Introduction to Functional Programming with Scheme

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An Introduction to
Functional Programming
with Scheme
Michael Norton

michael@docondev.com : mail
docondev.blogspot.com/ : blog
twitter.com/DocOnDev : the twitters

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SICP Study
Gamma Group

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Yes!

Gamma Group Week 1
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umm...

Gamma Group Week 3
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Hello?

Gamma Group Week 5
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Maths are
hard
Second order nonlinear ordinary differential equation

Third Order Nonlinear Partial Differential Equation

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SICP
I don’t recommend this text to
start with

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Texts I do recommend

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Consists Entirely of Functions

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Consists Entirely of Functions
Higher-order Functions

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Favors Immutability

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Referentially Transparent

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Limited Loop Structures

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• Consists Entirely of Functions
• Favors Immutability
• Referentially Transparent
• Limited Loop Structures

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LISP
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Symbolic Expressions

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Dynamically Typed

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List Processing
LISt Processing

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Lisp

• Symbolic Expressions
• Dynamically Typed
• List Processing

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Scheme
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Static (Lexical) Scope

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Static Scope
(define x 9)
(define (show-x) (display x))
(define test (lambda (x)
(show-x)
(display ‘,)(display x))

(test 3) => 9,3

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Tail Recursion

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Tail Recursion
(define (factorial n)
(define (fact-tail n m)
(if (= n 0) m
(fact-tail (- n 1) (* n m))))
(fact-tail n 1))

(factorial 4) => 24

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Shared Namespace

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Scheme

• Static Scope
• Tail Recursion
• Shared Namespace

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String Calculator Kata
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Requirements

Takes a String of integers and returns their sum
Can handle an unknown amount of integers
Can handle a custom delimiter
Delimiter notation “//[delimiter]n[numbers]”

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First Test
string-calculator-tests.ss
#lang scheme
(require (planet schematics/schemeunit:3)
(planet schematics/schemeunit:3/text-ui)
"string-calculator.ss")

(check-equal? (str-calc "") 0
"Empty string should return 0")

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FAIL!

. expand: unbound identiﬁer in module in: str-calc

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String Calculator Code
string-calculator.ss
#lang scheme
;; String Calculator Kata
(define (str-calc input) 0)

;; Expose these functions
(provide str-calc)

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PASS!

#t

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Second Test

#lang scheme
(require ... "string-calculator.ss")

(check-equal? (str-calc "") 0 "Should return 0")
(check-equal? (str-calc "1") 1 "Should return 1")

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FAIL!
#t
--------------------
FAILURE
name: check-equal?
location: (#<path:/string-calculator-tests.ss> 11 0 219 63)
expression: (check-equal? (str-calc "1") 1)
params: (0 1)
message: "Should return 1"
actual: 0
expected: 1
--------------------

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#lang scheme
(define (str-calc input)
(cond
((= (string-length input) 0) 0)
(else (string->number input))))

(provide str-calc)

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PASS!

#t
#t

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Third Test
#lang scheme

(check-equal? (str-calc "1,2") 3 "Should sum items")

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FAIL!
#t
#t
--------------------
FAILURE
name: check-equal?
location: (#<path:/string-calculator-tests.ss> 10 0 241 52)
expression: (check-equal? (str-calc "1,2") 3)
params: (#f 3)
message: "Should sum items"
actual: #f
expected: 3
--------------------

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(cond ((list? input)
(cond ((null? input) 0)
(else (+ (string->number (car input))
(str-calc (cdr input))))))
(else (str-calc (str-split input #,)))))

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PASS!

#t
#t
#t

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Fourth Test
#lang scheme

(check-equal? (str-calc "1,2,3,4") 10 "Should sum all items")

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PASS!

#t
#t
#t
#t

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Fifth Test
#lang scheme

(check-equal? (str-calc "1*2" #*) 3
"Should delimit on custom")

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FAIL!

. procedure str-calc: expects 1 argument, given 2: "1*2" #*

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(define (str-calc input [delim #,])
(else (str-calc (str-split input delim)))))

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PASS!
#t
#t
#t
#t
#t

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Sixth Test
(check-equal? (str-calc "1*2" #*) 3
(check-equal? (str-calc "1*2*3*4" #*) 10

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PASS!
#t
#t
#t
#t
#t
#t

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Change Tests
(check-equal? (str-calc "//*n1*2") 3
(check-equal? (str-calc "//*n1*2*3*4") 10

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(else (str-calc (str-split
(rm-delim input) (get-delim input)))))

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Delimiter Parser
delim-parse.ss
(define (rm-delim input) (cadr (split-delim input)))

(define (get-delim input) (car (split-delim input)))

(define (split-delim input)
(cond ((and (> (string-length input) 2)
(string=? (substring input 0 2) "//"))
(regexp-split #rx"n" (substring input 2)))
(else (cons "," (list input)))))

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Delimiter Tests
delim-parse-tests.ss
(require (planet schematics/schemeunit:3)
(planet schematics/schemeunit:3/text-ui)
"delimiter-parse.ss")

(check-equal? (get-delim "1") #, "Default delimiter")
(check-equal? (remove-delim "2,1") "2,1" "String")
(check-equal? (get-delim "//*n2*1") #* "Delimiter")
(check-equal? (remove-delim "//*n2*1") "2*1" "-Delimiter")

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Ruby - Mario Aquino
module Calculator
def self.calculate(expression)
raise ArgumentError, 'Must be a string' unless expression.is_a? String
raise ArgumentError, 'Must be numeric' unless expression =~ pattern

value = nil
expression.scan(pattern) do |left, operator, right|
value ||= left
value = eval(value + operator + right).to_s
end
value
end

private
def self.pattern
/(d+)s?([+-*/])s*(?=(d+))/
end
end

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Python - Gary Bernhardt
def add(string):
string = _normalize_delimiters(string)
if string:
return _add_numbers_in_string(string)
else:
return 0

def _normalize_delimiters(string):
string = _normalize_custom_delimiter(string)
string = string.replace('n', ',')
return string

def _normalize_custom_delimiter(string):
if string.startswith('//'):
delimiter_spec, string = string.split('n', 1)
delimiter = delimiter_spec[2:]
string = string.replace(delimiter, ',')
return string

def _add_numbers_in_string(string):
numbers = map(int, string.split(','))
_validate_numbers(numbers)
return sum(numbers)

def _validate_numbers(numbers):
if any(number < 0 for number in numbers):
raise ValueError

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F# - Mark Needham
module FSharpCalculator
open System
open System.Text.RegularExpressions

let split (delimeter:array<string>) (value:string) = value.Split (delimeter, StringSplitOptions.None)
let toDecimal value = Decimal.Parse value

let (|CustomDelimeter|NoCustomDelimeter|) (value:string) =
let delimeters (value:string) = Regex.Matches(value, "[([^]]*)]") |> Seq.cast |>
Seq.map (fun (x:Match) -> x.Groups) |>
Seq.map (fun x -> x |> Seq.cast<Group> |> Seq.nth 1) |>
Seq.map (fun x -> x.Value) |>
Seq.to_array

if (value.Length > 2 && "//".Equals(value.Substring(0, 2))) then
if ("[".Equals(value.Substring(2,1))) then CustomDelimeter(delimeters value)
else CustomDelimeter([| value.Substring(2, value.IndexOf("n") - 2) |])
else NoCustomDelimeter(",")

let digits value = match value with
| CustomDelimeter(delimeters) -> value.Substring(value.IndexOf("n")) |> split delimeters |> Array.map toDecimal
| NoCustomDelimeter(delimeter) -> value.Replace("n", delimeter) |> split [|delimeter |] |> Array.map toDecimal

let buildExceptionMessage negatives =
sprintf "No negative numbers allowed. You provided %s" (String.Join(",", negatives |> Array.map (fun x -> x.ToString())))

let (|ContainsNegatives|NoNegatives|) digits =
if (digits |> Array.exists (fun x -> x < 0.0m))
then ContainsNegatives(digits |> Array.filter (fun x -> x < 0.0m))
else NoNegatives(digits)

let add value = if ("".Equals(value) or "n".Equals(value)) then 0.0m
else match digits value |> Array.filter (fun x -> x < 1000m) with
| ContainsNegatives(negatives) -> raise (ArgumentException (buildExceptionMessage negatives))
| NoNegatives(digits) -> digits |> Array.sum

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C# - Anonymous
using System;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
namespace TDDFun
{
public class StringCalculator
{
public double Add(string numbers)
{
Double sum = 0;
if (string.IsNullOrEmpty(numbers))
{
sum = 0;
}
else
{
const string regex1 = “(//)”;
const string regex2 = “(.*?)”;
const string regex3 = “(n)”;
const string regex4 = “(.*?d)”;

var delimiters = new List<string>();
var r = new Regex(regex1 + regex2 + regex3 + regex4, RegexOptions.IgnoreCase | RegexOptions.Singleline);
Match m = r.Match(numbers);
if (m.Success)
{
string delimiterCollection = m.Groups[2].ToString();
int numberStartIndex = m.Groups[3].Index;
const string re5 = “([.*?])”;
var r2 = new Regex(re5, RegexOptions.IgnoreCase | RegexOptions.Singleline);

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C# - Anonymous (cont.)
MatchCollection m2 = r2.Matches(delimiterCollection);
if (m2.Count > 0)
{
foreach (Match x in m2)
{
delimiters.Add(x.ToString().Replace(“[", "").Replace("]“, “”));
}
}
else
{
delimiters.Add(delimiterCollection);
}
numbers = numbers.Remove(0, numberStartIndex + 1);
}
else
{
delimiters.Add(“n”);
delimiters.Add(“,”);
}

string[] splittedNumbers = numbers.Split(delimiters.ToArray(), StringSplitOptions.None);
ValiateNumbers(splittedNumbers);

foreach (string s in splittedNumbers)
{
double ss = Double.Parse(s);
sum += ss <= 1000 ? ss : 0;
}
}
return sum;
}

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private static void ValiateNumbers(IEnumerable<string> numbers)
{
double x;
var negativeNumbers = new List<string>();
foreach (string s in numbers)
{
Validator.IsRequiredField(Double.TryParse(s, out x), “Validation Error”);
if (Double.Parse(s) < 0)
{
negativeNumbers.Add(s);
}
}
Validator.IsRequiredField(negativeNumbers.Count <= 0,
“Negatives not allowed “ + ShowAllNegatives(negativeNumbers));
}

private static string ShowAllNegatives(List<string> negativeNumbers)
{
var sb = new StringBuilder();
int counter = 0;
negativeNumbers.ForEach(k =>
{
if (counter == 0)
{
sb.Append(k);
counter++;
}
else
{
sb.Append(“;” + k);
}

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});

return sb.ToString();
}
}

public static class Validator
{
public static void IsRequiredField(bool criteria, string message)
{
if (!criteria)
{
throw new ValidationException(message);
}
}
}

public class ValidationException : ApplicationException
{
public ValidationException(string message) : base(message)
{
}
}
}

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Thank You!
Michael Norton

michael@docondev.com : mail
docondev.blogspot.com/ : blog
twitter.com/DocOnDev : the twitters

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References
• Wikipedia
http://en.wikipedia.org/wiki/Scheme

• PLT Scheme
http://plt-scheme.org/

• MIT Press SICP
http://mitpress.mit.edu/sicp/

• MIT Press HTDP
http://www.htdp.org/

• U of CA, Berkley
http://www.cs.berkeley.edu/~bh/ss-toc2.html

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Introduction to Functional Programming with Scheme

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