From Binary to High-Level Languages: The Origin of Compilers and Recursion

Programmers often wonder how common features are implemented, but few consider how programming languages themselves are built on top of the CPU’s binary logic.

The CPU understands only switches, i.e., 0 and 1. Early programs were literal binary strings written on punched tape:

1101101010011010

1001001100101001

1100100011011110

1011101101010010

These raw bits are meaningless to humans, yet the CPU can execute them directly.

To make programming more human‑readable, the binary instructions were mapped to mnemonic assembly statements:

sub $8, %rsp

mov $.LC0, %edi

call puts

mov $0, %eax

Now programmers can think in terms of ADD, SUB, MOV instead of endless 0/1 streams.

Assembly is still a low‑level language; it requires explicit handling of every detail. To express more complex logic, programmers introduced control‑flow constructs:

if ***

...

else ***

...

and loops:

while ***

...

and reusable blocks (functions):

func abc:

...

These patterns form the basis of higher‑level languages. However, nesting of if , while , and functions can become arbitrarily deep, leading to the need for a systematic representation.

Recursion provides a natural way to describe such nested structures. A simple recursive definition of a programming grammar can be expressed as:

if : if bool statement else statement

for : while bool statement

statement : if | for | statement

From this grammar, a syntax tree (AST) can be built. Leaves of the tree correspond to simple statements that can be directly translated to machine instructions; the translation then propagates upward, eventually producing full machine code.

This process is what a compiler does: it parses human‑readable source code into an abstract syntax tree and then generates the corresponding CPU instructions.

The narrative also highlights that the same recursive idea appears in mathematics (e.g., the Fibonacci recurrence f(x) = f(x‑1) + f(x‑2) ) and in natural structures like trees, reinforcing the universality of recursion in both code and theory.