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;;; Copyright © 2021 Gerald Sussman and Chris Hanson
;;; Copyright © 2022 David Thompson <dthompson2@worcester.edu>
;;;
;;; This program is free software: you can redistribute it and/or
;;; modify it under the terms of the GNU General Public License as
;;; published by the Free Software Foundation, either version 3 of the
;;; License, or (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program. If not, see
;;; <http://www.gnu.org/licenses/>.
(use-modules (srfi srfi-1)
(ice-9 match))
;; Ideal gas law:
;; PV = nRT
;;
;; P is the pressure, V is the volume, n is the amount of the gas, R
;; is the gas constant, and T is the temperature.
(define pi (* 4 (atan 1 1)))
(define gas-constant 8.3144621) ; J/(K*mol)
(define (gas-law-volume pressure temperature amount)
(/ (* amount gas-constant temperature) pressure))
(define (sphere-radius volume)
(expt (/ volume (* 4/3 pi)) 1/3))
;; The choice of gas constant makes this program in SI units, so the
;; pressure is in newtons per square meter, the tempature is in
;; kelvins, the amount is in moles, the volume is in cubic meters, and
;; the radius is in meters.
;; The book does not implement make-unit-conversion nor unit:inverse,
;; so here's my take on it:
(define (make-unit-conversion procedure inverse)
(define (conversion n)
(procedure n))
(set-procedure-property! conversion 'inverse inverse)
conversion)
(define (unit:invert converter)
(procedure-property converter 'inverse))
;; From the book:
(define fahrenheit-to-celsius
(make-unit-conversion (lambda (f) (* 5/9 (- f 32)))
(lambda (c) (+ (* c 9/5) 32))))
(define celsius-to-kelvin
(let ((zero-celsius 273.15)) ; kelvins
(make-unit-conversion (lambda (c) (+ c zero-celsius))
(lambda (k) (- k zero-celsius)))))
;; 2.3.2 Implementing specializers
;; To be defined in exercise below
(define (make-converter input-unit output-unit)
#f)
(define (unit-specializer procedure implicit-output-unit . implicit-input-units)
(define (specializer specific-output-unit . specific-input-units)
(let ((output-converter (make-converter implicit-output-unit
specific-output-unit))
(input-converters (map make-converter
specific-input-units
implicit-input-units)))
(define (specialized-procedure . arguments)
(output-converter
(apply procedure
(map (lambda (converter argument)
(converter argument))
input-converters
arguments))))
specialized-procedure))
specializer)
(define (unit:* u1 u2)
(make-unit-conversion (compose u2 u1)
(compose (unit:invert u1)
(unit:invert u2))))
;; Exercise 2.11: Implementing unit conversions
;; a. As a warmup, write the procedures register-unit-conversion, and
;; make-converter.
(define *unit-conversions* (make-hash-table))
(define (register-unit-conversion input-unit output-unit procedure)
(hash-set! *unit-conversions* (list input-unit output-unit) procedure))
(define (make-converter input-unit output-unit)
(hash-ref *unit-conversions* (list input-unit output-unit)))
(register-unit-conversion 'fahrenheit 'kelvin
(unit:* fahrenheit-to-celsius celsius-to-kelvin))
;; b. Write the procedures for unit:/ and unit:expt
(define (unit:/ u1 u2)
(unit:* u1 (unit:invert u2)))
;; This only works for positive exponents.
(define (unit:expt unit power)
(define (mul i)
(if (= i 1)
unit
(unit:* unit (mul (- i 1)))))
(mul power))
;; c. Fill out a library of conversions for conventional units to SI
;; units. This requires conversion for mass and length. (Time is in
;; seconds in both systems. However, you may be interested in
;; minutes, hours, days, weeks, years, etc. Don't get stuck trying to
;; make this universal.)
(define inch-to-meter
(let ((ratio 0.0254))
(make-unit-conversion (lambda (inches) (* inches ratio))
(lambda (meters) (/ meters ratio)))))
(register-unit-conversion 'inch 'meter inch-to-meter)
(define pound-to-newton
(let ((ratio 4.448))
(make-unit-conversion (lambda (pounds) (* pounds ratio))
(lambda (newtons) (/ newtons ratio)))))
(register-unit-conversion 'pound 'newton pound-to-newton)
((unit:/ pound-to-newton inch-to-meter) 4) ; 700.472
((unit:expt inch-to-meter 3) 12) ; 0.000197
(define second-to-minute
(let ((seconds-per-minute 60))
(make-unit-conversion (lambda (seconds) (/ seconds seconds-per-minute))
(lambda (minutes) (* minutes seconds-per-minute)))))
(register-unit-conversion 'second 'minute second-to-minute)
(define minute-to-hour
(let ((minutes-per-hour 60))
(make-unit-conversion (lambda (minutes) (/ minutes minutes-per-hour))
(lambda (hours) (* hours minutes-per-hour)))))
(register-unit-conversion 'minute 'hour minute-to-hour)
(register-unit-conversion 'second 'hour (unit:* second-to-minute minute-to-hour))
;; d. Make some useful compounds, like velocity and acceleration.
(define second-to-second
(make-unit-conversion (lambda (seconds) seconds)
(lambda (seconds) seconds)))
;; Need an identity conversion.
(register-unit-conversion 'second 'second second-to-second)
(register-unit-conversion '(/ meter second) '(/ inch second)
(unit:/ (unit:invert inch-to-meter) second-to-second))
((unit:/ (unit:invert inch-to-meter) second-to-second) 1)
;; e. For a real project, extend this specializer system for some
;; other data conversion of some other program, having nothing to do
;; with units.
;; Calling it a unit conversion doesn't make sense in this context
;; where we are dealing with naming conventions, not units, but that's
;; fine for the sake of just getting through this exercise.
(define camel-case-to-snake-case
(make-unit-conversion (lambda (str)
(list->string
(let loop ((i 0))
(if (< i (string-length str))
(let ((c (string-ref str i)))
(if (char-set-contains? char-set:upper-case c)
(if (= i 0)
(cons (char-downcase c) (loop (+ i 1)))
(cons* #\_ (char-downcase c)
(loop (+ i 1))))
(cons c (loop (+ i 1)))))
'()))))
(lambda (str)
(list->string
(let loop ((i 0))
(if (< i (string-length str))
(let ((c (string-ref str i)))
(cond
((= i 0)
(cons (char-upcase c) (loop (+ i 1))))
((eqv? c #\_)
(cons (char-upcase (string-ref str (+ i 1)))
(loop (+ i 2))))
(else
(cons c (loop (+ i 1))))))
'()))))))
(define snake-case-to-lisp-case
(make-unit-conversion (lambda (str)
(string-map (lambda (c)
(if (eqv? c #\_) #\- c))
str))
(lambda (str)
(string-map (lambda (c)
(if (eqv? c #\-) #\_ c))
str))))
((unit:* camel-case-to-snake-case snake-case-to-lisp-case) "FooBar")
;; f. Another big extension is to build 'make-converter' so that it
;; can derive compound conversions, as required, from previously
;; registered conversions. This will require a graph search.
;; Yeah... I'm gonna use Guile's pattern matcher to make my life
;; easier, even though the book doesn't cover pattern matching until
;; later.
(define (make-converter input-unit output-unit)
(let ((unit-pair (list input-unit output-unit)))
(or (hash-ref *unit-conversions* unit-pair) ; cache hit
(match unit-pair ; cache miss
(((and ('/ in1 in2) in) (and ('/ out1 out2) out))
(let ((conversion (unit:/ (make-converter in1 out1)
(make-converter in2 out2))))
(register-unit-conversion in out conversion)
conversion))
(((and ('* in1 in2) in) (and ('* out1 out2) out))
(let ((conversion (unit:* (make-converter in1 out1)
(make-converter in2 out2))))
(register-unit-conversion in out conversion)
conversion))
;; This doesn't verify that the exponents are the same, but
;; it's good enough for this exercise.
(((and ('expt in (? number? power)) input)
(and ('expt out (? number? _)) output))
(let ((conversion (unit:expt (make-converter in out) power)))
(register-unit-conversion input output conversion)
conversion))
(((? symbol?) (? symbol?))
(error "primitive converter not registered for" unit-pair))))))
;; Should be a cache miss for both divisions, then cache hit for
;; pound->newton, then cache misses for the expts, then cache hit for
;; inch->meter. Subsequent calls should be immediate cache hits.
((make-converter '(/ pound (expt inch 3)) '(/ newton (expt meter 3))) 10) ; ~2714336
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