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Lighten dependencies of Data.Nat.Induction #1698

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Merged
MatthewDaggitt merged 2 commits into from
Feb 26, 2022
Merged

Lighten dependencies of Data.Nat.Induction #1698

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Lightened dependencies of Data.Nat.Induction
MatthewDaggitt Jan 24, 2022
1a3804e
Merge branch 'master' into induction-dependencies
MatthewDaggitt Feb 26, 2022
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22 changes: 10 additions & 12 deletions src/Data/Nat/Induction.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -8,16 +8,14 @@

module Data.Nat.Induction where

open import Function
open import Data.Nat.Base
open import Data.Nat.Properties using (<⇒<′)
open import Data.Product
open import Data.Unit.Polymorphic
open import Data.Unit.Polymorphic.Base
open import Function.Base
open import Induction
open import Induction.WellFounded as WF
open import Level using (Level)
open import Relation.Binary.PropositionalEquality
open import Relation.Unary

private
variable
Expand All @@ -35,11 +33,11 @@ Rec : ∀ ℓ → RecStruct ℕ ℓ ℓ
Rec ℓ P zero = ⊤
Rec ℓ P (suc n) = P n

recBuilder : ∀ {ℓ} → RecursorBuilder (Rec ℓ)
recBuilder : RecursorBuilder (Rec ℓ)
recBuilder P f zero = _
recBuilder P f (suc n) = f n (recBuilder P f n)

rec : ∀ {ℓ} → Recursor (Rec ℓ)
rec : Recursor (Rec ℓ)
rec = build recBuilder

------------------------------------------------------------------------
Expand All @@ -49,18 +47,18 @@ CRec : ∀ ℓ → RecStruct ℕ ℓ ℓ
CRec ℓ P zero = ⊤
CRec ℓ P (suc n) = P n × CRec ℓ P n

cRecBuilder : ∀ {ℓ} → RecursorBuilder (CRec ℓ)
cRecBuilder : RecursorBuilder (CRec ℓ)
cRecBuilder P f zero = _
cRecBuilder P f (suc n) = f n ih , ih
where ih = cRecBuilder P f n

cRec : ∀ {ℓ} → Recursor (CRec ℓ)
cRec : Recursor (CRec ℓ)
cRec = build cRecBuilder

------------------------------------------------------------------------
-- Complete induction based on _<′_

<′-Rec : ∀ {ℓ} → RecStruct ℕ ℓ ℓ
<′-Rec : RecStruct ℕ ℓ ℓ
<′-Rec = WfRec _<′_

-- mutual definition
Expand All @@ -73,7 +71,7 @@ cRec = build cRecBuilder
<′-wellFounded′ (suc n) n <′-base = <′-wellFounded n
<′-wellFounded′ (suc n) m (<′-step m<n) = <′-wellFounded′ n m m<n

module _ {ℓ} where
module _ {ℓ : Level} where
open WF.All <′-wellFounded ℓ public
renaming ( wfRecBuilder to <′-recBuilder
; wfRec to <′-rec
Expand All @@ -83,7 +81,7 @@ module _ {ℓ} where
------------------------------------------------------------------------
-- Complete induction based on _<_

<-Rec : ∀ {ℓ} → RecStruct ℕ ℓ ℓ
<-Rec : RecStruct ℕ ℓ ℓ
<-Rec = WfRec _<_

<-wellFounded : WellFounded _<_
Expand All @@ -105,7 +103,7 @@ module _ {ℓ} where
<-wellFounded-skip (suc k) zero = <-wellFounded 0
<-wellFounded-skip (suc k) (suc n) = acc (λ m _ → <-wellFounded-skip k m)

module _ {ℓ} where
module _ {ℓ : Level} where
open WF.All <-wellFounded ℓ public
renaming ( wfRecBuilder to <-recBuilder
; wfRec to <-rec
Expand Down