Changes

| accessdate = 2012-03-27}}</ref>

| accessdate = 2012-03-27}}</ref>

Computer users nowadays may not realise the severe technical constraints which applied to programming in the mid 1950's. Modern personal computers have the entire central processing unit on a single chip (integrated circuit), have main memories (RAM) containing many hundred of millions of bytes, and have processing speeds of several million instructions per second. The IBM 704 computer (fairly advanced for its time) had a central processor made up of many thousands of electronic valves (each the size of a light bulb), had a main memory of only four thousand 36-bit words, and had a processing speed of perhaps forty thousand instructions per second (modern mobile phones are more powerful than this).

Computer users nowadays may not realise the severe technical constraints which applied to programming in the mid 1950s. Modern personal computers have the entire central processing unit on a single chip (integrated circuit), have main memories (RAM) containing many hundred of millions of bytes, and have processing speeds of several million instructions per second. The IBM 704 computer (fairly advanced for its time) had a central processor made up of many thousands of electronic valves (each the size of a light bulb), had a main memory of only four thousand 36-bit words, and had a processing speed of perhaps forty thousand instructions per second (modern mobile phones are more powerful than this).

Most compilers in the 1950's and 1960's were written in low-level assembly languages; there wasn't much choice at that time since the computer hardware wasn't capable of supporting compilers written in high-level languages. The use of high-level languages for writing compilers became more mainstream with the advent of Pascal in 1970<ref>{{Cite web  

Most compilers in the 1950s and 1960s were written in low-level assembly languages; there wasn't much choice at that time since the computer hardware wasn't capable of supporting compilers written in high-level languages. The use of high-level languages for writing compilers became more mainstream with the advent of Pascal in 1970<ref>{{Cite web  

| title = Pascal-P: The portable Pascal compiler  

| title = Pascal-P: The portable Pascal compiler  

| url = http://www.moorecad.com/standardpascal/PascalP.html  

| url = http://www.moorecad.com/standardpascal/PascalP.html  

</ref> Some compilers can optionally generate extra code to check for many of these errors, and there are some software packages which can provide the same effect. Unfortunately this extra checking code can slow a program down by a factor of 10 or 20 times.

</ref> Some compilers can optionally generate extra code to check for many of these errors, and there are some software packages which can provide the same effect. Unfortunately this extra checking code can slow a program down by a factor of 10 or 20 times.

Research is continuing on the problem of proving that a program is correct. This is an extremely difficult problem - it has been shown that proving whether or not a program actually stops is [[undecidable]]. Furthermore the proofs are often a lot longer than the programs being proved so there is the additional problem of checking that the proof itself is correct. Bruce Schneier reports <ref>

Research is continuing on the problem of proving that a program is correct. This is an extremely difficult problem - it has been shown that proving whether or not a program actually stops is [[undecidable]]. Furthermore, the proofs are often a lot longer than the programs being proved so there is the additional problem of checking that the proof itself is correct. Bruce Schneier reports <ref>

{{cite web

{{cite web

| url=http://www.schneier.com/blog/archives/2009/10/proving_a_compu.html

| url=http://www.schneier.com/blog/archives/2009/10/proving_a_compu.html