OCaml - Exercises 1

Exercise : Basic types

For these exercises, the integers are expected to be ≥ 0. Do not consider negative cases.

• Write a function e1q1 with type int → string → string such that

  e1q1 0 "ab"	""
  e1q1 1 "ab"	"ab"
  e1q1 2 "ab"	"abab"
  e1q1 n s	s repeated n times

• Write a function e1q4 with type int → int such that

  e1q4 0	0
  e1q4 1	1
  e1q4 10	2
  e1q4 99	2
  e1q4 999	3
  e1q4 n	the number of digits of n (except for 0, where it returns 0)

• Write a function e1q2 with type int → string → string such that

  e1q2 0 ":"	""
  e1q2 7 ":"	"7:"
  e1q2 72 ":"	"2:7:"
  e1q2 987 ":"	"7:8:9:"
  e1q2 n s	the (reversed) digits of n, interleaved with s

  Note: to get the last digit of a number, use n mod 10.
  Remember also string_of_int.
• Write a function e1q3 similar to e1q2, but the digits are in the right order (not reversed):
  e1q3 987 "#" returns "9#8#7#"
• Write a function e1q5 with type int → bool → bool such that

  e1q5 0 b	true (whatever b is)
  e1q5 n true	returns true iff all digits of n are even
  e1q5 n false	returns true iff all digits of n are odd
  e1q5 17359 false	true
  e1q5 17369 false	false
  e1q5 288062 true	true
  e1q5 298462 true	false

• Write a function e1q6 with type int → int → bool such that

  e1q6 n m	true iff all digits of n are smaller or equal than the corresponding digits of m (prefixing with zeroes if necessary).
  e1q6 0 0	true
  e1q6 1234 2345	true
  e1q6 1234 999	false (because 999 is actually 0999)
  e1q6 999 1648	false
  e1q6 333 1444	true

Exercise : Curried functions

• Write a higher-order, polymorphic function curry3 with type (α × β × γ → δ) → α → β → γ → δ which maps a 3-argument uncurried function to a curried function.
  Try it with let ccat (a,b,c) = a ^ b ^ c
• Write the converse function: uncurry3 with type (α → β → γ → δ) → α × β × γ → δ which maps a 3-argument curried function to an uncurried function.
• Write a function apply3 with type (α → β) × (γ → δ) × (ε → ζ) → α × γ × ε → β × δ × ζ which takes two arguments: a triple of functions and a triple of values. It returns a triple of results (the first function applied to the first value, the second function applied to the second value, ...).
• Write a function sort2 with type (α → β) → (α → β) → α → (α → β) × (α → β) which takes three arguments: two functions, f and g, and an argument x. It returns the pair f,g if f(x) is smaller than g(x), otherwise it returns the pair g,f
• Write a function comp3 with type (α → β) → (γ → α) → (δ → γ) → δ → β which takes three arguments: three functions f, g, and h, and returns their composition: f∘g∘h

Exercise : Pattern-matching

• Write a function ext_and (extended and) with type bool → bool → bool → bool such that ext_and a b c returns a AND b when c is true, and returns not (a AND b) when c is false. Do not use any logical operator (such as &&, ||, not). Do not use IF.

  ext_and false true true	false
  ext_and false true false	true
  ext_and true true false	false
  ext_and true true true	true

• Write a function encode_char with type char → char which (bijectively) transforms each vowel to another vowel of your choice, and keeps consonant as is. Use it to define encode with type string → string which transforms a string to another string by transforming each character. You need String.map

  encode "I am a superhero."	Y em e sopirhira.
  encode "Les bons etudiants"	Lis bans itodyents