Planet Scheme

For the complete post, please visit http://jeapostrophe.github.com/2013-05-20-forth-post.html.

It is a classic problem from computer science to determine the number of ways in which coins can be combined to form a particular target; as an example, there are 31 ways to form 40 cents from an unlimited supply of pennies (1 cent), nickels (5 cents), dimes (10 cents) and quarters (25 cents), ranging from the 3-coin set (5 10 25) to the 40-coin set consisting only of pennies.

The solution is usually stated in recursive form: if c is the first coin in the set of coins cs and n is the target, the solution is the number of ways to reach the target after removing c from cs plus the number of ways to reach n − c using all the coins in cs. The algorithm to make a list of the coins, instead of the count, is the same, but keeping track of the list of coins instead of the count.

Your task is to write two functions, one to determine the count and one to determine the list of coins. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

This post is mainly mathematical. We left it out of our introduction to categories for brevity, but we should lay these definitions down and some examples before continuing on to universal properties and doing more computation. The reader should feel … Continue reading →

The ISLISP programming language is a member of the Lisp family of programming languages. It attempts to bridge the gap between the various incompatible members of the Lisp family of languages (most notably Common Lisp, Eulisp, LeLisp, and Scheme) by focusing on standardizing those areas of widespread agreement. It is a small language, closer to the size of Scheme than to Common Lisp, for example.

The most recent change to the specification occurred in 2007.

The design of ISLISP had these design goals:

• Compatible with existing Lisp dialects where feasible.
• Provide basic functionality.
• Object-oriented.
• Designed with extensibility in mind.
• Gives priority to industrial needs over academic needs.
• Promotes efficient implementations and applications.

(via islisp.info)

John Cowan mentioned it on scheme-reports, so I was curious.

Today’s exercise comes from the book Making the Alphabet Dance: Recreational Wordplay by Ross Eckler, but I found it at http://www.math.cmu.edu/~bkell/alpha-order/:

Assume we have a list of all the words in the English language. Under the normal ordering of the alphabet in English (A, B, C, …, Z), some number of these words have all their letters in alphabetical order (for example, DEEP, FLUX, and CHIMPS). However, if we change the ordering of the alphabet, we will change the number of words having their letters in “alphabetical” order. What arrangement of the letters of the alphabet maximizes this number?

Your task is to write a program to find such an arrangement. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

My girlfriend and I decided we want a print of my recent artistic creation from the post Bezier Curves and Picasso. I set up an account at Society6, which does professional art printing (framed or unframed).  I can’t imagine anyone … Continue reading →

Mickey Scheme is an interpreter for R7RS Scheme written in C++

For the complete post, please visit http://jeapostrophe.github.com/2013-05-13-vi-post.html.

Simplicity and the Artist Some of my favorite of Pablo Picasso’s works are his line drawings. He did a number of them about animals: an owl, a camel, a butterfly, etc. This piece called “Dog” is on my wall: These … Continue reading →

According to their masthead, the MindCipher website is “a social repository of the world’s greatest brain teasers, logic puzzles and mental challenges.” Some of the problems lend themselves to brute force computation, others are better solved with pencil-and-paper or solely with mental effort. We look at three MindCipher exercises today.

1: Coin Flip: On Monday, you flip a coin all day. You start flipping it until you see the pattern Head, Tail, Head. You record the number of flips required to reach this pattern, and start flipping again (and counting up from 1 again) until you see that pattern again, you record the second number, and start again. At the end of the day you average all of the numbers you’ve recorded. On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

2: 1978: The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true?

3: Sum of Two Prime Numbers: If p, q > 2 are consecutive in set of primes. Since p,q can only be odd number, (p+q) is an even number.

Can (p+q)/2 be prime?

Your task is to solve the three problems given above; write a computer program to help you if you wish. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

Racket version 5.3.4 is now available from

http://racket-lang.org/

• Extflonums (80-bit floating-point numbers) are supported on some x86/x86_64 platforms — including Windows, and including platforms where Racket is compiled to use SSE instructions for flonum arithmetic. Thanks to Michael Filonenko.
• OS X: DrRacket and all of the other apps are now signed with an official key.
• Tally Maze: a new game based an enumeration of 2d mazes.
• The Optimization Coach, a DrRacket plugin, has been moved from the Racket distribution to the Racket package repository. Install it with: raco pkg install optimization-coach.
• Redex: define-union-language now merges productions when languages define the same nonterminals. Thanks to William Bowman.
• The srfi/19 library is now compatible with the date structure type exported by racket/base.

We are pleased to announce that (third RacketCon) will take place on September 29, 2013 at Northeastern University in Boston.  This year, we plan to bring in several speakers from industry, as well as host talks from Racket developers and users.

Lunch will be provided.

On the Saturday (28th) before RacketCon, we plan to hold a hackathon to work on various Racket projects.

Registration will open during the summer, and we will post a detailed schedule of events around the same time. The conference website is at

http://con.racket-lang.org/

Today’s exercise provides three little exercises on linked lists, designed to help beginning programmers learn more about how lists work; there is also a special invitation for more experienced programmers.

1. Write a function that takes an input list and an interval n and returns a new list with all the elements of the original list, in order, except that every nth item has been removed. For instance, given the input list (1 2 3 4 5 6 7 8 9 10) and n = 4, the function should return the list (1 2 3 5 6 7 9 10).

2. Write a function that takes an input list and returns a new list with all the elements of the original list, in order, except that in the case of duplicate elements all of the duplicates except the first has been removed. For instance, all of the following lists should be transformed into the list (1 2 3 4 5): (1 2 3 4 5), (1 1 2 3 4 5), (1 2 1 3 1 4 1 5 1), and (1 2 2 3 3 3 4 4 4 4 5 5 5 5 5).

3. Write a function that takes an input list and splits the list in half; for instance, given the input list (1 2 3 4 5) the two outputs are the lists (1 2) and (3 4 5). If the list has odd length the middle element can be placed in either half, at your option, so the lists (1 2 3) and (4 5) are an alternate acceptable solution for the example problem.

Your task is to write the three indicated functions. If you find that to be too simple, write one or more exercises for your student friends. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

For the complete post, please visit http://jeapostrophe.github.com/2013-05-06-texture--post.html.

I recently decided to add a few new ways for readers to keep up with what’s going on at Math ∩ Programming. These come in the form of a Google+ community and a Facebook group. I also have a seasoned Twitter … Continue reading →