Questions tagged [lambda-calculus]

Church's formal system used in computatability, programming languages and proof theory to represent effective functions, programs and their computation, and proofs.

265 questions
Filter by
Sorted by
Tagged with
4 votes
0 answers
466 views

• 32.4k
25 votes
1 answer
2k views

• 113
9 votes
1 answer
351 views

Reading list on rewriting systems?

I am new to studying rewriting systems as a first year PhD student. I would like to propose a special topics course on rewriting theory, and I want to make sure I don't leave any of the original ...
5 votes
2 answers
669 views

Do Higher-Order Functions provide more power to Functional Programming?

My original question was: Is Kappa calculus less powerful than Lambda calculus? Does the lack of Higher-Order functions on a programming language excludes some programs that could only be written in ...
• 161
9 votes
1 answer
272 views

Origin of Church encodings

In which paper did Alonzo Church first describe Church encoding? I can't find any articles that actually cite the paper, but I am interested in reading it.
• 193
3 votes
2 answers
193 views

Labels for terms in the lambda calculus

In the lambda calculus, are there commonly accepted names for $x$ and $M$ when they appear in $\lambda x [M]$ ? Something along the lines of "binder" and "bindee"?
• 133
16 votes
1 answer
1k views

Can boolean algebra be expressed in simply typed lambda caclulus?

Boolean algebra can be expressed in untyped lambda calculus in (for example) this way. ...
16 votes
6 answers
2k views

What is the point of calling $\lambda$-calculus an algebra?

What is the difference of calling $\lambda$-calculus an algebra instead of a calculus? I raise this question because I read somewhere the line "$\lambda$-calculus is not a calculus but an algebra" (...
• 2,775
-6 votes
1 answer
260 views

Lambda Calculus - are these two expressions equivalent? [closed]

(λa.(λb.λc.b)) and (λa.λb.λc.b) I was wondering if someone could explain, using mostly English, what that lambda-calculus expression is supposed to mean, and whether there is any difference between ...
• 11
3 votes
2 answers
425 views

Does using Normal Order Evaluation instead of Normal Order Reduction lose the Normalization theorem?

Normal Order Reduction (NOR) reduce the leftmost, outermost redex. Normal Order Evaluation (NOE) reduce the leftmost, outermost redex, but not within the body of abstractions. So (λw. (λx.x) z) is ...
• 149
13 votes
6 answers
3k views

Functions that typed lambda calculus cannot compute

I just want to know some examples of the functions that can be computed by the untyped lambda calculus but not by typed lambda calculi. As I am a beginner, some reiteration of background information ...
7 votes
1 answer
327 views

How to define eta-equivalence for F-omega types?

There are (at least) two styles for defining a (declarative) equivalence judgement for a typed lambda calculus: via a plain relation $t_1 = t_2$, via an indexed relation $\Gamma \vdash t_1 = t_2 : T$...
• 1,310
1 vote
1 answer
343 views

Can "$x(\lambda y.P\;)z$" be $\beta$-reduced?

Consider the untyped $\lambda$-calculus expression $$x(\lambda y.P\;)z$$ ...where (FWIW) $z$ is not free in $P$, and $P$ does not contain a redex. Can this expression be $\beta$-reduced? I've ...
• 531
6 votes
1 answer
436 views

• 181
12 votes
1 answer
459 views

• 32.4k