Difference Between Applicative And Normal Order Evaluation

Difference Between Applicative And Normal Order Evaluation

Difference Between Applicative And Normal Order Evaluation – In the realm of programming languages, the evaluation of expressions plays a crucial role in determining the execution order and behavior of programs. Two common evaluation strategies employed by programming languages are applicative order evaluation and normal order evaluation. While both approaches serve the purpose of evaluating expressions, they differ significantly in their execution semantics and impact on program behavior. In this article, we’ll explore the difference between applicative and normal order evaluation, shedding light on their characteristics, advantages, and use cases.

Applicative Order Evaluation: Eager and Deterministic

Applicative order evaluation, also known as call-by-value evaluation, is a strategy in which function arguments are evaluated before applying the function. In applicative order evaluation, expressions are evaluated eagerly, meaning that arguments are computed and substituted into the function body before the function is invoked. This results in a deterministic evaluation order, where each argument is evaluated exactly once, regardless of whether its value is needed.

Key Characteristics of Applicative Order Evaluation:

1. Eager Evaluation

In applicative order evaluation, function arguments are evaluated eagerly, meaning that their values are computed before being passed to the function.

2. Deterministic Execution

The evaluation order in applicative order evaluation is deterministic, with each argument being evaluated exactly once, regardless of its usage within the function body.

3. Predictable Behavior

Due to its deterministic nature, applicative order evaluation often leads to predictable program behavior, making it easier to reason about and debug.

Example of Applicative Order Evaluation

Consider the following function definition in a programming language with applicative order evaluation:

“`python
def square(x):
print(‘Evaluating square function’)
return x * x

result = square(3 + 4)
“`

In this example, the expression `3 + 4` is evaluated first, resulting in the value `7`. Then, the `square` function is invoked with the argument `7`, and the result is printed. The output would be:
“`
Evaluating square function
“`

Normal Order Evaluation: Lazy and Non-Deterministic

Normal order evaluation, also known as call-by-name evaluation, is a strategy in which function arguments are not evaluated until they are needed by the function body. In normal order evaluation, expressions are evaluated lazily, meaning that arguments are substituted into the function body unevaluated and evaluated only if their values are required during execution. This results in a non-deterministic evaluation order, where arguments may be evaluated multiple times if their values are needed multiple times within the function body.

Key Characteristics of Normal Order Evaluation:

1. Lazy Evaluation

In normal order evaluation, function arguments are evaluated lazily, meaning that their values are computed only if and when they are needed by the function body.

2. Non-Deterministic Execution

The evaluation order in normal order evaluation is non-deterministic, with arguments potentially being evaluated multiple times if their values are required multiple times within the function body.

3. Potential for Efficiency

Lazy evaluation in normal order evaluation can lead to more efficient execution, as it avoids unnecessary computations for arguments that are not used.

Example of Normal Order Evaluation:

Consider the same function definition as before, but with normal order evaluation:

“`python
def square(x):
print(‘Evaluating square function’)
return x * x

result = square(3 + 4)
“`

In this example, the expression `3 + 4` is not evaluated immediately. Instead, the unevaluated expression `3 + 4` is passed as an argument to the `square` function. When the function is invoked, the expression `3 + 4` is evaluated inside the function body. The output would be:
“`
Evaluating square function
“`

Difference Between Applicative and Normal Order Evaluation

1. Evaluation Strategy

The primary difference between applicative and normal order evaluation lies in their evaluation strategies. Applicative order evaluation evaluates function arguments eagerly before applying the function, while normal order evaluation evaluates arguments lazily, only when their values are needed.

2. Determinism

Applicative order evaluation is deterministic, with each argument evaluated exactly once, regardless of its usage within the function body. In contrast, normal order evaluation is non-deterministic, with arguments potentially being evaluated multiple times if their values are required multiple times within the function body.

3. Efficiency vs. Laziness

Applicative order evaluation prioritizes efficiency by eagerly evaluating arguments before applying the function, while normal order evaluation prioritizes laziness by deferring argument evaluation until it is necessary.

The difference between applicative and normal order evaluation lies in their evaluation strategies, determinism, and trade-offs between efficiency and laziness. While applicative order evaluation offers predictability and efficiency by eagerly evaluating arguments before applying the function, normal order evaluation offers laziness and potential for efficiency gains by deferring argument evaluation until it is needed. The choice between applicative and normal order evaluation depends on the specific requirements and characteristics of the programming language, the nature of the expressions being evaluated, and the desired trade-offs between efficiency and laziness.