<p>I know once could start from the popular Church encodings of booleans, ints, etc and arbitrarily obfuscate and complicate them to obtain new representations of the same concepts, but are there other popular encodings that aren't sourced this way?</p>

CC BY-SA 4.0
2019-12-13T12:09:40.423Z
There is the [Scott encoding](https://en.wikipedia.org/wiki/Mogensen–Scott_encoding).
Andrej Bauer
CC BY-SA 4.0
2019-12-14T13:18:27.113Z
I can recommend the paper ["Efficiency of Lambda-Encodings in Total Type
Theory"](https://www.cambridge.org/core/journals/journal-of-functional-programming/article/efficiency-of-lambdaencodings-in-total-type-theory/61BB015E068EAC16C6C31D5F7654F3AD). It shows the Church, Scott, Parigot and Embedded Iterators encodings and compares their time/space efficiency.
Labbekak
<lambda-calculus>
Other popular lambda calculus encodings besides Church's?
Radu Stoenescu
# Other popular lambda calculus encodings besides Church's?

(Asked by: username_0 on 2019-12-13)

I know once could start from the popular Church encodings of booleans, ints, etc and arbitrarily obfuscate and complicate them to obtain new representations of the same concepts, but are there other popular encodings that aren't sourced this way?

**Tags:** lambda-calculus
> **Comments:**
> **username_1**: There is the [Scott encoding](https://en.wikipedia.org/wiki/Mogensen–Scott_encoding).  
> **username_2**: I can recommend the paper ["Efficiency of Lambda-Encodings in Total Type Theory"](https://www.cambridge.org/core/journals/journal-of-functional-programming/article/efficiency-of-lambdaencodings-in-total-type-theory/61BB015E068EAC16C6C31D5F7654F3AD). It shows the Church, Scott, Parigot and Embedded Iterators encodings and compares their time/space efficiency.  

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