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Boolean values, predicate procedures, and list filters

Summary: In this laboratory, you will have the opportunity to explore a number of issues relating to predicates, Boolean values, conditional operations, and list filters.

Preparation

a. Do the traditional lab preparation. That is,

  • Start DrRacket.
  • Check for update the csc151 package.
  • Require the csc151 package with (require csc151).

b. Load the list of cities by with zip codes.

(define zips (read-csv-file "/home/username/Desktop/us-zip-codes.csv"))

Exercises

Exercise 1: Writing your own predicates

a. Write a unary predicate, in-iowa?, that takes one row (element) from the collection of cities and returns #t if that element is in Iowa and #f otherwise.

> (in-iowa? '("50112" 41.685324 -92.630258 "Grinnell" "IA" "Poweshiek"))
#t
> (in-iowa? '("50208" 41.718107 -93.012335 "Newton" "IA" "Jasper"))
#t
> (in-iowa? '("02158" 42.385096 -71.208399 "Newton" "MA" "Middlesex"))
#f

b. Write a unary predicate, has-longitude?, that takes one row (element) from the collection of cities and returns #t if that element has a numeric longitude and #f otherwise.

> (has-longitude? '("04236" 44.189655 -70.136683 "Greene" "ME" "Androscoggin"))
#t
> (has-longitude? '("98282" "" "" "Camano Island" "WA" "Island"))
#f

c. Write a unary predicate, missing-latitude?, that takes one row (element) from the collection of cities and returns #t if that element lacks a numeric latitude and #f otherwise.

> (missing-latitude? '("04236" 44.189655 -70.136683 "Greene" "ME" "Androscoggin"))
#f
> (missing-latitude? '("98282" "" "" "Camano Island" "WA" "Island"))
#t

Exercise 2: Predicates with comparisons

a. Write a unary predicate, west-of-grinnell?, that holds only when an entry is strictly west of Grinnell, which has longitude -92.630258. You may assume that the entry has a real number in the longitude position.

> (west-of-grinnell? '("60637" 41.811929 -87.68732 "Chicago" "IL" "Cook"))
#f
> (west-of-grinnell? '("92222" 32.782242 -114.561905 "Bard" "CA" "Imperial"))
#t
> (west-of-grinnell? '("98282" "" "" "Camano Island" "WA" "Island"))
. . ../../Applications/Racket v6.5/collects/racket/private/kw.rkt:929:25: <: contract violation
  expected: real?
  given: ""
  argument position: 1st
  other arguments...:

b. Write a unary predicate, in-narrow-band?, which holds only when an entry has a longitude between -90.3 and -96.5, exclusive. You may assume that the entry has a numeric longitude.

> (in-narrow-band? '("55460" 45.015914 -93.47188 "Minneapolis" "MN" "Hennepin"))
#t
> (in-narrow-band? '("68524" 40.879252 -96.815309 "Lincoln" "NE" "Lancaster"))
#f

Exercise 3: Some simple filters

a. Using filter and in-iowa?, create a list of all the cities in Iowa that are in the zips table.

b. Using that filtered list, find how many zip codes there are in Iowa.

c. Using filter and missing-latitude?, Create a list of all the entries in zips that lack a latitude.

Exercise 4: More filters

a. What do you expect to happen if you filter zips using west-of-grinnell?, as in the following?

> (define zips-wog (filter west-of-grinnell? zips))

b. Check your answer experimentally.

c. As you likely predicated and found, the west-of-grinnell? predicate can’t work on cities that lack a longitude. Write a new predicate, wog?, that is like west-of-grinnell?, but also returns #f if the row (entry) lacks a longitude.

Exercise 5: Exploring and

a. What value do you expect to get for (and "one" 2 'three)?

b. Check your answer experimentally.

c. What value do you expect to get for (and "one" 2 #f 'three)?

d. Check your answer experimentally.

e. What value do you expect to get for (and "one" 2 #t 'three)?

f. Check your answer experimentally.

g. What value do you expect to get for (and "one" 2 'three #t)?

h. Check your answer experimentally.

i. What value do you expect to get for (and 1 2 3)?

j. Check your answer experimentally.

k. Describe, in your own words, the policy that leads to those results.

Exercise 6: Exploring or

a. What value do you expect to get for (or "one" 2 'three)?

b. Check your answer experimentally.

c. What value do you expect to get for (or "one" 2 #f 'three)?

d. Check your answer experimentally.

e. What value do you expect to get for (or "one" 2 #t 'three)?

f. Check your answer experimentally.

g. What value do you expect to get for (or "#f" "one" 2 'three)?

h. Check your answer experimentally.

i. What value do you expect to get for (or "#t" "one" 2 'three)?

j. Check your answer experimentally.

k. What value do you expect to get for (or 1 2 3)?

j. Check your answer experimentally.

m. Describe, in your own words, the policy that leads to those results.

Exercise 7: Further explorations of and and or

a. Determine the value and returns when called with no parameters.

b. Explain why you think the designers of Scheme had and return that value.

c. Determine the value and returns when called with one, two, and three integers as parameters.

d. Explain why you think the designers of Scheme had and return that value.

e. Determine the value or returns when called with no parameters.

f. Explain why you think the designers of Scheme had or return that value.

g. Determine the value or returns when called with only integers as parameters.

h. Explain why you think the designers of Scheme had or return that value.

If you are puzzled by some of the answers, you may want to look at the notes on this problem.

Exercise 8: Combining predicates with negate, conjoin, and disjoin.

The second self check in the reading on filtering lists asked you to identify the purpose of a variety of predicates.

Write predicates with equivalent purposes that are intended to work with the zip code data, rather than the capital data. Add a one-line comment to each answer that explains what the predicate computes.

For Those With Extra Time

Extra 1: Finding state bounds

Write a procedure, westernmost, that takes two inputs , a list of cities in the “zip code format” (zip code, latitude, longitude, city, state, county) and a state abbreviation. It should then produce the longitude of the westernmost city in that state. You may assume that all of the cities in the state have valid zip codes.

Extra 2: Confusing cities

Some city names appear in multipple states. Write a procedure, which-states, which takes two inputs, a list of cities in the “zip code” format and a city name. Your procedure should then return a list of all the states in which that city appears. (It’s okay if there are duplicates.)

Notes

Notes on problem 7

The expression (and) has value true (#t) because “and has a value of true if none of the parameters have value false”. This call has no parameters, which means none are false.

Alternately, you can think of #t as the “and-itive identity”. That is, (and #t x) is x. When given no parameters, and returns its identity value.

The expression (or) has value false (#f) because “or has value false if none of the parameters is non-false”. Since this call has no parameters, none are non-false.

Alternately, you can think of #f as the “or-itive identity”. That is, (or ... x) is x. When given no parameters, or returns its identity value.

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