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Lots of speedups (#116)

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Patrick Stevens
2020-04-16 13:41:51 +01:00
committed by GitHub
parent 1bcb3f8537
commit 9b80058157
63 changed files with 1082 additions and 564 deletions
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Setoids/Orders/Partial/Definition.agda Normal file
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Orders.Total.Definition
open import Orders.Partial.Definition
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Setoids.Orders.Partial.Definition where
record SetoidPartialOrder {a b c : _} {A : Set a} (S : Setoid {a} {b} A) (_<_ : Rel {a} {c} A) : Set (a ⊔ b ⊔ c) where
open Setoid S
field
<WellDefined : {a b c d : A} → (a ∼ b) → (c ∼ d) → a < c → b < d
irreflexive : {x : A} → (x < x) → False
<Transitive : {a b c : A} → (a < b) → (b < c) → (a < c)
_<=_ : Rel {a} {b ⊔ c} A
a <= b = (a < b) || (a ∼ b)
partialOrderToSetoidPartialOrder : {a b : _} {A : Set a} (P : PartialOrder {a} A {b}) → SetoidPartialOrder (reflSetoid A) (PartialOrder._<_ P)
SetoidPartialOrder.<WellDefined (partialOrderToSetoidPartialOrder P) a=b c=d a<c rewrite a=b | c=d = a<c
SetoidPartialOrder.irreflexive (partialOrderToSetoidPartialOrder P) = PartialOrder.irreflexive P
SetoidPartialOrder.<Transitive (partialOrderToSetoidPartialOrder P) = PartialOrder.<Transitive P