session 2
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@ -38,3 +38,9 @@ Because it is the simplest recursive data structure. It is a recursive data stru
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The tree is simply too complex. Linked lists are easy.
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The tree is simply too complex. Linked lists are easy.
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## [16th of March - Deriving types]
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> How does one do this systematically?
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> Lazy and singly-linked lists, what's the relation?
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@ -10,6 +10,10 @@
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| Proof on lists | Proving properties of functions that operate on lists | 😕 |
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| Proof on lists | Proving properties of functions that operate on lists | 😕 |
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| Proof on trees/ADTs | Proving properties of functions that operate on trees or ADTs | 😕 |
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| Proof on trees/ADTs | Proving properties of functions that operate on trees or ADTs | 😕 |
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## Deducing types systematically
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### (:).(:)
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```hs
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```hs
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expr = (:) . (:)
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expr = (:) . (:)
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@ -41,24 +45,24 @@ expr :: a -> [[a] -> [a]] -> [[a] -> [a]]
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```
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```
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### `f = \x y -> x (x (x y))` [^1]
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```hs
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```hs
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f = \x y -> x (x (x y))
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f = \x y -> x (x (x y))
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```
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```
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Rigorous solution of the above.
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## Questions
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## Look into
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> How does one do the equations?
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> How does one do the equations?
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> CLI is functional lol
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> CLI is functional?
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> Lazy and singly-linked lists
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> Lazy and singly-linked lists, what's the relation?
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> Y combinator - ?
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> Y combinator?
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## Resources
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## Resources
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- [course](https://www.cis.upenn.edu/~cis1940/spring15/lectures.html)
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- [course](https://www.cis.upenn.edu/~cis1940/spring15/lectures.html)
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- [standard list](https://hackage.haskell.org/package/base-4.21.0.0/docs/Data-List.html)
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- [standard list](https://hackage.haskell.org/package/base-4.21.0.0/docs/Data-List.html)
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[^1]: need to find the actual rigorous way of doing this
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