Exercises

Mandatory exercises

• Exercise 1: exhibiting expressions of a given type
• Exercise 2: exhibiting more expressions of a given type
• Exercise 3: lexical scope at work
• Exercise 5: a gorgeous unit-test function for string concatenation
• Exercise 6: an all-too-common error
• Exercise 7: tinkering with the generator of random proofs
• Exercise 9: associating left and right

Recommended exercises

• Exercise 4: exhibiting even more expressions of a given type
• Exercise 8: implementing Strachey’s generator of love letters

Exercise 9

A question about the design of OCaml:

• in its language of expressions, applications implicitly associate to the left, i.e., String.get "hello world" 0 is parsed as (String.get "hello world") 0;
• in its language of types, function types implicitly associate to the right, i.e., string -> int -> char is parsed as string -> (int -> char).

Justify this choice.

Exercise 10

Consider the following definition:

let length_of_string_concatenation s1 s2 =
  String.length (s1 ^ s2) = String.length s1 + String.length s2;;

What is the result of applying length_of_string_concatenation to any two strings?

• true, always?
• false, always?
• sometimes true, sometimes false?

Justify your answer.

Version

Added Exercise 10 [14 Feb 2020]

Created [07 Feb 2020]