

; Task: Write a function to return the tax-due, given taxable-income.
;  (for single tax-payers; we'll stop after 3 brackets)
;  ($10275 => 10%; $41775 => 12%;  else 22% )
; https://taxfoundation.org/2022-tax-brackets
; see also, 5min on how brackets work: https://www.youtube.com/watch?v=VJhsjUPDulw



; To-model:
; A taxable-income is either:
;  - an amount less than $0       (a "loss"), OR
;  - an amount in [$0, 9875)      (a "modest income"), OR
;  - an amount in [$9875,40125)   (a "middle income"), OR
;  - an amount in [$40125,∞)      (a "high income")
|#


(define LO 10275)
(define MED 41775)
; examples of the data:
  ; TODO IN CLASS



; Datatype Def'n (version 1)
#;(define (taxable-income? val)
    (real? val))
;
; This works, but we're going to be more thorough, and make some specific helpers:

; Datatype Def'ns [see note below]:
(define (income-loss? x)   (< -inf.0 x 0))
(define (income-modest? x) (and (<= 0 x) (< x 10275)))
(define (income-middle? x) (and (<= 10275 x) (< x 41775)))
(define (income-high? x)   (and (<= 41775 x) (< x +inf.0)))
; interpretations: x is an amount *in dollars*.   ; <-- always mention units!


; Now, the one function we really were after:
(define (taxable-income? val)
  (and (real? val)
       (or (income-loss? val)
           (income-modest? val)
           (income-middle? val)
           (income-high? val))))
;
; Okay, this datatype-definition is admittedly overly heavyweight -- I'd be happy with:
; "Datatype definition:   (define taxable-income? real?)"   or even just
; ";We represent taxable-income as a real".
; Both would satisfy Step 1 of the design-recipe.
; Our heavyweight egghead solution does provide a couple of other nice bits though:
;    - the predicate's definition reflects the four variants inherent to taxable-incomes.
;    - we have attached program-names corresponding to the technical terms tax-accountants use ("middle income")
;    - we could naturally use those predicates in our code
; But yeah IRL I'd probably go with `(define taxable-income? real?)`, myself.




; func-for-taxable-income : taxable-income -> ??
;
(define (func-for-taxable-income a-ti)
  ;(-> taxable-income ???)
  ; Return ???
  (cond [... ...]    ; FILL IN HERE
        [... ...]
        [... ...]
        [... ...]))



; TODO: Write a function to return the tax-due, given taxable-income.
 

#| 
; TODO: Step 4: develop test cases:
(check-expect (tax -30) 0)
(check-expect (tax 0) 0)
(check-expect (tax 10) 1)
(check-expect (tax LO) (* LO 0.10))
(check-expect (tax (+ LO 1.00)) (+ (* LO 0.10) 0.12))
(check-expect (tax (+ LO 0.01)) (+ (* LO 0.10) 0.0012))
(check-expect (tax (+ LO 1000)) 'TODO)

(check-expect (tax MED) 'TODO)
(check-expect (tax (+ MED 10000)) 'TODO)
 

(define (tax a-ti)
  ;(-> taxable-income non-negative-real?)
  ; return the tax-due, given taxable-income `a-ti`.
  ; FILL-IN
  -9999.99)


#|
; An alternate implementation, using `let*`:

; tax : number -> number
;  return the tax-due, given taxable-income.
;  (for single tax-payers; we'll stop after 3 tax-tiers)

(define (tax income)
  (cond [(<= income  9950) (* 0.10 income)]
        [(<= income 40525) (+ (* 0.10 9950) (* 0.15 (- income 9950)))]
        [else              (let* {[tier2 (- 40525 9950)]
                                  [excess (- income 40525)]}
                             (+ (* 0.10 9075)
                                (* 0.15 tier2) 
                                (* 0.25 excess)))]))
|#



; Update:
; a taxable-income-ENTRY is either:
;  - 'exempt         (interpretation: income is exempt-- tax-treaty?), OR
;  - #false          (interpretation: no taxes filed!), OR
;  - a real number in (-∞, 0]        (interpretation: a loss), OR
;  - a real number in (0, 9950]      (interpretation: a modest income), OR
;  - a real number in (9950,40525]   (interpretation: a middle income), OR
;  - a real number in (40525,∞)      (interpretation: a high income)
;
; What do you think of *this* data-def'n?


; Examples of the data -- taxable-income-entry:
10000
37000.5
6000
'exempt
#false

; template
(define (function-for-tie a-tie)
  (cond [(symbol? a-tie) ...]
        [(false? a-tie) ...]
        [(and (real? a-tie) (<= a-tie 9950))   ...]
        [... ...]
        [... ...]))


; (**) or, collapse the last three cases, and just say it's a "taxable-income"
;      as previously defined?



(define (func-for-taxable-income-entry a-tie)
  (cond [(symbol? a-tie)  ...]
        [(boolean? a-tie) ...]
        [(<= a-tie 9950)  ...]
        [.. ..]
        [.. ..]))


; DESIGN QUESTION:
; Should we make `tax2` call `tax` as a helper?
; I'd say, Answer: depending on our data-def'n:
;   if we included 5 branches in 'taxable-income-entry', we should have 5 branches.
;   Otherwise three.
; But that just begs the question: what is the right data-def'n --
;   should it have 'exempt,#f,taxable-income or should it have 5 branches?
; I tend towards the former.





  

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

;  More examples of union types:



; A student-query-result
;    - a username (interpretation: RU username of an existing student), OR
;    - #false (interpretation: no such person found), OR
;    - 'private (interpretation: person exists, but information is non-public).
;

; Datatype definition:
#;(define (student-query-result? x)
   (or (username? x)          
       (false? x)             ; interpretation: no such person
       (equal? x 'private)))  ; interpretation: info is to be kept private

; Datatype definition:
#;(define (username? x)    ; interpretation: an RU student's username
  (and (string? x)
       (<= 1 (string-length x) 16)   ; "cmartinezmurillo@"
       (regexp-match? #px"[a-z][a-z0-9]+" x)))



; (e.g. looking at a csv file, tsv file, or file w/ hard-spaced columns)
; A column-determiner is:
;  - a character       (char to split by), OR
;  - a positive-int    (the column-width)
;
; datatype def'n:
(define (column-determiner? x)
    (or (char? x)
        (and (integer? x) (positive? x))))





(check-expect (column-determiner? #\a) #true)
(check-expect (column-determiner? "a") #false)
(check-expect (column-determiner? "") #false)
(check-expect (column-determiner? "abc") #false)

(check-expect (column-determiner? 17) #true)
(check-expect (column-determiner? -17) #false)
(check-expect (column-determiner? 2.3) #false)
(check-expect (column-determiner? 0) #false)
(check-expect (column-determiner? -2.3) #false)


; path-or-string
;
; datatype def'n:
#| requires full-racket for `path?`:
(define (path-or-string? x)
   (or (path? x)
       (string? x)))
|#

; regexp-or-string
;
; datatype def'n:
(define (regexp-or-string? x)
   (or (regexp? x) (pregexp? x)   ; two different types, in racket ?!
       (string? x)))

(check-expect (regexp-or-string? "") #true)
(check-expect (regexp-or-string? "h") #true)
(check-expect (regexp-or-string? "hello") #true)
(check-expect (regexp-or-string? #px"") #true)
(check-expect (regexp-or-string? #px"h") #true)
(check-expect (regexp-or-string? #px"hello") #true)
(check-expect (regexp-or-string? #px"([hnbc]ow\\s)+") #true)

(check-expect (regexp-or-string? 23) #false)
(check-expect (regexp-or-string? 'bye) #false)

; /usr/sbin/periodic uses a configuration-file entry to determine how it handles output:
;
; -  If this is set to a path name (beginning with a `/' character), output is simply logged to that file.
; -  If this value does not begin with a `/' and is not empty, it is assumed to contain a list of email
;        addresses, and the output is mailed to them.
; -  If this value is the empty string (or, is not set), output is sent to standard output.




; Another Example of a union type:
; In Star Wars, we wish to represent the
; fire-power of a weapon:
; For blasters, it's easy -- bigger is better!
; But light-sabers are more complicated: each color
; has its own strenghts and weaknesses relative to each other.
; SO: a fire-power is:
;   a positive number (for blasters),
;   OR a symbol (the color of a light-saber).
; Examples of the data:
43.2
'purple


; A Student is represented as:
; - A String  (interpretation: a first & last name), OR
; - a number  (interpretation: an ID number).
;
; datatype def'n:
(define (student? x)
    (or (string? x) 
	(number? x)))




; An address is represented as:
; - A String (interpretation: a street-address in standard post-office format) OR 
; -  null    (interpretation: the address exists, but is unknown to us).


; A card-rank is:
;   - 2..10
;   - one-of 'A, 'K, 'Q, 'J
;   - 'Joker
;
; Datatype defitinition:
(define (card-rank? itm)
    (or (and (natural? itm) (<= 2 itm 10))
        (member itm (list 'A 'K 'Q 'J))
        (equal? itm 'Joker)))


; a color-spec is:
;   - a string (interpretation: one of the standard css-color-names), OR
;   - an struct with RGB fields (interpretation: red, green, and blue components of the color)


; a date is:
;  - string,            (interpretation; a date, in format "yyyy-mmm-dd"), OR
;  - an int in 1..366,  (interpretation: day-of-the-current-year) OR
;  - a java.util.Date object (interpretation: Date -- see that class for details)
;
; Note that in this case, all three variants might be denoting the same underlying info.  
; And in real code, you'd want your code to have one "canonical" way it represents 
; the info, along with functions to do a "one time" translation the other variants 
; into your preferred representation.
;
; E.g., you might use java.util.Date pretty much everywhere in your code base,
;  and then have a Date constructor that took in an string "yyyy-mm-dd",
;  and a constructor that took in an int(day-of-current-year).
; This doesn't really need a full union-type, BUT it can sure be convenient
;  if your clients can pass any of those three into your functions
;  (without making them have to call the `Date` constructor themselves).
;
; This accounts for SOME uses of union-types, but not all.


; a problem-report is:
;  - an natnum (interpretation: an index into array of existing problem-tickets), OR
;  - a string (interpretation: a new problem, to be submitted)


;  A file-or-fname is:
;   - a string (interpretation: filename), OR
;   - a list-of-directories (a "path"), OR
;   - a file-descriptor (interpretation: the already-opened file)
;
;  [ It's a real-world pain to have functions that want to open a file
;     and work with it,
;     and then call a helper-function which requires the filename ...]

; a transaction is:
; - double (interpretation: Cash transactions: Discount)
; - int (interpretation: Check transactions: CheckNumber)
; - string-and-two-ints (interpretation: Credit transactions: Card Number and Expiration Date)


; A number-of-allowed-occurrences is:
;   - a number (interpretation: the one allowed number),
;   - a pair of numbers (interpretation: an interval -- min and max)
;   - a list-of-intervals  (interpretation: allow the union of the intervals)
;   - an indicator function  (interpretation: allow a number if the function returns #true when given that number)
;
; E.g. an auto-grader for hw counts #occurs of "sqrt", and
;     might want exactly 3, or between 2 and 5, or either 2-5 or 7-9, or a prime-number-of-occurrences.




#|   Thoughts on the uses of union-types (and what we did before hearing about them).

NOTE that sometimes a sentinel value is used, but it has to be shoe-horned
into the existing type-system: Consider java's String#indexOf -- what does
it return for not-found?  What might python/racket/javascript use instead?
What might be a union-type, to describe the result?

NOTE that if we have a type "T, OR <one-sentinel-value>", in java we'll
use a class, and use `null` to represent that one sentinel value.
    Examples: Map#get;
 This has its issues [SO easy to forget that a var declared to hold a `String`
 might not hold a string => Null Pointer Exception;
 what if `null` might be a valid-info instead of a sentinel, e.g. java.util.Map#get(U)
 leads to weird library principles like "you can't associate an object with `null`".]

NOTE that Java can hack functions that take in a union-type, by overloading.
However, they can't *return* something of a union-type.

Dynamically-typed languages like javascript, python, racket
   use union-types routinely (by mentioning them in comments)
Some statically-typed languages DO let you define union-types.
    (ML, Ada's "variant record", Haskell)


 |#




#|  ; Another example, worked out: enumerated types.
    ; (But it's not a very exciting example.)

; Task: `turn`, for changing a stop-light.
;  ...wait, what data type to use?

; Data Definition:
; A slc ("stoplight color") is one of:
;  - 'red,          (interpretation: stop) OR
;  - 'yellow        (interpretation: stop-if-safe) , OR
;  - 'green,        (interpretation: go), OR
;  - 'flashing-yellow (interpretation: proceed with caution), OR
;  - 'flashing-red    (stop, then proceed when safe)

;Examples of the data (duh):
'red
'yellow
'green
'flashing-yellow
'flashing-red




(check-expect (turn 'red) 'green)
(check-expect (turn 'green) 'yellow)
(check-expect (turn 'yellow) 'red)
(check-expect (turn 'flashing-red) 'flashing-red)
(check-expect (turn 'flashing-yellow) 'flashing-yellow)


; turn : slc -> slc
; return the next color for a stop-light.
;
(define (turn curr-color)
  (cond [(symbol=? curr-color 'red)             'green]
        [(symbol=? curr-color 'yellow)          'red]
        [(symbol=? curr-color 'green)           'yellow]
        [(symbol=? curr-color 'flashing-yellow) 'flashing-yellow]
        [(symbol=? curr-color 'flashing-red)    'flashing-red]
        [else                                   (error 'turn "fell off cond?!")]
        ; It's already an error in beginning-student, to fall off the end of a cond.
        ; So I show this just for fun.  (But in full-racket it's not an error,
        ; even when I wish it was, so in full-racket I *may* write such an `else`.)
        ))


; Task: write penalty-for-running-a-light.
(check-expect (penalty-for-running-a-light 'red) 50)
(check-expect (penalty-for-running-a-light 'yellow) 0)
(check-expect (penalty-for-running-a-light 'green) 0)
(check-expect (penalty-for-running-a-light 'flashing-yellow) 25)
(check-expect (penalty-for-running-a-light 'flashing-red) 99)

; penalty-for-running-a-light : slc -> non-negative-real
; Return the fine for running a stoplight, in USD.
;
(define (penalty-for-running-a-light curr-color)
  (cond [(symbol=? curr-color 'red)             50]
        [(symbol=? curr-color 'yellow)           0]
        [(symbol=? curr-color 'green)            0]
        [(symbol=? curr-color 'flashing-yellow) 25]
        [(symbol=? curr-color 'flashing-red)    99]
        ))

; Step 3, TEMPLATE, for ANY function processing a slc:

; func-for-slc : slc -> ???
(define (func-for-slc a-slc)
  (cond [(symbol=? a-slc 'red)             ...]
        [(symbol=? a-slc 'yellow)          ...]
        [(symbol=? a-slc 'green)           ...]
        [(symbol=? a-slc 'flashing-yellow) ...]
        [(symbol=? a-slc 'flashing-red)    ...]
        ))


|#
|#