12th Computer Science Lesson 1
Functions Important 5 Marks Questions

1.What are called Parameters and write a note on i) Parameter without Type ii) Parameter with Type (9) Ch1 Q1

Parameters are the variables in a function definition and arguments are the values which are passed to a function definition.

Parameter without Type

(requires: b>=0 )
(returns: a to the power of b)
let rec pow a b:=
if b=0 then 1
else a * pow a (b-1)

• In the function definition, b is the parameter and the value passed to b during a function call is called an argument.
• The precondition (requires) specifies the condition that must be satisfied before the function is executed.
• The postcondition (returns) specifies the result produced by the function after execution.
• In the given function, data types are not explicitly mentioned. Some programming language compilers can automatically determine the data types using a process called type inference.

🔍 Type Inference in the Function

• In the above function definition if expression can return 1 in the then branch, shows that as per the typing rule the entire if expression has type int.
• Since the if expression is of type ‘int’, the function’s return type also be ‘int’.
• ‘b’ is compared to 0 with the equality operator, so ‘b’ is also a type of ‘int’.
• Since ‘a’ is multiplied with another expression using the * operator, ‘a’ must be an int.

Parameter with Type

(requires: b>=0 )
(returns: a to the power of b )
let rec pow (a: int) (b: int) : int :=
if b=0 then 1
else a * pow a (b-1)

• When we write the type annotations for ‘a’ and ‘b’ the parentheses are mandatory.
• Generally we can leave out these annotations, because it’s simpler to let the compiler infer them.
• There are times we may want to explicitly write down types.
• This is useful on times when you get a type error from the compiler that doesn’t make sense.
• Explicitly annotating the types can help with debugging such an error message.

The syntax to define functions is close to the mathematical usage: the definition is introduced by the keyword let, followed by the name of the function and its arguments; then the formula that computes the image of the argument is written after an := sign. If you want to define a recursive function: use “let rec” instead of “let”.