------------------------------------------------------------------------ -- The lenses fst and snd ------------------------------------------------------------------------ -- This module uses univalence without tracking such uses in the types -- of functions, and it is not parametrised by a notion of equality, -- it uses path equality. {-# OPTIONS --guardedness #-} module README.Fst-snd where open import Equality.Path open import Equality.Path.Univalence open import Prelude open import Equivalence.Erased.Cubical equality-with-paths as EEq using (_≃ᴱ_) import Lens.Non-dependent.Higher.Coinductive.Small.Erased equality-with-paths as S import Lens.Non-dependent.Higher.Erased equality-with-paths as E private variable a : Level A B : Type a -- A static variant of one consequence of S.Lens≃ᴱLensᴱ. Applications -- of static functions are normalised by (at least) the GHC backend. Lens→Lens : E.Lens A B → S.Lens univ A B Lens→Lens = _≃ᴱ_.from (S.Lens≃ᴱLensᴱ ⊠ univ) {-# STATIC Lens→Lens #-} -- A lens for the first projection. fst : S.Lens univ (A × B) A fst = Lens→Lens E.fst -- A lens for the second projection. -- -- With the implementation that this lens had at the time of writing -- (dependencies may later have changed) it turned out that when the -- lens was compiled using the non-strict GHC backend of a certain -- development version of Agda and GHC 9.0.1, then GHC's flag -- -ddump-simpl suggested that you ended up with code that could lead -- to a space leak: the code for the setter was something like -- -- \p y -> Pair (case p of { Pair x _ -> x }) y -- -- (where names have been changed, and code related to coercions and -- casts has been removed). -- -- Note that, unlike the lens snd^C discussed in "Compiling Programs -- with Erased Univalence", this one (as well as the one below) takes -- two universe level arguments. snd-with-space-leak : S.Lens univ (A × B) B snd-with-space-leak = Lens→Lens E.snd -- A lens for the second projection. -- -- This variant did not seem to have the problem exhibited by -- snd-with-space-leak: the code for the setter was something like -- -- \p y -> case p of { Pair x _ -> Pair x y }. snd : S.Lens univ (A × B) B snd = S.with-other-setter (Lens→Lens E.snd) (λ { (x , _) y → (x , y) }) ((λ (x , _) y → (x , y)) ≡⟨⟩ E.Lens.set E.snd ≡⟨ sym $ proj₂ $ proj₂ (S.Lens≃ᴱLensᴱ-preserves-getters-and-setters ⊠ univ univ) E.snd ⟩∎ S.Lens.set (Lens→Lens E.snd) ∎)