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Arithmetic operations in simply typed lambda calculus
Manage episode 416402104 series 2823367
Content provided by Aaron Stump. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Aaron Stump or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://player.fm/legal.
It is maybe not so well known that arithmetic operations -- at least some of them -- can be implemented in simply typed lambda calculus (STLC). Church-encoded numbers can be given the simple type (A -> A) -> A -> A, for any simple type A. If we abbreviate that type as Nat_A, then addition and multiplication can both be typed in STLC, at type Nat_A -> Nat_A -> Nat_A. Interestingly, things change with exponentiation, which we will consider in the next episode.
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Manage episode 416402104 series 2823367
Content provided by Aaron Stump. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Aaron Stump or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://player.fm/legal.
It is maybe not so well known that arithmetic operations -- at least some of them -- can be implemented in simply typed lambda calculus (STLC). Church-encoded numbers can be given the simple type (A -> A) -> A -> A, for any simple type A. If we abbreviate that type as Nat_A, then addition and multiplication can both be typed in STLC, at type Nat_A -> Nat_A -> Nat_A. Interestingly, things change with exponentiation, which we will consider in the next episode.
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Similar to Iowa Type Theory Commute
Show notes are at https://stevelitchfield.com/sshow/chat.html
…
continue reading
Three nerds discussing tech, Apple, programming, and loosely related matters.
…
continue reading
Discover a whole new take on Artificial Intelligence with Squirro's educational podcast! Join host Lauren Hawker Zafer, a top voice in Artificial Intelligence on LinkedIn, for insightful chats that unravel the fascinating world of tech innovation, use case exploration and AI knowledge. Dive into candid discussions with accomplished industry experts and established academics. With each episode, you'll expand your grasp of cutting-edge technologies and their incredible impact on society, and y ...
…
continue reading
Hanselminutes is Fresh Air for Developers. A weekly commute-time podcast that promotes fresh technology and fresh voices. Talk and Tech for Developers, Life-long Learners, and Technologists.
…
continue reading
On The Bike Shed, hosts Joël Quenneville and Stephanie Minn discuss development experiences and challenges at thoughtbot with Ruby, Rails, JavaScript, and whatever else is drawing their attention, admiration, or ire this week.
…
continue reading
Download This Show is your weekly guide to the world of media, culture, and technology. From social media to gadgets, streaming services to privacy issues. Each week Marc Fennell and a team of people far smarter than him (his words, not ours) take a fun deep dive into how technology is reshaping our lives.
…
continue reading
A podcast about web design and development.
…
continue reading
A podcast featuring panelists of engineers from Netflix, Twitch, & Atlassian talking over drinks about all things software engineering.
…
continue reading
Embedded is the show for people who love gadgets. Making them, breaking them, and everything in between. Weekly interviews with engineers, educators, and enthusiasts. Find the show, blog, and more at embedded.fm.
…
continue reading
The director’s commentary track for Daring Fireball. Long digressions on Apple, technology, design, movies, and more.
…
continue reading
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Go offline with the Player FM app!
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