70 lines
2.4 KiB
Markdown
70 lines
2.4 KiB
Markdown
---
|
||
created_at: '2016-02-04T23:03:15.000Z'
|
||
title: Why Church chose lambda (2009)
|
||
url: http://www.wisdomandwonder.com/link/3022/why-church-chose-lambda
|
||
author: networked
|
||
points: 56
|
||
story_text:
|
||
comment_text:
|
||
num_comments: 9
|
||
story_id:
|
||
story_title:
|
||
story_url:
|
||
parent_id:
|
||
created_at_i: 1454626995
|
||
_tags:
|
||
- story
|
||
- author_networked
|
||
- story_11037982
|
||
objectID: '11037982'
|
||
|
||
---
|
||
Todd
|
||
[asked](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033320.html)
|
||
“Why \[did Church choose\] lambda and not some other Greek letter?”.
|
||
Here are three
|
||
answers:
|
||
|
||
### 1
|
||
|
||
[Matthias](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033321.html):
|
||
|
||
> The story is that in the 10s and 20s, mathematicians and logicians
|
||
> used ^ as a notation for set abstraction, as in ^i : i is prime.
|
||
> Church used ^\` (i.e., a primed version of this symbol) for function
|
||
> abstraction, because functions are just sets with extra properties.
|
||
> The first type setter/secretary read it as λ and Church was fine with.
|
||
> True or not? I don’t know but it’s fun.
|
||
|
||
### 2
|
||
|
||
[This
|
||
paper](http://www-maths.swan.ac.uk/staff/jrh/papers/JRHHislamWeb.pdf)
|
||
(link provided by Dave Herman
|
||
[here](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033322.html)):
|
||
|
||
> (By the way, why did Church choose the notation “λ”? In \[Church,
|
||
> 1964, §2\] he stated clearly that it came from the notation “xˆ” used
|
||
> for class-abstraction by Whitehead and Russell, by first modifying
|
||
> “xˆ” to “ˆx” to distinguish function abstraction from
|
||
> class-abstraction, and then changing “ˆ” to “λ” for ease of printing.
|
||
> This origin was also reported in \[Rosser, 1984, p.338\]. On the other
|
||
> hand, in his later years Church told two enquirers that the choice was
|
||
> more accidental: a symbol was needed and “λ” just happened to be
|
||
> chosen.)
|
||
|
||
### 3
|
||
|
||
[This
|
||
paper](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.7908)
|
||
(link provided by Dave Herman
|
||
[here](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033322.html)):
|
||
|
||
> We end this introduction by telling what seems to be the story how the
|
||
> letter ‘λ’ was chosen to denote function abstraction. In \[100\]
|
||
> Principia Mathematica the notation for the function f with f(x) = 2x +
|
||
> 1 is 2xˆ +1. Church originally intended to use the notation xˆ .2x+1.
|
||
> The typesetter could not position the hat on top of the x and placed
|
||
> it in front of it, resulting in ˆx.2x + 1. Then another typesetter
|
||
> changed it into λx.2x + 1.
|