5 ms·

To Dissect a Mockingbird: A Graphical Notation for the Lambda Calculus (1996)

42 points by louthy 13y ago

Sniffnoy 13y ago
I'm going to repeat my comment from last time this came up-- this is a really neat way of getting around the use of dummy variables, but why does he only talk about beta reduction and never mention eta reduction? Describing eta reduction in this notation is still easy.
tromp 13y ago
My alternative graphical notation: http://www.cwi.nl/~tromp/cl/diagrams.html http://www.cwi.nl/~tromp/cl/diagrams.html (also linked to at the bottom of the article) Example: predecessor function on Church numerals: ┬────────── ┼─────┬──── ┼─────┼─┬── │ ──┬─┼ ┼ ┬ │ ┬─┼─┼ │ │ │ │ ├─┘ │ │ │ ├─┘ │ │ └─┤ │ │ └─────┤ │ └─┘
symmetricsaurus 13y ago
I did like this. There is a certain elegance[1] to diagram based descriptions of mathematical/physical concepts. Another that is maybe more similar in that it removes a lot of dummy variables(indices in this case) is the Penrose graphical notation[2] for tensors. I have actually never calculated anything using these diagrams so I don't know how practical they are. [1]:http://en.wikipedia.org/wiki/Feynman_diagram http://en.wikipedia.org/wiki/Feynman_diagram [2]:http://en.wikipedia.org/wiki/Penrose_graphical_notation http://en.wikipedia.org/wiki/Penrose_graphical_notation
arethuza 13y ago
Given this and the other relevant article on the front page about CSS I'm now going to spend the rest of the day wondering if you can implement Starling and Kestrel in CSS rather than getting work done.... :-) [I know the answer is almost certainly "you can't" - but I am intrigued as to how close you can get]
cscheid 13y ago
Reminds me of the Bret Victor's "Alligator Eggs!": http://worrydream.com/AlligatorEggs/ http://worrydream.com/AlligatorEggs/
peteretep 13y ago
I read this a while ago, and have been telling people that Haskell's `id` stands for `idiot` since then...
judk 13y ago
The notation is interesting, but the "bird song "metaphor" makes me suspect that this paper inspired the misguided era of monad metaphors that followed. Birds, burritos, spacesuits ...

42 points by louthy 13y ago

I'm going to repeat my comment from last time this came up-- this is a really neat way of getting around the use of dummy variables, but why does he only talk about beta reduction and never mention eta reduction? Describing eta reduction in this notation is still easy.

tromp 13y ago

My alternative graphical notation: http://www.cwi.nl/~tromp/cl/diagrams.html http://www.cwi.nl/~tromp/cl/diagrams.html (also linked to at the bottom of the article) Example: predecessor function on Church numerals: ┬────────── ┼─────┬──── ┼─────┼─┬── │ ──┬─┼ ┼ ┬ │ ┬─┼─┼ │ │ │ │ ├─┘ │ │ │ ├─┘ │ │ └─┤ │ │ └─────┤ │ └─┘

symmetricsaurus 13y ago

I did like this. There is a certain elegance[1] to diagram based descriptions of mathematical/physical concepts. Another that is maybe more similar in that it removes a lot of dummy variables(indices in this case) is the Penrose graphical notation[2] for tensors. I have actually never calculated anything using these diagrams so I don't know how practical they are. [1]:http://en.wikipedia.org/wiki/Feynman_diagram http://en.wikipedia.org/wiki/Feynman_diagram [2]:http://en.wikipedia.org/wiki/Penrose_graphical_notation http://en.wikipedia.org/wiki/Penrose_graphical_notation

arethuza 13y ago

Given this and the other relevant article on the front page about CSS I'm now going to spend the rest of the day wondering if you can implement Starling and Kestrel in CSS rather than getting work done.... :-) [I know the answer is almost certainly "you can't" - but I am intrigued as to how close you can get]

cscheid 13y ago

Reminds me of the Bret Victor's "Alligator Eggs!": http://worrydream.com/AlligatorEggs/ http://worrydream.com/AlligatorEggs/

peteretep 13y ago

I read this a while ago, and have been telling people that Haskell's `id` stands for `idiot` since then...

judk 13y ago

The notation is interesting, but the "bird song "metaphor" makes me suspect that this paper inspired the misguided era of monad metaphors that followed. Birds, burritos, spacesuits ...