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wadler 2019-11-12 21:05:11 +00:00
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src/plfa/part1/Lists.lagda.md
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@ -1089,12 +1089,13 @@ into two lists that merge to give the original list, where all
elements of one list satisfy the predicate, and all elements of elements of one list satisfy the predicate, and all elements of
the other do not satisfy the predicate. the other do not satisfy the predicate.
Define the following variant of the traditional `filter` function on lists, Define the following variant of the traditional `filter` function on
which given a decidable predicate and a list returns all elements of the lists, which given a decidable predicate and a list returns a list of
list satisfying the predicate: elements that satisfy the predicate and a list of elements that don't,
with their corresponding proofs.
split : ∀ {A : Set} {P : A → Set} (P? : Decidable P) (xs : List A) split : ∀ {A : Set} {P : A → Set} (P? : Decidable P) (zs : List A)
→ ∃[ ys ] ∃[ zs ] ( merge xs ys zs × All P ys × All (¬_ ∘ P) zs ) → ∃[ xs ] ∃[ ys ] ( merge xs ys zs × All P xs × All (¬_ ∘ P) ys )
``` ```
-- Your code goes here -- Your code goes here