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### Recursive definitions, How it is done?

I read that recursive definitions, refer to the definition of a function in that function body, cannot be done in $\lambda$-calculus, but recursion can be achieved by using $Y$ combinator. As I know, ...
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### Is this a generic way to convert any recursive procedure to tail-recursion?

It seems that I've found a generic way to convert any recursive procedure to tail-recursion: Define a helper sub-procedure with an extra "result" parameter. Apply what would be applied to the ...
116 views

### Undecidable definition of pure function?

I am trying to come up with a formal definition for functional purity in a simple programming language (think JavaScript). What I've got so far is this: DEFINITION: A statement is impure if ...
864 views

### Does the Y combinator contradict the Curry-Howard correspondence?

The Y combinator has the type $(a \rightarrow a) \rightarrow a$. By the Curry-Howard Correspondence, because the type $(a \rightarrow a) \rightarrow a$ is inhabited, it must correspond to a true ...
90 views

### Recursive equations vs. inference rules

It seems to me that recursive equations can always be presented as inference rules. For the forward direction, an example is addition over Peono numerals (built from $O$ and $S(\_)$)  \begin{align}...