; Author: Eric Aaron
; Purpose: A little bit of Scheme programming for Colby College CS375
; Fall 2022 semester
; this code runs on https://inst.eecs.berkeley.edu/~cs61a/fa14/assets/interpreter/scheme.html
  
; These Scheme definitions are for our LList datatype only
; This file contains some defintions, some small examples, 
;   and a few starter tips about general Scheme syntax,
;   in case you want to try more Scheme programming.  
; Author's note / Disclaimer: I am not a Scheme expert, so although I will 
;                try to help all CS375 students with Scheme questions, 
;                I may not havethe answers! Please be forewarned!

  
; Some Scheme definitions for LLists--using our LList datatype.
; cons is just cons--no change needed!
(define first car)
(define rest cdr)

; just because I like the syntax "empty?" more than "null?"
(define empty? null?)

; here's an auxiliary function, computing the max of two numbers
; Input: Two numbers v1, v2
; Output: The larger of v1 and v2
(define (max v1 v2)
  (if (> v1 v2)
      v1
      v2))

; here's an example algo on LLists
; Input: LList L containing only positive integers
; Output: Largest value occurring in L, or 0 if L is empty
(define (LLMax L)
  (if (empty? L)
      0
      (max (first L) (LLMax(rest L)))))

; here are some test cases--not exhaustive, just illustrative
(LLMax (cons 3 (cons 7 (cons 5 ()))))
(LLMax (cons 7 (cons 5 (cons 3 ()))))

; Some general Scheme syntax to use:
; in general, the syntax (f x0 x1 ... xn) evaluates to the application of 
;   function f on arguments x0, x1, ... xn
; use prefix notation for arithmetic operations, e.g., (+ 3 7) and (* 2 5) 
;                                                      both evaluate to 10
; use (null? <T>) to check if T is empty
; use (= v0 v1) to check if integers v0 and v1 are equal
; use (< v0 v1) and (> v0 v1) to check less than / greater than on integers
; use (list? <L>) to check if L is a list [for the LList remove exercises]
; use #t, #f for boolean values true, false--e.g., (< 3 5) evaluates to #t, 
;                                            because 3 is less than 5