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|---|---|
open import Agda.Builtin.Nat using (Nat; suc; zero; _+_)
module test where
data _even : Nat → Set where
ZERO : zero even
STEP : ∀ x → x even → suc (suc x) even
proof₁ : suc (suc (suc (suc zero))) even
proof₁ = ?
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module Data.Char.Classifier where
open import Data.Char.Classifier.Primitive public
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module Data.Option.Equiv.Id where
import Lvl
open import Data.Option
open import Data.Option.Functions
open import Data.Option.Equiv
open import Relator.Equals
open import Relator.Equals.Proofs.Equiv
open import Structure.Function
open import Structure.Function.Domain
open import Type
private variable ℓ : Lvl.Le... | {
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{-# OPTIONS --allow-unsolved-metas #-}
open import Common.Size
-- An abuse of sized types, but as you wish...
data D (i : Size) : Set where
c : (j : Size< i) (k : Size< j) (l : Size< k) (m : Size< l) → D m → D i
c' : (j : Size< i) → D j → D i
works : ∀ i → D i → Set
works i (c j k l m d) = works j (c' k (c' l ... | {
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-- Andreas, 2011-04-07
module IrrelevantTelescope where
data Wrap .(A : Set) : Set where
wrap : A -> Wrap A
-- cannot use A, because it is declared irrelevant
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-- Andreas, 2015-10-28 Issue 1407
-- (Issue 1023 raised its ugly head again!)
{-# OPTIONS -v term.with.inline:30 #-} --KEEP! Triggered bug on agda-2.4.2.5.
-- {-# OPTIONS -v term.with.inline:70 #-}
-- {-# OPTIONS -v tc.with.display:30 #-}
record _×_ (A B : Set) : Set where
constructor pair
field fst : A
s... | {
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open import Type
module Graph.Walk.Properties {ℓ₁ ℓ₂} {V : Type{ℓ₁}} where
open import Lang.Instance
open import Logic
import Lvl
open import Graph{ℓ₁}{ℓ₂}(V)
open import Graph.Walk{ℓ₁}{ℓ₂}{V}
open import Relator.Equals.Proofs.Equiv
open import Type.Properties.MereProposition
module _ (_⟶_ : Graph) where
-- `... | {
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Library.Arithmetic where
open import Light.Level using (Setω ; Level)
open import Light.Variable.Levels
record Arithmetic (Operand : Set ℓ) : Setω where
field _+_ _∗_ : Operand → Operand → Operand
open Arithmetic ⦃ ...... | {
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open import Formalization.PredicateLogic.Signature
module Formalization.PredicateLogic.Classical.NaturalDeduction (𝔏 : Signature) where
open Signature(𝔏)
open import Data.ListSized
import Lvl
open import Formalization.PredicateLogic.Syntax(𝔏)
open import Formalization.PredicateLogic.Syntax.Substitution(𝔏)
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module Tactic.Reflection where
open import Prelude hiding (abs; _>>=_) renaming (_>>=′_ to _>>=_)
open import Builtin.Reflection public
open import Tactic.Reflection.DeBruijn public
open import Tactic.Reflection.Telescope public
open import Tactic.Reflection.Substitute public
open import Tactic.Reflectio... | {
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------------------------------------------------------------------------------
-- The unary numbers are LTC-PCF total natural numbers
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-uni... | {
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{-# OPTIONS --universe-polymorphism #-}
module Issue204.Dependency where
postulate
Level : Set
zero : Level
suc : Level → Level
{-# BUILTIN LEVEL Level #-}
{-# BUILTIN LEVELZERO zero #-}
{-# BUILTIN LEVELSUC suc #-}
record R (ℓ : Level) : Set (suc ℓ) where
data D (ℓ : Level) : Set (suc ℓ) where
mod... | {
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-- Copyright: (c) 2016 Ertugrul Söylemez
-- License: BSD3
-- Maintainer: Ertugrul Söylemez <esz@posteo.de>
module Algebra.Category where
open import Algebra.Category.Category public
open import Algebra.Category.Groupoid public
open import Algebra.Category.Semigroupoid public
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Base.Types
import LibraBFT.Impl.Consensus.Consensus... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
-- This module defines an intermediate (between an implementation and Ab... | {
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------------------------------------------------------------------------
-- An implementation of tree sort, formally proved to return a
-- permutation of the input
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
open import Prelude hidin... | {
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module Type.Identity where
import Lvl
open import Type
private variable ℓ : Lvl.Level
private variable T : Type{ℓ}
-- Identity type.
-- Also called: Propositional equality.
-- Two terms are identical/equal when their data representation are the same.
data Id {T : Type{ℓ}} : T → T → Type{ℓ} where
instance intr... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Convenient syntax for "equational reasoning" using a partial order
------------------------------------------------------------------------
-- Example uses:
--
-- u≤x : u ≤ x
-- u≤x = begin
-- u ≈⟨ u... | {
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{-
Homotopy colimits of graphs
-}
{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Colimit.Base where
open import Cubical.Core.Glue
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv
open import Cubical.... | {
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module Pos where
import Prelude
import Equiv
import Datoid
import Nat
open Prelude
open Equiv
open Datoid
abstract
Pos : Set
Pos = Nat.Nat
one : Pos
one = Nat.zero
suc : Pos -> Pos
suc = Nat.suc
suc' : Nat.Nat -> Pos
suc' n = n
_+_ : Pos -> Pos -> Pos
m +... | {
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module Monad where
open import Level
open import Category
import Functor
import Nat
import Adjoint
open Category.Category
open Functor.Functor
open Nat.Export
open Nat.Nat
open Adjoint.Export
record Monad {c₀ c₁ ℓ} (C : Category c₀ c₁ ℓ) : Set (suc (c₀ ⊔ c₁ ⊔ ℓ)) where
field
MFunctor : Functor.Functor C C
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module char where
open import bool
open import nat
open import eq
open import product
open import product-thms
----------------------------------------------------------------------
-- datatypes
----------------------------------------------------------------------
postulate
char : Set
{-# BUILTIN CHAR char #-}
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{-# OPTIONS --without-K --safe #-}
-- https://personal.cis.strath.ac.uk/conor.mcbride/pub/DepRep/DepRep.pdf
module Experiment.Outrageous.#03 where
open import Experiment.Outrageous.#02
data U : Set
El : U → Set
data U where
:Zero: :𝟏: :𝟐: :ℕ: : U
:Π: :Σ: : (S : U) → (El S → U) → U
El :Zero: = Zero
El :𝟏: ... | {
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------------------------------------------------------------------------------
-- Fairness of the ABP channels
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
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{-# OPTIONS --without-K --safe #-}
module Math.NumberTheory.Fibonacci.Nat where
-- agda-stdlib
open import Data.Nat
open import Data.Nat.Properties
-- agda-misc
open import Math.NumberTheory.Fibonacci.Generic +-0-commutativeMonoid 0 1
renaming
( fibRec≈fib to fibRec≡fib
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{-# OPTIONS --without-K #-}
open import Base
open import Homotopy.PushoutDef
open import Homotopy.VanKampen.Guide
module Homotopy.VanKampen.SplitCode {i} (d : pushout-diag i)
(l : legend i (pushout-diag.C d)) (a₁ : pushout-diag.A d) where
open pushout-diag d
open legend l
open import Homotopy.Truncation
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open import Oscar.Prelude
open import Oscar.Class.IsEquivalence
module Oscar.Class.Setoid where
record Setoid 𝔬 ℓ : Ø ↑̂ (𝔬 ∙̂ ℓ) where
constructor ∁
field
{Object} : Ø 𝔬
ObjectEquivalence : Object → Object → Ø ℓ
⦃ `IsEquivalence ⦄ : IsEquivalence ObjectEquivalence
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module Issue4267.B where
open import Issue4267.A0
postulate
X : Set
-- Crucial for bug: omitting signature of ra,
-- letting Agda infer its type.
ra = record {A = X}
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{-# OPTIONS --without-K #-}
open import HoTT
open import homotopy.elims.SuspSmash
open import homotopy.elims.CofPushoutSection
-- Σ(X∧Y) ≃ X * Y
module homotopy.SuspSmash {i j} (X : Ptd i) (Y : Ptd j) where
private
{- path lemmas -}
private
reduce-x : ∀ {i} {A : Type i} {x y z : A} (p : x == y) (q : z == y... | {
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open import MJ.Types
import MJ.Classtable.Core as Core
module MJ.Syntax.Erase {c}(Ct : Core.Classtable c) where
open import Prelude hiding (erase)
open import Data.Maybe as Maybe using (Maybe; just; nothing)
open import Data.Maybe.All as MayAll
open import Data.Vec as Vec hiding (_∈_)
open import Data.Star as Star
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------------------------------------------------------------------------
-- The Agda standard library
--
-- This module is DEPRECATED. Please use Data.Vec.Recursive.Categorical
-- instead.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Product.N... | {
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{-# OPTIONS --safe #-}
{- A typeclass for converting between type disciplines #-}
module CF.Transform.Compile.ToJVM where
open import Level
open import Function
open import Data.Product as P
open import Data.List as L
open import Data.List.Properties as LP
open import Data.List.Membership.Propositional
open import Da... | {
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------------------------------------------------------------------------------
-- Arithmetic properties used by the McCarthy 91 function
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-... | {
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{-
This second-order signature was created from the following second-order syntax description:
syntax CTLC | ΛC
type
N : 0-ary
_↣_ : 2-ary | r30
¬_ : 1-ary | r30
term
app : α ↣ β α -> β | _$_ l20
lam : α.β -> α ↣ β | ƛ_ r10
throw : α ¬ α -> β
callcc : ¬ α.α -> α
theory
(ƛβ) b : α... | {
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open import DeBruijn
infix 8 _*
_* : ∀ {n} → Term n → Term n
(# x) * = # x
(ƛ M) * = ƛ M *
((ƛ M) · N) * = M * [ N * ]
(L · N) * = L * · N *
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.NType2
open import lib.PathFunctor
open import lib.PathGroupoid
open import lib.types.Bool
open import lib.types.IteratedSuspension
open import lib.types.LoopSpace
open import lib.types.Nat
open import lib.types.Paths
open import lib.types.Pi
open imp... | {
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-- Jesper, 2019-05-28: test case for #3812
{-# OPTIONS --rewriting #-}
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
record Box (A : Set) : Set where
constructor box
field unbox : A
open Box
postulate
A : Set
r s : Box A
rew₂ : r .unbox ≡ s .unbox
{-# REWRITE rew₂ #-}
Box-... | {
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{-# OPTIONS --without-K #-}
open import HoTT
open import homotopy.HSpace
open import homotopy.PushoutComm using (flip; Pushout-comm)
module homotopy.HopfConstruction {i} (A : Type i) (c : is-connected 0 A)
(hA : HSpaceStructure A) where
open HSpaceStructure hA
open ConnectedHSpace A c hA
{-
Using the fact that [μ... | {
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module WarningOnImport.Impo where
B = Set
A = B
{-# WARNING_ON_USAGE A "Deprecated: Use B instead" #-}
{-# WARNING_ON_IMPORT "Deprecated: Use Impossible instead" #-}
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Base.Types
open import LibraBFT.Impl.Consensus.Persisten... | {
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{-# OPTIONS --without-K #-}
open import HoTT
open import cohomology.Exactness
open import cohomology.Theory
module cohomology.Sn {i} (OT : OrdinaryTheory i) where
open OrdinaryTheory OT
C-Sphere-≠ : (n : ℤ) (m : ℕ) → (n ≠ ℕ-to-ℤ m)
→ C n (⊙Sphere m) == LiftUnit-Group
C-Sphere-≠ n O neq = C-dimension n neq
C-Spher... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- An inductive definition of the heterogeneous sublist relation
-- This is a generalisation of what is commonly known as Order
-- Preserving Embeddings (OPE).
-------------------------------------------------------... | {
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open import Relation.Binary.Core
module PLRTree.Drop.Complete {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.Sum
open import PLRTree {A}
open import PLRTree.Complete {A}
open import PLRTree.Compound {A}
open import PLRTree.Drop _≤_ tot≤
open impor... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Equivalence.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Categories.Category
open import Cubical.Categories.Functor
open import Cubical.Categories.NaturalTransformation
open Precategory
open Functor
private
vari... | {
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-- Let-definitions cannot pattern match (or be recursive). Use where for that.
module NotAValidLetBinding where
data N : Set where
z : N
s : N -> N
bad = let pred : N -> N
pred z = z
pred (s n) = n
in pred (s (s z))
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Diagram.Equalizer.Properties {o ℓ e} (C : Category o ℓ e) where
open import Categories.Diagram.Equalizer C
open import Categories.Morphism C
open import Categories.Morphism.Reasoning C
private
module C = Category C
open C
va... | {
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-- Andreas, 2011-10-02
module IrrelevantLet where
postulate
A : Set
test : (.A → A) → .A → A
test = λ f a →
let .b : A
b = f a
in f a
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data Size : Set where
↑ : Size → Size
↑ ()
data N : Size → Set where
suc : ∀{i} (a : N i) → N (↑ i)
data Val : ∀{i} (t : N i) → Set where
val : ∀{i} (n : N i) → Val (suc n)
record R (j : Size) : Set where
field num : N j
data W {j} (ft : R j) : Set where
immed : (v : Val (R.num ft)) → W ft
postulate
E :... | {
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{-# OPTIONS --sized-types #-}
open import Relation.Binary.Core
module BubbleSort {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.List
open import Data.Product
open import Data.Sum
open import Size
open import SList
swap* : {ι : Size} → A → SList A {ι} → SL... | {
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module Issue2649-2 where
open import Issue2649-1
open module M (A : Set) (a : A) = MyModule A a public
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open import Data.String using (String)
open import Data.List using (List; []; _∷_)
open import Data.Nat using (ℕ)
open import Data.Product
open import Data.Bool
open import Data.Maybe
open import Data.Vec as V using (Vec; []; _∷_)
open import Data.Fin as F using (Fin; zero; suc)
open import Reflection using (TC)
open ... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import stash.modalities.gbm.GbmUtil
open import stash.modalities.GbmCodes
module stash.modalities.Gbm {ℓ} (M : Modality ℓ)
{A : Type ℓ} {B : Type ℓ}
(Q : A → B → Type ℓ)
(H : BM-Relation M Q) where
open Modality M
import stash.modalities.gb... | {
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------------------------------------------------------------------------
-- Traditional non-dependent lenses with erased lens laws
------------------------------------------------------------------------
-- At the time of writing there are counterparts in this file of more
-- or less everything in Lens.Non-dependent.T... | {
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------------------------------------------------------------------------------
-- LTC-PCF terms properties
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# ... | {
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{-# OPTIONS --safe #-}
module README where
-- Formalization for "Decidability of Conversion for Setoid Type Theory"
-- Git repository: https://github.com/CoqHott/logrel-mltt/
------------------
-- INTRODUCTION --
------------------
-- A minimal library necessary for formalization:
-- The empty type and its elimin... | {
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open import Data.Nat using (suc)
open import Substitution using (rename-subst-commute; subst-commute)
open import DeBruijn
infix 3 _—→_
data _—→_ : ∀ {n} → Term n → Term n → Set where
—→-ξₗ : ∀ {n} {M M′ N : Term n}
→ M —→ M′
---------------
→ M · N —→ M′ · N
—→-ξᵣ : ∀ {n} {M N N′ : Term n}
... | {
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------------------------------------------------------------------------
-- Instantiates the ring solver with two copies of the same ring
------------------------------------------------------------------------
open import Algebra.RingSolver.AlmostCommutativeRing
module Algebra.RingSolver.Simple (r : AlmostCommutativ... | {
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Literals where
module Definition where
module Natural where open import Light.Literals.Definition.Natural public
module Negative where open import Light.Literals.Definition.Negative public
module Natural where op... | {
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module Eq.LogicalTheory where
open import Prelude
open import T
open import DynTheory
open import SubstTheory
open import Contexts
open import Eq.Defs
open import Eq.KleeneTheoryEarly
-- Closed equivalence is contained in open
closed-logical-imp-open : ∀{A} → LogicalEq A ⊆ OLogicalEq [] A
closed-logical-imp-open {A} ... | {
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-- Pattern matching on a datatype in Prop is disallowed
{-# OPTIONS --enable-prop #-}
open import Agda.Builtin.Bool
data TestProp : Prop where
p₁ p₂ : TestProp
toBool : TestProp → Bool
toBool p₁ = true
toBool p₂ = false
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{-# OPTIONS --safe #-}
module Cubical.Algebra.DirectSum.DirectSumFun.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Nat renaming (_+_ to _+n_ ; _·_ to _·n_)
open import Cubical.Data.Nat.Order
open import Cubical.Data.Sigma
open import Cubical... | {
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{-# OPTIONS --safe #-}
module Issue2487-2 where
import Issue2487.A
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{-# OPTIONS --erased-cubical --safe #-}
module MakeTracks where
open import Data.Fin using (Fin; #_; toℕ)
open import Data.List using (List; _∷_; []; map; concat; _++_; replicate; zip; length; take; drop)
open import Data.Nat using (_*_; ℕ; suc; _+_)
open import Data.Nat.Show using (show)
open i... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module Oscar.Data.Term.ThickAndThin {𝔣} (FunctionName : Set 𝔣) where
open import Oscar.Class.ThickAndThin
open import Oscar.Data.Term FunctionName
import Oscar.Data.Term.ThickAndThin.internal FunctionName as ⋆
instance ThickAndThinTerm : ThickAndThin Term
ThickAndThin.thin Thi... | {
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open import dynamics-core
module focus-formation where
-- every ε is an evaluation context -- trivially, here, since we don't
-- include any of the premises in red brackets about finality
focus-formation : ∀{d d' ε} → d == ε ⟦ d' ⟧ → ε evalctx
focus-formation (FHPlus1 sub) = ECPlus1 (focus-formation sub)
foc... | {
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{- This file describes properties of computable relations. -}
open import bool
open import level
open import eq
open import product
open import product-thms
module bool-relations {ℓ : level}{A : Set ℓ} (_≤A_ : A → A → 𝔹) where
reflexive : Set (ℓ)
reflexive = ∀ {a : A} → a ≤A a ≡ tt
transitive : Set (ℓ)
transitive ... | {
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.types.Truncation
open import lib.types.Groupoid
open import lib.types.PathSet
module lib.types.FundamentalGroupoid {i} (A : Type i) where
fundamental-groupoid : Groupoid
fundamental-groupoid = record
{ El = A
; Arr = _=₀_ {A = A}
; Ar... | {
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module _ where
open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
module Vars (A : Set) where
variable
x : A
-- Was
-- An internal error has occurred. Please report this as a bug.
-- Location of the error: src/full/Agda/TypeChecking/Reduce/Fast.hs:148
-- Should be
-- Cannot use generalized v... | {
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module Data.Logic where
open import Haskell.Prelude renaming (zero to Z; suc to S)
open import Relation.Nullary.Decidable
open import Data.Nat.DivMod
open import Data.Nat.Properties
open import Agda.Primitive
{-# FOREIGN AGDA2HS
import Data.Nat
#-}
---- Equational reasoning
useEq : {x y : Bool} -> x ≡ y -> .(IsTrue ... | {
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module Languages.ILL.Intermediate where
open import Utils.HaskellTypes
open import Utils.HaskellFunctions
open import Languages.ILL.TypeSyntax
{-# IMPORT Languages.ILL.Intermediate #-}
data IPattern : Set where
PTriv : IPattern
PVar : String → IPattern
PTensor : IPattern → IPattern → IPattern
{-# COMPILED_DATA... | {
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open import Level using (0ℓ)
open import Function using (_$_; _∘_)
open import Relation.Nullary using (yes; no)
open import Relation.Nullary.Decidable using (False; True)
open import Relation.Nullary.Negation using (contradiction)
open import Relation.Binary
using (Reflexive; Transitive; Trans; Antisymmetric; Asymme... | {
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module localInstances where
open import Agda.Builtin.Nat renaming (Nat to ℕ)
open import Agda.Builtin.Bool
open import Common.String
open import Common.List
record Eq (A : Set) : Set where
field eq : A → A → Bool
strlen : String → ℕ
strlen s = length (stringToList s)
if_then_else_ : {A : Set} → Bool → A → A → A
i... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Base
open import lib.PathGroupoid
module lib.PathFunctor where
{- Nondependent stuff -}
module _ {i j} {A : Type i} {B : Type j} (f : A → B) where
!-ap : {x y : A} (p : x == y)
→ ! (ap f p) == ap f (! p)
!-ap idp = idp
ap-! : {x y : A} (p : x == y)
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{-# OPTIONS --rewriting #-}
open import Agda.Builtin.Bool
open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
record R : Set where
constructor mkR
field
f : Nat
data Box : Set → Set₁ where
box : (A : Set) → Box A
data D (A : Set) : Set₁ where
c : Box ... | {
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{-# OPTIONS -v tc.unquote:30 #-}
open import Common.Prelude
open import Common.Reflection
open import Agda.Builtin.Sigma
data Box : Bool → Set where
box : (b : Bool) → Box b
works : (b : Bool) → Box b → Bool
works b (box .b) = unquote (give (var 0 []))
works₂ : (b : Bool) → Box b → Bool
unquoteDef works₂ = defineF... | {
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open import Level
open import Ordinals
module Topology {n : Level } (O : Ordinals {n}) where
open import zf
open import logic
open _∧_
open _∨_
open Bool
import OD
open import Relation.Nullary
open import Data.Empty
open import Relation.Binary.Core
open import Relation.Binary.PropositionalEquality
import BAlgbra... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Lists where all elements satisfy a given property
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.List.Relation.Unary.All where
open impo... | {
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{-# OPTIONS --without-K #-}
{--
Make a version of this file with plain PI and ℕ as a model
Make another version with PI+NEG+FRAC (meadow style) and ℚ as a model
Keep extending; add imaginary numbers and try ℂ as a model
then add square roots and try algebraic numbers as a model
An orthogonal direction is to try ... | {
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module is-free where
open import lib
open import cedille-types
open import ctxt-types
open import syntax-util
open import general-util
are-free-e = 𝔹
check-erased = tt
skip-erased = ff
are-free-in-t : Set → Set₁
are-free-in-t T = ∀{A} → are-free-e → trie A → T → 𝔹
are-free-in-term : are-free-in-t term
are-free-i... | {
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open import AEff
open import EffectAnnotations
open import Types hiding (``)
open import Relation.Binary.PropositionalEquality hiding ([_] ; Extensionality)
--open ≡-Reasoning
module Renamings where
-- SET OF RENAMINGS BETWEEN CONTEXTS
Ren : Ctx → Ctx → Set
Ren Γ Γ' = {X : VType} → X ∈ Γ → X ∈ Γ'
-- IDENTITY, COM... | {
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module Numeral.Natural.Oper.Proofs.Multiplication where
open import Logic.Propositional
open import Numeral.Natural
open import Numeral.Natural.Oper
open import Numeral.Natural.Oper.Proofs
open import Numeral.Natural.Oper.Proofs.Order
open import Numeral.Natural.Relation
open import Numeral.Natural.Relation.Order
open... | {
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{-# OPTIONS --safe --warning=error #-}
open import Sets.EquivalenceRelations
open import Setoids.Setoids
open import Groups.FreeGroup.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Decidable.Sets
open import Numbers.Naturals.Order
open import LogicalFormulae
open impor... | {
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module _ where
postulate
A : Set
_,_ : A → A → A
module M where
module Mx (x : A) where
module M where
module My (y : A) where
f : A
f = x , y
postulate
a b c : A
module M′ = M
module Ma = M′.Mx.M a
module Mab = Ma.My b
g : A
g = Mab.f
-- Original bug report --
record I (A :... | {
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{-# OPTIONS --without-K #-}
open import Base
module Spaces.LoopSpaceDecidableWedgeCircles {i} (A : Set i) (eq : has-dec-eq A)
where
open import Spaces.WedgeCircles A renaming (wedge-circles to WA; base to baseWA)
open import Algebra.FreeGroup A renaming (freegroup to FA)
open import Algebra.FreeGroupProps A
open i... | {
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{-# OPTIONS --without-K --exact-split --safe #-}
module Fragment.Equational.Theory.Bundles where
open import Fragment.Algebra.Signature
open import Fragment.Equational.Theory.Base
open import Fragment.Equational.Theory.Combinators
open import Data.Nat using (ℕ)
module _ where
data MagmaOp : ℕ → Set where
• :... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Relation.Unary where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Un... | {
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{-# OPTIONS --safe --warning=error #-}
open import Boolean.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Logic.PropositionalLogic
open import Functions.Definition
open import Numbers.Naturals.Order
open import Vectors
module Logic.PropositionalLogicExamp... | {
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{-# OPTIONS --type-in-type --guardedness #-}
module IO.Exts where
import IO.Primitive as Prim
open import Class.Monad
open import Class.Functor
open import Data.List
open import Data.Nat using (ℕ)
open import Data.String
open import Data.Sum
open import Data.Unit
open import Function
open import IO using (IO; run; re... | {
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{-# OPTIONS --no-qualified-instances #-}
open import Data.List
open import Relation.Unary
open import Relation.Ternary.Core
open import Relation.Ternary.Structures
open import Relation.Ternary.Structures.Syntax
import JVM.Printer.Printer as Printer
import JVM.Model as Model
module JVM.Syntax.Bytecode.Printer {ℓ T}
... | {
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-- Discrete category over a type A
-- A must be an h-groupoid for the homs to be sets
{-# OPTIONS --safe #-}
module Cubical.Categories.Instances.Discrete where
open import Cubical.Categories.Category.Base
open import Cubical.Categories.Functor.Base
open import Cubical.Foundations.GroupoidLaws
open import Cubical.Foun... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A categorical view of Colist
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --sized-types #-}
module Codata.Colist.Categorical where
open import Codata.... | {
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-- Fixed on AIM XIV 2011-09-09 AA, UN
-- {-# OPTIONS -v tc.lhs.unify:50 #-}
module Issue292 where
data ⊥ : Set where
infix 3 ¬_
¬_ : Set → Set
¬ P = P → ⊥
infix 4 _≅_
data _≅_ {A : Set} (x : A) : ∀ {B : Set} → B → Set where
refl : x ≅ x
record Σ (A : Set) (B : A → Set) : Set where
constructor _,_
field
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Bicategory.Helpers where
-- quite a bit of the code below is taken from Categories.2-Category
open import Data.Nat using (_+_)
open import Function using (flip)
open import Data.Product using (_,_; curry)
open import Categories.Category
open import Categories.... | {
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-- Andreas, 2015-08-11, issue reported by Martin Stone Davis
-- {-# OPTIONS -v impossible:10 -v interaction.give:20 #-}
open import Data.AVL using (Tree; empty)
open import Data.Vec using (Vec)
open import Data.String using (String)
open import Relation.Binary using (StrictTotalOrder)
open import Data.Nat.Properties ... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Base.Types
import LibraBFT.Impl.Consensus.Network ... | {
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module DivMod where
-- From examples/simple-lib
open import Lib.Vec
open import Lib.Nat
open import Lib.Id
open import Lib.Logic
open import Lib.Fin
-- Certified implementation of division and modulo
module Direct where
data DivMod : Nat -> Nat -> Set where
dm : forall {b} q (r : Fin b) -> DivMod (toNat r + q... | {
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{-# OPTIONS -v 2 #-}
module Leftovers.Junk where
open import Data.Bool
open import Relation.Binary.PropositionalEquality
id : ∀ {X : Set} → X → X
id x = x
the : ∀ X → X → X
the X = id {X}
badEq :
let f = the (Bool -> Bool -> Bool) (λ x → λ {true → false ; false → true})
in f true ≡ f false
badEq = {!!} -- ref... | {
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module Integer.Difference.Properties where
open import Data.Product as Σ
open import Data.Product.Relation.Pointwise.NonDependent
open import Data.Unit
open import Equality
open import Integer.Difference
open import Natural as ℕ using (ℕ; zero; suc)
open import Quotient as /
open import Relation.Binary
open import Syn... | {
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{-# OPTIONS --without-K #-}
open import Base
open import Homotopy.PullbackDef
-- We only consider the universal property internally to a fixed
-- universe [Set i]. If we don’t, we would have to consider an universe
-- polymorphic [P] and I don’t want to quantify over universe polymorphic things
module Homotopy.Pullba... | {
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{-# OPTIONS --cubical --safe #-}
module BCK where
open import Prelude hiding (B; C)
infixl 4 _$$_
data BCK : Type where
_$$_ : BCK → BCK → BCK
B C K : BCK
open import Data.List
stack : BCK → Maybe BCK
stack xs = go xs []
where
go : BCK → List BCK → Maybe BCK
go (f $$ x) xs = go f (x ∷ xs)
go B (f ∷ g ∷... | {
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