diff options
| -rw-r--r-- | BFF.agda | 53 | ||||
| -rw-r--r-- | Everything.agda | 1 | ||||
| -rw-r--r-- | GetTypes.agda | 35 | ||||
| -rw-r--r-- | Instances.agda | 18 | ||||
| -rw-r--r-- | Structures.agda | 60 |
5 files changed, 150 insertions, 17 deletions
@@ -15,11 +15,13 @@ open import Relation.Binary using (Setoid ; DecSetoid ; module DecSetoid) open import FinMap open import Generic using (sequenceV ; ≡-to-Π) +open import Structures using (Shaped ; module Shaped) +open import Instances using (VecShaped) import CheckInsert -open import GetTypes using (VecVec-to-PartialVecVec) +open import GetTypes using (VecVec-to-PartialVecVec ; PartialVecVec-to-PartialShapeVec) -module PartialVecBFF (A : DecSetoid ℓ₀ ℓ₀) where - open GetTypes.PartialVecVec public using (Get) +module PartialShapeBFF (A : DecSetoid ℓ₀ ℓ₀) where + open GetTypes.PartialShapeVec public using (Get ; module Get) open module A = DecSetoid A using (Carrier) renaming (_≟_ to deq) open CheckInsert A @@ -27,27 +29,48 @@ module PartialVecBFF (A : DecSetoid ℓ₀ ℓ₀) where assoc []V []V = just empty assoc (i ∷V is) (b ∷V bs) = (assoc is bs) >>= (checkInsert i b) + enumerate : {S : Set} {C : Set → S → Set} → (ShapeT : Shaped S C) → (s : S) → C (Fin (Shaped.arity ShapeT s)) s + enumerate ShapeT s = fill s (allFin (arity s)) + where open Shaped ShapeT + + denumerate : {S : Set} {C : Set → S → Set} → (ShapeT : Shaped S C) → {α : Set} {s : S} → (c : C α s) → Fin (Shaped.arity ShapeT s) → α + denumerate ShapeT c = flip lookupV (Shaped.content ShapeT c) + + bff : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → Get.Container G Carrier (Get.|gl₁| G i) → Vec Carrier (Get.|gl₂| G j) → Maybe (Get.Container G (Maybe Carrier) (Get.|gl₁| G j)) + bff G {i} j s v = let s′ = enumerate ShapeT (|gl₁| i) + t′ = get s′ + g = fromFunc (denumerate ShapeT s) + g′ = delete-many t′ g + t = enumerate ShapeT (|gl₁| j) + h = assoc (get t) v + h′ = (flip union (reshape g′ (arity (|gl₁| j)))) <$> h + in ((λ f → fmap f t) ∘ flip lookupM) <$> h′ + where open Get G + + sbff : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → Get.Container G Carrier (Get.|gl₁| G i) → Vec Carrier (Get.|gl₂| G j) → Maybe (Get.Container G Carrier (Get.|gl₁| G j)) + sbff G j s v = bff G j s v >>= Get.sequence G + +module PartialVecBFF (A : DecSetoid ℓ₀ ℓ₀) where + open GetTypes.PartialVecVec public using (Get) + open module A = DecSetoid A using (Carrier) renaming (_≟_ to deq) + open CheckInsert A + + open PartialShapeBFF A public using (assoc) + enumerate : {n : ℕ} → Vec Carrier n → Vec (Fin n) n - enumerate {n} _ = allFin n + enumerate {n} _ = PartialShapeBFF.enumerate A VecShaped n enumeratel : (n : ℕ) → Vec (Fin n) n - enumeratel = allFin + enumeratel = PartialShapeBFF.enumerate A VecShaped denumerate : {n : ℕ} → Vec Carrier n → Fin n → Carrier - denumerate = flip lookupV + denumerate = PartialShapeBFF.denumerate A VecShaped bff : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → Vec Carrier (Get.|gl₁| G i) → Vec Carrier (Get.|gl₂| G j) → Maybe (Vec (Maybe Carrier) (Get.|gl₁| G j)) - bff G i s v = let s′ = enumerate s - t′ = Get.get G s′ - g = fromFunc (denumerate s) - g′ = delete-many t′ g - t = enumeratel (Get.|gl₁| G i) - h = assoc (Get.get G t) v - h′ = (flip union (reshape g′ (Get.|gl₁| G i))) <$> h - in (flip mapV t ∘ flip lookupM) <$> h′ + bff G j s v = PartialShapeBFF.bff A (PartialVecVec-to-PartialShapeVec G) j s v sbff : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → Vec Carrier (Get.|gl₁| G i) → Vec Carrier (Get.|gl₂| G j) → Maybe (Vec Carrier (Get.|gl₁| G j)) - sbff G j s v = bff G j s v >>= sequenceV + sbff G j s v = PartialShapeBFF.sbff A (PartialVecVec-to-PartialShapeVec G) j s v module VecBFF (A : DecSetoid ℓ₀ ℓ₀) where open GetTypes.VecVec public using (Get) diff --git a/Everything.agda b/Everything.agda index 7383dd5..5ca5550 100644 --- a/Everything.agda +++ b/Everything.agda @@ -3,6 +3,7 @@ module Everything where import Generic import Structures +import Instances import FinMap import CheckInsert import GetTypes diff --git a/GetTypes.agda b/GetTypes.agda index eb72cea..0db3f31 100644 --- a/GetTypes.agda +++ b/GetTypes.agda @@ -12,6 +12,8 @@ open import Relation.Binary using (Setoid) open Injection using (to) open import Generic using (≡-to-Π) +open import Structures using (Shaped ; module Shaped) +open import Instances using (VecShaped) module ListList where record Get : Set₁ where @@ -49,3 +51,36 @@ VecVec-to-PartialVecVec G = record ; get = get ; free-theorem = free-theorem } where open VecVec.Get G + +module PartialShapeVec where + record Get : Set₁ where + field + Shape : Set + Container : Set → Shape → Set + ShapeT : Shaped Shape Container + + I : Setoid ℓ₀ ℓ₀ + gl₁ : I ↪ EqSetoid Shape + gl₂ : I ⟶ EqSetoid ℕ + + |I| = Setoid.Carrier I + |gl₁| = _⟨$⟩_ (to gl₁) + |gl₂| = _⟨$⟩_ gl₂ + + open Shaped ShapeT using (fmap) + + field + get : {A : Set} {i : |I|} → Container A (|gl₁| i) → Vec A (|gl₂| i) + free-theorem : {α β : Set} → (f : α → β) → {i : |I|} → get {_} {i} ∘ fmap f ≗ mapV f ∘ get + + open Shaped ShapeT public + +PartialVecVec-to-PartialShapeVec : PartialVecVec.Get → PartialShapeVec.Get +PartialVecVec-to-PartialShapeVec G = record + { ShapeT = VecShaped + ; I = I + ; gl₁ = gl₁ + ; gl₂ = gl₂ + ; get = get + ; free-theorem = free-theorem + } where open PartialVecVec.Get G diff --git a/Instances.agda b/Instances.agda new file mode 100644 index 0000000..faff6f8 --- /dev/null +++ b/Instances.agda @@ -0,0 +1,18 @@ +module Instances where + +open import Data.Nat using (ℕ) +open import Data.Vec using (Vec) +open import Function using (id) +open import Relation.Binary.PropositionalEquality using (refl) + +open import Structures using (Shaped) + +VecShaped : Shaped ℕ Vec +VecShaped = record + { arity = id + ; content = id + ; fill = λ _ → id + ; isShaped = record + { content-fill = λ _ → refl + ; fill-content = λ _ _ → refl + } } diff --git a/Structures.agda b/Structures.agda index f1fd85b..10abd42 100644 --- a/Structures.agda +++ b/Structures.agda @@ -1,10 +1,17 @@ module Structures where open import Category.Functor using (RawFunctor ; module RawFunctor) -open import Function using (_∘_ ; id) +open import Category.Monad using (module RawMonad) +open import Data.Maybe using (Maybe) renaming (monad to MaybeMonad) +open import Data.Nat using (ℕ) +open import Data.Vec as V using (Vec) +import Data.Vec.Properties as VP +open import Function using (_∘_ ; flip ; id) open import Function.Equality using (_⟶_ ; _⇨_ ; _⟨$⟩_) open import Relation.Binary using (_Preserves_⟶_) -open import Relation.Binary.PropositionalEquality as P using (_≗_ ; _≡_ ; refl) +open import Relation.Binary.PropositionalEquality as P using (_≗_ ; _≡_ ; refl ; module ≡-Reasoning) + +open import Generic using (sequenceV) record IsFunctor (F : Set → Set) (f : {α β : Set} → (α → β) → F α → F β) : Set₁ where field @@ -29,3 +36,52 @@ record Functor (f : Set → Set) : Set₁ where open RawFunctor rawfunctor public open IsFunctor isFunctor public + +record IsShaped (S : Set) + (C : Set → S → Set) + (arity : S → ℕ) + (content : {α : Set} {s : S} → C α s → Vec α (arity s)) + (fill : {α : Set} → (s : S) → Vec α (arity s) → C α s) + : Set₁ where + field + content-fill : {α : Set} {s : S} → (c : C α s) → fill s (content c) ≡ c + fill-content : {α : Set} → (s : S) → (v : Vec α (arity s)) → content (fill s v) ≡ v + + fmap : {α β : Set} → (f : α → β) → {s : S} → C α s → C β s + fmap f {s} c = fill s (V.map f (content c)) + + isFunctor : (s : S) → IsFunctor (flip C s) (λ f → fmap f) + isFunctor s = record + { cong = λ g≗h c → P.cong (fill s) (VP.map-cong g≗h (content c)) + ; identity = λ c → begin + fill s (V.map id (content c)) + ≡⟨ P.cong (fill s) (VP.map-id (content c)) ⟩ + fill s (content c) + ≡⟨ content-fill c ⟩ + c ∎ + ; composition = λ g h c → P.cong (fill s) (begin + V.map (g ∘ h) (content c) + ≡⟨ VP.map-∘ g h (content c) ⟩ + V.map g (V.map h (content c)) + ≡⟨ P.cong (V.map g) (P.sym (fill-content s (V.map h (content c)))) ⟩ + V.map g (content (fill s (V.map h (content c)))) ∎) + } where open ≡-Reasoning + + fmap-content : {α β : Set} → (f : α → β) → {s : S} → content {β} {s} ∘ fmap f ≗ V.map f ∘ content + fmap-content f c = fill-content _ (V.map f (content c)) + fill-fmap : {α β : Set} → (f : α → β) → (s : S) → fmap f ∘ fill s ≗ fill s ∘ V.map f + fill-fmap f s v = P.cong (fill s ∘ V.map f) (fill-content s v) + + sequence : {α : Set} {s : S} → C (Maybe α) s → Maybe (C α s) + sequence {s = s} c = fill s <$> sequenceV (content c) + where open RawMonad MaybeMonad + +record Shaped (S : Set) (C : Set → S → Set) : Set₁ where + field + arity : S → ℕ + content : {α : Set} {s : S} → C α s → Vec α (arity s) + fill : {α : Set} → (s : S) → Vec α (arity s) → C α s + + isShaped : IsShaped S C arity content fill + + open IsShaped isShaped public |