2020-05-04-am.rkt

#lang racket

;; this module defines the sim-AQSE3 language, which
;; simulates AQSE3, by providing
;; only a few key forms from Racket. Specifically: lambda,
;; function calls, if, constants, and a few arithmetic
;; operators.
(module sim-AQSE3 racket
    (provide
     (rename-out [lambda lam]
                 [1-form-module-begin #%module-begin])
     #%top
     #%datum
     #%app
     + - * / = <=
     if)
  (define-syntax-rule (1-form-module-begin e)
    (#%module-begin e)))

;; exercise 0: Give the name `f` to the function that
;; accepts an argument `x` and computes x^2 + 4x + 4.
;; apply `f` to seven.

;; exercise 1: Use the trick discussed in class to define
;; a `fact` function that computes the factorial of a given
;; number. Use it to compute the factorial of 12.

;; exercise 2: Define a 'pow' function that accepts a base
;; and a (natural number) exponent, and computes the base to
;; the power of the exponent. Don't worry about non-natural
;; number exponents (6^1.5, 5^-4).

;; exercise 3: use `fact` and `pow` to build a "sin" function
;; that accepts a number x and a number of terms `n`, and computes
;; (sin x) using `n` terms of the taylor expansion. (Note that
;; this is a little ambigious; do zero-coefficient terms count?
;; You can go either way on this.) Use this function to compute
;; the sine of 1 radian to an error of no more than ten to the minus
;; 30th.

(module my-mod (submod ".." sim-AQSE3)

  ;; WRITE YOUR PROGRAM IN HERE
  1234

  )


(require 'my-mod)