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Move things around, add more to fields (#16)

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Patrick Stevens
2019-01-10 22:36:55 +00:00
committed by GitHub
parent 02434c01f9
commit 9e22ba78f5
31 changed files with 288 additions and 102 deletions
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Groups/FreeGroups.agda Normal file
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{-# OPTIONS --safe --warning=error #-}
open import LogicalFormulae
open import Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Naturals
open import FinSet
open import Groups
module FreeGroups where
data FreeCompletion {a : _} (A : Set a) : Set a where
letter : A → FreeCompletion A
inv : A → FreeCompletion A
data FreeGroup {a : _} (A : Set a) : Set a where
emptyWord : FreeGroup A
append : FreeCompletion A → FreeGroup A → FreeGroup A
reduceWord : {a : _} {A : Set a} → (FreeGroup {a} A) → FreeGroup A
reduceWord emptyWord = emptyWord
reduceWord (append (letter x) emptyWord) = append (letter x) emptyWord
reduceWord (append (letter x) (append (letter x1) w)) = append (letter x) (reduceWord (append (letter x1) w))
reduceWord (append (letter x) (append (inv x₁) w)) = {!!}
reduceWord (append (inv x) w) = {!!}
freeGroupSetoid : {a : _} (A : Set a) → Setoid A
Setoid._∼_ (freeGroupSetoid A) = {!!}
Setoid.eq (freeGroupSetoid A) = {!!}
freeGroup : {a : _} (A : Set a) → Group (freeGroupSetoid A) {!!}
freeGroup A = {!!}