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Diffstat (limited to 'FreeTheorems.agda')
-rw-r--r-- | FreeTheorems.agda | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/FreeTheorems.agda b/FreeTheorems.agda index f37cada..2695491 100644 --- a/FreeTheorems.agda +++ b/FreeTheorems.agda @@ -6,16 +6,28 @@ open import Data.Vec using (Vec) renaming (map to mapV) open import Function using (_∘_) open import Relation.Binary.PropositionalEquality using (_≗_) +import GetTypes + module ListList where get-type : Set₁ get-type = {A : Set} → List A → List A + open GetTypes.ListList public + postulate free-theorem : (get : get-type) → {α β : Set} → (f : α → β) → get ∘ map f ≗ map f ∘ get + assume-get : get-type → Get + assume-get get = record { get = get; free-theorem = free-theorem get } + module VecVec where get-type : (ℕ → ℕ) → Set₁ get-type getlen = {A : Set} {n : ℕ} → Vec A n → Vec A (getlen n) + open GetTypes.VecVec public + postulate free-theorem : {getlen : ℕ → ℕ} → (get : get-type getlen) → {α β : Set} → (f : α → β) → {n : ℕ} → get {_} {n} ∘ mapV f ≗ mapV f ∘ get + + assume-get : {getlen : ℕ → ℕ} → (get : get-type getlen) → Get + assume-get {getlen} get = record { getlen = getlen; get = get; free-theorem = free-theorem get } |