DanilaFe/agda-spa
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Make 'MonotonicPredicate' into another typeclass

Browse Source 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-13 20:56:56 -07:00
parent 7571cb7451
commit 2f91ca113e
1 changed files with 6 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

12
MonotonicState.agda
View File

@ -93,9 +93,8 @@ Both P Q = (λ { s (t₁ , t₂) → (P s t₁ × Q s t₂) })
-- states'. We call such predicates monotonic as well, since they respect the -- states'. We call such predicates monotonic as well, since they respect the
-- ordering relation. -- ordering relation.
MonotonicPredicate : ∀ {T : S → Set s} {{ _ : Relaxable T }} → record MonotonicPredicate {T : S → Set s} {{ r : Relaxable T }} (P : DependentPredicate T) : Set s where
DependentPredicate T → Set s field relaxPredicate : ∀ (s₁ s₂ : S) (t₁ : T s₁) (s₁≼s₂ : s₁ ≼ s₂) →
MonotonicPredicate {T} {{r}} P = ∀ (s₁ s₂ : S) (t₁ : T s₁) (s₁≼s₂ : s₁ ≼ s₂) →
P s₁ t₁ → P s₂ (Relaxable.relax r s₁≼s₂ t₁) P s₁ t₁ → P s₂ (Relaxable.relax r s₁≼s₂ t₁)
-- A MonotonicState "monad" m has a certain property if its ouputs satisfy that -- A MonotonicState "monad" m has a certain property if its ouputs satisfy that
@ -106,11 +105,12 @@ always P m = ∀ s₁ → let (s₂ , t , _) = m s₁ in P s₂ t
⟨⊗⟩-reason : ∀ {T₁ T₂ : S → Set s} {{ _ : Relaxable T₁ }} ⟨⊗⟩-reason : ∀ {T₁ T₂ : S → Set s} {{ _ : Relaxable T₁ }}
{P : DependentPredicate T₁} {Q : DependentPredicate T₂} {P : DependentPredicate T₁} {Q : DependentPredicate T₂}
{P-Mono : MonotonicPredicate P} {{P-Mono : MonotonicPredicate P}}
{m₁ : MonotonicState T₁} {m₂ : MonotonicState T₂} → {m₁ : MonotonicState T₁} {m₂ : MonotonicState T₂} →
always P m₁ → always Q m₂ → always (Both P Q) (m₁ ⟨⊗⟩ m₂) always P m₁ → always Q m₂ → always (Both P Q) (m₁ ⟨⊗⟩ m₂)
⟨⊗⟩-reason {P-Mono = P-Mono} {m₁ = m₁} {m₂ = m₂} aP aQ s ⟨⊗⟩-reason {{P-Mono = P-Mono}} {m₁ = m₁} {m₂ = m₂} aP aQ s
with p ← aP s with p ← aP s
with (s' , (t₁ , s≼s')) ← m₁ s with (s' , (t₁ , s≼s')) ← m₁ s
with q ← aQ s' with q ← aQ s'
with (s'' , (t₂ , s'≼s'')) ← m₂ s' = (P-Mono _ _ _ s'≼s'' p , q) with (s'' , (t₂ , s'≼s'')) ← m₂ s' =
(MonotonicPredicate.relaxPredicate P-Mono _ _ _ s'≼s'' p , q)