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Heron-Centric: Ruminations of a Language Designer
What is the type of 42?
by Christopher Diggins
October 25, 2006
In Joy any number is an executable program, which pushes the the number on to the stack. This begs the question: what is the type of 42? In Cat I created two separate types, but now I am rethinking that choice.


When I was designing Cat I started with the assumption that the type of a number such as 42, must be a function which pushes a primitive integer type onto the stack. So the type of 42 would be:

42 : ()->(int)
The type of a function which yielded 42 would be:
[42] : ()->(()->(int))
In Joy the operation for evaluating functions is "i". The equivalent in Cat is "eval". The type of eval in Cat currently is:
eval : (A (A:any*)->(B:any*))->(B)
This meant that the following was badly typed in Cat:
42 eval
This is because eval expected a function on the top of the stack, but 42 produced a primitive on the top of the stack. You would have to instead write:
[42] eval

The decision for this type design was based on two things:

  1. That kind of type system was more familiar to me
  2. The programs more closely mapped to assembly language as-is
In assembly an operation which yields 42 and the value 42 are very different things. My thought was that I wanted to be able to trivially map Cat functions to assembly code. My concern is that the execution loop of an assembly program where values were executable would be non-trivial. I assumed you would need a switch statement and this would signficiantly hurt performance (Cat is striving to become a full competitor with real assembly code, so performance is a big concern). I am no longer convinced that this would actually be a problem.

The first issue is writing the type of numbers. It appears that what is needed is the ability to name new types and express them recursively:

42 : int;
int = ()->(int);
The next challenge is converting to assembly code. I haven't worked out all of the details, but I believe that when generating assembly, I need to simply insert type conversion routines at key places (i.e. where an integer is being executed, or treated like a function).

Do all this seem sane and rational?

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About the Blogger

Christopher Diggins is a software developer and freelance writer. Christopher loves programming, but is eternally frustrated by the shortcomings of modern programming languages. As would any reasonable person in his shoes, he decided to quit his day job to write his own ( ). Christopher is the co-author of the C++ Cookbook from O'Reilly. Christopher can be reached through his home page at

This weblog entry is Copyright © 2006 Christopher Diggins. All rights reserved.

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