Write You a Haskell Stephen Diehl

for an expression g(f(x), f(x)), this is always equivalent to g(a, a). In other words the values computed
by functions can always be substituted freely at all occurrences.
e central idea of functional programming is to structure our programs in such a way that we can reason
about them as a system of equations just like we can in mathematics. e evaluation of a pure function
is one in which side effects are prohibited, a function may only return a result without altering the world
in any observable way.
e implementation may perform effects, but central to this definition is the unobservability of such
effects. A function is said to be referentially transparent if replacing a function with its computed value
output yields the same observable behavior.
By contrast impure functions are ones which allow unrestricted and observable side effects. e invocation
of an impure function always allows for the possibility of performing any functionality before
yielding a value.
// impure: mutation side effects
function f() {
x += 3;
return 42;
}
// impure: international side effects
function f() {
launchMissiles();
return 42;
}
e behavior of a pure function is independent of where and when it is evaluated, whereas the behavior
of an impure function is intrinsically tied to its execution order.
Functional programming is defined simply as programming strictly with pure referentially transparent
functions.
Static Typing
Types are a formal language integrated with a programming language that refines the space of allowable
behavior and degree of expressible programs for the language. Types are the world’s most popular formal
method for analyzing programs.
In a language like Python all expressions have the same type at compile time, and all syntactically valid
programs can be evaluated. In the case where the program is nonsensical the runtime will bubble up
exceptions during evaluation. e Python interpreter makes no attempt to analyze the given program
for soundness at all before running it.
>>> True & ”false”
Traceback (most recent call last):
8