Closures and Evaluation of Function Application, Order of Evaluation in OCaml

Jan 25, 2024

---

Functions with more than one argument

# let add_three x + y + z = x + y + z;;
val add_three : int -> int -> int -> int = <fun> 
# let t = add_three 6 3 2;;
val t : int = 11
# let add_three = 
  fun x -> (fun y -> (fun z -> x + y + z));;
val add_three : int -> int -> int -> int = <fun> 

• What is the value of add_three?
• \(\textcolor{blue}{\text{Let $\rho_{add\_three}$ be the environment before the declaration}}\)
• Remeber:
\(\begin{align*} &\textcolor{blue}{\text{let add three = }} \\ &\qquad\textcolor{blue}{\text{fun x $\rightarrow$ (fun y $\rightarrow$ (fun z $\rightarrow$ x + y + z))}} \\ &\text{Value:} \textcolor{blue}{< x \rightarrow \text{ fun y $\rightarrow$ (fun z $\rightarrow$ x + y + z)}, \rho_{add\_three >}} \end{align*}\)

Partial application of functions

---

let h = add_three 5 4;;
val h : int -> int = <fun>
h 3;; 
- : int = 12
h 7;; 
- : int = 16

Partial application also called sectioning

Functions as arguments

---

# let thrice f x = f(f(f x));;
val thrice : ('a -> 'a) -> ('a -> 'a) = <fun>
# let g = thrice plus_two;;
val g : int -> int = <fun>
# g 4;;
- : int = 10
# thrice (fun s -> "Hi!" ^ s) "Good-bye!";; 
- : string = "Hi! Hi! Hi! Good-bye!"