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Results tagged with lambda-calculus
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user 82
λ-calculus is a formal system for function definition, function application and recursion which forms the mathematical basis of functional programming.
15
votes
Accepted
Is there a difference between $\lambda xy.xy$ and $\lambda x.\lambda y.xy$?
These are just differences of notations. $λxyz.t$ is short for $λx.λy.λz.t$. No magic here.
Indeed, $\mbox{pair}=λxyp.pxy$ but you tend to emphasize that $\mbox{pair}\,t\,u$ is a function $λp.ptu$ by …
- 9,548
1
vote
Accepted
Showing the function=? is impossible
Using the halting problem seems like the good solution. Suppose you have a function red that takes the code of a function (or λ-term) (or a untyped function), reduces one step (or β-redex) in it and r …
- 9,548
17
votes
Characterization of lambda-terms that have union types
I just want to explain why intersection types are well-suited to characterize classes of normalization (strong, head or weak), whereas other type systems can not. (simply-typed or system F).
The key …
- 9,548
11
votes
Accepted
Do Higher Order Functions provide more power to Functional Programming?
In a functional programming language that is powerful enough (for example, with data types to implement closures) you can eliminate all uses of higher order by the transformation of defunctionalizatio …
- 9,548
13
votes
Representing Negative and Complex Numbers Using Lambda Calculus
Lambda-calculus can encode most data structures and basic types. For example, you can encode a pair of existing terms in the lambda calculus, using the same Church encoding that you usually see to enc …
- 9,548