The Heart Of A Compiler
Written by Mike James   
Thursday, 01 April 2021
Article Index
The Heart Of A Compiler
Formula translation
A Solution

Fortran at last!

This order of evaluation problem was what faced the IBM team who had been assembled (no pun intended) to make the assault on computer science’s equivalent of getting a man on the moon - the automatic translation of arithmetic expressions.

The team, under the leadership of John Backus, was to construct a compiler for a computer language that could compile any arithmetic expression that a programmer cared to throw at it.

To do this they had to invent a way of writing down and making use of the rules of grammar for artificial languages such as programming languages and mathematical expressions. They invented the production rules as described above and a method of using the rules to parse the language and generate the correct assembly code.

The trick is to convert the expression into a syntax tree which makes clear the relationships between the operators and their priorities. Once you have the syntax tree then you can use it to generate the operations in the correct order by simply "walking" the tree.  For a more detailed explanation see: Grammar and Torture.

The six-month project actually took two years before the first compiler was available in 1956 and it took until April 1957 before working compilers were distributed to customers. It consisted of 25,000 lines of machine code on a magnetic tape and it was distributed, complete with bugs, to every IBM 704 installation.

The language was called FORTRAN standing for FORmula TRANslation and when they finally got it to work it revolutionized programming and made IBM the number one computer company for decades.

Notice that the name of the language was derived from FORMula TRANslation. Even though the language had lots of other new features, it was the fact that it could successfully convert an arbitrary arithmetic expression or formula into machine code that was its great claim to fame. Once you work out how to do this particular job the rest of the compiler was a matter of comparatively simple book keeping.


Related Articles

Assemblers and assembly language

Grammar and Torture

John Backus - the Father of Fortran

Brackets are Trees


Computer Memory and Pigeonholes


How Memory Works

Inside the Computer - Addressing

Inside the processor


The Essence Of Programming

Variables revisited


What Programmers Know



  1. The Computer - What's The Big Idea?*
  2. The Memory Principle - Computer Memory and Pigeonholes*
  3. Principles of Execution - The CPU
  4. The Essence Of Programming
  5. Variables - Scope, Lifetime And More*
  6. Binary Arithmetic
  7. Hexadecimal*
  8. Binary - Negative Numbers*
  9. Floating Point Numbers*
  10. Inside the Computer - Addressing
  11. The Mod Function
  12. Recursion
  13. The Lost Art Of The Storage Mapping Function *
  14. Hashing - The Greatest Idea In Programming
  15. Advanced Hashing
  16. XOR - The Magic Swap*
  17. Programmer's Introduction to XML
  18. From Data To Objects*
  19. What Exactly Is A First Class Function - And Why You Should Care*
  20. Stacks And Trees*
  21. The LIFO Stack - A Gentle Guide*
  22. Data Structures - Trees
  23. Inside Random Numbers
  24. The Monte Carlo Method
  25. Cache Memory And The Caching Principle
  26. Data Compression The Dictionary Way
  27. Dates Are Difficult*
  28. Sequential Storage*
  29. Magic of Merging*
  30. Power of Operators
  31. The Heart Of A Compiler*
  32. The Fundamentals of Pointers
  33. Functional And Dysfunctional Programming*

* Recently revised

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Last Updated ( Thursday, 01 April 2021 )