Description
This exercise consists of a few short functions to help you familiarize yourself with OCaml. You can review the content of the discussion in [notes.rb](notes.rb), which includes the topics and examples from the discussion video. Also, check out [utop-tutorial.md](utop-tutorial.md) for an introduction to using `utop`.
## Part 1: Type inference
At the top of [disc3.ml](src/disc3.ml), there are a few function definitions. Try determining the types of these functions and check your answers with `utop`. This portion of the discussion is not tested (and thus not graded), but these kinds of exercises may appear on quizzes and exams!
## Part 2: Type definitions
You will have to fill in definitions for the functions `tf1`, `tf2`, `tf3` such that they have the type that is expected in the `.mli`. The operation of the function does not matter, as long as they have the correct types.
#### `tf1 a`
– **Type**: `string -> int`
#### `tf2 a b c`
– **Type**: `’a -> ‘b -> ‘b -> bool`
#### `tf3 a b`
– **Type**: `’a list -> ‘a list -> ‘a`
– **Note**: For this one, you can assume that the lists `a` and `b` are not empty.
## Part 3: Functions
#### `concat str1 str2`
– **Type**: `string -> string -> string`
– **Description**: Appends `str2` to the end of `str1`.
– **Examples**:
“`ocaml
concat “” “” = “”
concat “” “abc” = “abc”
concat “xyz” “” = “xyz”
concat “abc” “xyz” = “abcxyz”
“`
#### `add_to_float integer flt`
– **Type**: `int -> float -> float`
– **Description**: Adds `integer` and `flt` and returns a float representation of the sum.
– **Examples**:
“`ocaml
add_to_float 3 4.8 = 7.8
add_to_float 0 0.0 = 0.0
“`
#### `fib n`
– **Type**: `int -> int`
– **Description**: Calculates the nth [Fibonacci number](https://en.wikipedia.org/wiki/Fibonacci_number).
– **Examples**:
“`ocaml
fib 0 = 0
fib 1 = 1
fib 2 = 1
fib 3 = 2
fib 6 = 8
“`
## Part 4: Lists
#### `add_three lst`
– **Type**: `int list -> int list`
– **Description**: Adds 3 to each element in `lst`.
– **Examples**:
“`ocaml
add_three [] = []
add_three [1] = [4]
add_three [1; 3; 5] = [4; 6; 8]
“`
#### `filter n lst`
– **Type**: `int -> int list -> int list`
– **Description**: Given an integer `n` and a list `lst`, Remove elements from `lst` that are greater than `n`.
– **Examples**:
“`ocaml
filter 2 [1; 2; 3; 3; 2; 1] = [1; 2; 2; 1]
filter 5 [-1; 2; 3; 4] = [-1; 2; 3; 4]
“`
#### `double lst`
– **Type**: `’a list -> ‘a list`
– **Description**: Given a list `lst`, return a new list that has two copies of every element in `lst`.
– **Examples**:
“`ocaml
double [1;2;3;4] = [1;1;2;2;3;3;4;4]
double [“a”; “b”; “c”] = [“a”; “a”; “b”; “b”; “c”; “c”]
“`
