The if statement
Prolog
I was learning a bit of prolog and came to a new insight relating to the if
statement after working a few times with the neck operator (:-).
For what it's worth, prolog uses the neck operator as a way to express the relationship is implied by and it is the building block for prolog programs. (if we can even call them programs).
The material conditional (if statement)
The neck operator is known by many names, such as the material conditional in the mathematical world, but we know it as the ubiquitous if statements found in modern programming languages.
Just as a reminder, the material conditional is a logical operator that has the following truth table.
| P | Q | P -> Q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
A study in modern programming
go programming language
I'm going to use go as the programming language for the illustration purposes.
The material conditionals are expressed in go are using the if statement with
the following form:
if *P* { *Q* }example 1
Let's consider an example where P is true:
var x int
if true {
x = 42
}According to the truth table, when P is true, then Q must also be true, otherwise we encounter a contradiction.
The effects of this is that x is 42.
example 2
Let's consider an example where P is false.
var x int
x = 42 // not strictly necessarily.
if false {
x = 42
}According to the truth table, when P is false, then Q does not necessarily need to be true.
What this means is that x does not need to be 42 for the program to be a tautology. We could let x be anything and the program would still be sound.
anecdotes
The go programming language is an imperative language.
In languages that are not declarative, the = is an assignment operator rather
than the mathematical equality relationship.
In some sense, we can interpret the assignment operator as a way to converge to equality by making the LHS equal to the RHS.
Programming languages can improve this convergence by making the LHS immutable. It gets significantly more challenging as we tend to declarativeness.