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module Prelude.Variables where open import Agda.Primitive open import Agda.Builtin.Nat open import Agda.Builtin.List variable ℓ ℓ₁ ℓ₂ ℓ₃ : Level A B C : Set ℓ F M : Set ℓ₁ → Set ℓ₂ x y z : A xs ys zs : List A n m : Nat
-- Solver for functors {-# OPTIONS --without-K --safe #-} open import Categories.Category open import Categories.Functor renaming (id to idF) module Experiment.Categories.Solver.MultiFunctor {o ℓ e} where import Categories.Morphism.Reasoning as MR open import Level open import Relation.Binary using (Rel) infixr 9...
-- Andreas, 2017-05-17, issue #2574 reported by G. Allais open import Issue2574Import -- The imported module should be clickable. open import Issue2574ImportBlank -- The imported module should be clickable.
-- Currently this test case is broken. Once Issue 3451 has been fixed -- it should be moved to test/Fail (and this comment should be -- removed). -- The option --guardedness turns off sized types. {-# OPTIONS --guardedness #-} open import Agda.Builtin.Size record Stream (A : Set) (i : Size) : Set where coinductiv...
module Class.MonadTrans where open import Class.Monad open import Level record MonadTrans {a} (T : (Set a -> Set a) -> Set a -> Set a) : Set (suc a) where field embed : {A : Set a} {M : Set a -> Set a} {{_ : Monad M}} -> M A -> T M A open MonadTrans {{...}} public
module Numeral.Natural.Relation.Order where import Lvl open import Functional open import Logic open import Logic.Propositional open import Logic.Predicate open import Numeral.Natural open import Numeral.Natural.Oper open import Relator.Equals open import Relator.Equals.Proofs open import Relator.Ordering -- Inequali...
module Eq.ObsTheory where open import Prelude open import T open import DynTheory open import SubstTheory open import Contexts open import Eq.Defs open import Eq.KleeneTheory open ObservEq ---- Proofs about observational equivalence -- observational equivalence being an equiv reln follows trivially from kleene equiv...
{-# OPTIONS --without-K #-} module function.fibration where open import level open import sum open import equality.core open import function.core open import function.isomorphism.core open import function.isomorphism.coherent open import function.isomorphism.lift open import function.isomorphism.univalence open impor...
{-# OPTIONS --without-K --rewriting #-} open import HoTT module Reflective where record ReflectiveSubuniverse {ℓ} : Type (lsucc ℓ) where field P : Type ℓ → Type ℓ R : Type ℓ → Type ℓ η : (A : Type ℓ) → A → R A -- replete : (A B : Type ℓ) → P A → A ≃ B → P B
{-# OPTIONS --safe #-} module Cubical.Categories.Morphism where open import Cubical.Foundations.Prelude open import Cubical.Data.Sigma open import Cubical.Categories.Category private variable ℓ ℓ' : Level -- C needs to be explicit for these definitions as Agda can't infer it module _ (C : Category ℓ ℓ') where...
------------------------------------------------------------------------ -- Pi with partiality algebra families as codomains ------------------------------------------------------------------------ {-# OPTIONS --erased-cubical --safe #-} module Partiality-algebra.Pi where open import Equality.Propositional.Cubical o...
-- {-# OPTIONS -v tc.with.strip:40 #-} module Issue824 where record R : Set where data D : Set → Set₁ where d : ∀ {A} → D A → D A postulate d′ : D R data P : R → D R → Set₁ where p : {x : R} {y : D R} → P x y → P x (d y) Foo : P _ (d d′) → Set₁ Foo (p _) with Set Foo (p _) | _ = Set -- Bug.agda:18,1-19,20 -...
------------------------------------------------------------------------ -- Call-by-value (CBV) reduction in pure type systems (PTS) ------------------------------------------------------------------------ module Pts.Reduction.Cbv where open import Data.Fin.Substitution open import Data.Fin.Substitution.ExtraLemmas o...
module LocalVsImportedModuleClash where X = TODO--This-shouldn't-happen-if-the-scope-checker-does-it's-job
{-# OPTIONS --without-K --safe #-} module Categories.NaturalTransformation.NaturalIsomorphism.Equivalence where -- a certain notion of equivalence between Natural Isomorphisms. open import Level open import Data.Product using (_×_; _,_; map; zip) open import Relation.Binary using (IsEquivalence) open import Categori...
{-# OPTIONS --safe #-} module Cubical.Algebra.Group.Instances.DiffInt where open import Cubical.HITs.SetQuotients open import Cubical.Foundations.Prelude open import Cubical.Data.Int.MoreInts.DiffInt renaming (ℤ to ℤType ; _+_ to _+ℤ_ ; _-_ to _-ℤ_) open import Cubical.Algebra.Group.Base open import Cubical.Algebra.Se...
open import Common.Size postulate A : Set f : Size → A -- k' < k < j <= i + 2 =/=> ∃ l < i test : ∀ i (j : Size< (↑ ↑ ↑ i)) (k : Size< j) (k' : Size< k) → Size → Set → (((l : Size< i) → A) → A) → A test i j k k' _ _ ret = ret λ l → f l
module RTP where open import RTN public {- data Bool : Set where False : Bool True : Bool -} postulate Int : Set String : Set Float : Set Char : Set {-# BUILTIN FLOAT Float #-} {-# BUILTIN STRING String #-} {-# BUILTIN CHAR Char #-} -- postulate primShowBool : Bool -> St...
open import Agda.Primitive using (lzero; lsuc; _⊔_; Level) open import Relation.Binary.PropositionalEquality using (_≡_; refl; subst) open import Relation.Binary using (Setoid) -- A formalization of raw syntax module Syntax where -- Syntactic classes data ObjectClass : Set where Ty Tm : ObjectClass data ...
-- 2011-10-01 Andreas module EtaContractIrrelevant where import Common.Level data _≡_ {a}{A : Set a}(x : A) : A → Set where refl : x ≡ x subst : ∀ {a b}{A : Set a}(P : A → Set b){x y : A} → x ≡ y → P x → P y subst P refl x = x postulate Val : Set Pred = Val → Set fam : Pred → Set1 fam A = {a : Val} → .(A a...
------------------------------------------------------------------------ -- Termination ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} open import Prelude module Delay-monad.Termination {a} {A : Type a} where open import Equality.Propositional open import Logi...
-- Module shadowing using generated modules for records and datatypes module Issue260a where module D where data D : Set where
interleaved mutual data Nat : Set record IsNat (n : Nat) : Set isNat : (n : Nat) → IsNat n
module string-thms where open import bool open import eq open import string postulate =string-refl : (s : string) → s =string s ≡ tt =string-to-≡ : (a b : string) → a =string b ≡ tt → a ≡ b ≡string-to-= : (a b : string) → a ≡ b → a =string b ≡ tt ≡string-to-= a .a refl = =string-refl a
{-# OPTIONS --without-K #-} module hott.truncation.core where open import sum open import equality open import function.core open import function.fibration open import function.extensionality open import function.isomorphism open import sets.nat.core open import hott.equivalence open import hott.level.core open import...
module Human.Humanity where -- Use agda-prelude instead of agda-stdlib? open import Human.JS public open import Human.Unit public open import Human.Nat public open import Human.List public open import Human.Bool public open import Human.String public open import Human.IO public open import Human.Float public open imp...
------------------------------------------------------------------------ -- The Agda standard library -- -- Interleavings of lists using setoid equality ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Relation.Binary using (Setoid) module Data.L...
-- Andreas, 2015-12-29 record ⊤ : Set where data P : ⊤ → Set where c : P record{} test : (x : ⊤) (p : P x) → Set test _ c with ⊤ test _ y | z = ⊤ -- Expected error: with-clause pattern mismatch. -- The error should be printed nicely, like: -- -- With clause pattern x is not an instance of its parent pattern -- re...
{- Product of structures S and T: X ↦ S X × T X -} {-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Structures.Product where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Equiv open import Cubical.Foundations.Transport open import...
{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Algebra.Group.EilenbergMacLane.WedgeConnectivity where open import Cubical.Algebra.Group.EilenbergMacLane.Base open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels open import Cubical.Algebra.Group.Base open import Cubi...
-- Andreas, 2014-10-23 -- If you must, you can split on a shadowed hidden var... data ℕ : Set where zero : ℕ suc : ℕ → ℕ f : {n n : ℕ} → Set₁ f = Set where g : {n n : ℕ} → Set → Set g _ = {!.n!}
{- 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...
{-# OPTIONS --without-K --safe #-} -- a categorical (i.e. non-skeletal) version of Lawvere Theory, -- as per https://ncatlab.org/nlab/show/Lawvere+theory module Categories.Theory.Lawvere where open import Data.Nat using (ℕ) open import Data.Product using (Σ; _,_) open import Level open import Categories.Category.Ca...
{-# OPTIONS --without-K --safe #-} module Data.Maybe.Base where open import Level data Maybe (A : Type a) : Type a where nothing : Maybe A just : A → Maybe A maybe : {B : Maybe A → Type b} → B nothing → ((x : A) → B (just x)) → (x : Maybe A) → B x maybe b f nothing = b maybe b f (just x) = f x mapMaybe : ...
{-# OPTIONS --cubical --safe #-} -- First and second species counterpoint module Counterpoint where open import Data.Bool using (Bool; true; false; if_then_else_; _∨_; _∧_; not) open import Data.Fin using (Fin; #_) open import Data.Integer using (+_) open import Data.List using (List; []; _∷_; mapMaybe; map; zip; _++...
{-# OPTIONS --rewriting #-} open import Agda.Builtin.Equality open import Agda.Builtin.Equality.Rewrite open import Agda.Builtin.Unit postulate A : Set a : A f : {X : Set} → X → A g : {X : Set} → A → X rew-fg : {X : Set} (a : A) → f (g {X} a) ≡ a {-# REWRITE rew-fg #-} test : f tt ≡ a test = refl
module VecFlip where open import AgdaPrelude goodNil : Vec Nat Zero goodNil = Nil Nat badNil : Vec Zero Nat badNil = Nil Nat
{-# OPTIONS --without-K --rewriting #-} open import HoTT module groups.HomSequence where infix 15 _⊣|ᴳ infixr 10 _→⟨_⟩ᴳ_ data HomSequence {i} : (G : Group i) (H : Group i) → Type (lsucc i) where _⊣|ᴳ : (G : Group i) → HomSequence G G _→⟨_⟩ᴳ_ : (G : Group i) {H K : Group i} → (G →ᴳ H) → HomSequence H K →...
------------------------------------------------------------------------------ -- Conversion rules for inequalities ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism...
--{-# OPTIONS --with-K #-} open import Data open import Data.Tuple using (_⨯_ ; _,_) open import Logic.Predicate import Lvl open import Syntax.Number import Type as Meta -- `Constants` is the type of all possible constant terms. -- `Sort` is a subset of `Constants` that indicate the sorts of the type system...
------------------------------------------------------------------------ -- Vectors ------------------------------------------------------------------------ module Data.Vec where open import Data.Nat open import Data.Fin using (Fin; zero; suc) open import Data.List as List using (List) open import Data.Product using ...
module bool where open import level ---------------------------------------------------------------------- -- datatypes ---------------------------------------------------------------------- open import unit open import empty data 𝔹 : Set where tt : 𝔹 ff : 𝔹 -- this is an alias for Mac users who cannot see bl...
{-# OPTIONS --without-K --rewriting #-} open import HoTT open import homotopy.PushoutSplit module cw.cohomology.CofiberGrid {i j k} {A : Type i} {B : Type j} {C : Type k} (f : A → B) (g : B → C) where {- A -------> B -----------> C | | _/| | | _/ | | ...
{-# OPTIONS --without-K --safe #-} open import Categories.Category module Categories.Diagram.Pullback.Limit {o ℓ e} (C : Category o ℓ e) where open import Data.Product using (∃₂; _,_) open import Function using (_$_) open import Categories.Category.Instance.Span open import Categories.Functor open import Categories...
{-# OPTIONS --without-K --safe #-} module Dodo.Binary.Domain where -- Stdlib imports open import Level using (Level; _⊔_) open import Function.Base using (flip; _∘_) open import Data.Product using (_×_; _,_; ∃; ∃-syntax; proj₁; proj₂) open import Data.Sum using (_⊎_; inj₁; inj₂; swap) open import Relation.Un...
{-# OPTIONS --without-K --safe #-} module Dodo.Binary.Empty where -- Stdlib imports open import Level using (Level; _⊔_) open import Relation.Nullary using (¬_) open import Relation.Binary using (REL; Rel) -- # Definitions -- | A predicate stating no inhabitants exist for the given relation Empty₂ : ∀ {a b ℓ : Lev...
module Text.Greek.SBLGNT.Heb where open import Data.List open import Text.Greek.Bible open import Text.Greek.Script open import Text.Greek.Script.Unicode ΠΡΟΣ-ΕΒΡΑΙΟΥΣ : List (Word) ΠΡΟΣ-ΕΒΡΑΙΟΥΣ = word (Π ∷ ο ∷ ∙λ ∷ υ ∷ μ ∷ ε ∷ ρ ∷ ῶ ∷ ς ∷ []) "Heb.1.1" ∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.1" ∷ word (π ∷ ο ∷ ∙λ ∷ ...
------------------------------------------------------------------------------ -- Totality of predecessor function ------------------------------------------------------------------------------ {-# OPTIONS --allow-unsolved-metas #-} {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types ...
postulate F : Set → Set _ : {@0 A : Set} → F λ { → A }
-- Andreas 2019-11-06, issue #4172, examples by nad. -- Single constructor matches for non-indexed types should be ok -- even when argument is erased, as long as pattern variables -- are only used in erased context on the rhs. -- https://github.com/agda/agda/issues/4172#issue-517690102 record Erased (A : Set) : Set ...
S : Set; S = S
------------------------------------------------------------------------ -- A formalization of the polymorphic lambda calculus extended with -- iso-recursive types ------------------------------------------------------------------------ -- Author: Sandro Stucki -- Copyright (c) 2015 EPFL -- The code in this directory...
-- Andreas, 2016-09-28 -- Level constraints X <= a and a <= X should solve X = a. -- {-# OPTIONS -v tc.constr.add:40 #-} open import Common.Level module _ (a : Level) where mutual X : Level X = _ data C : Set (lsuc X) where c : Set a → C -- constrains X by a <= X data D : Set (lsuc a) where c : S...
{-# OPTIONS --allow-unsolved-metas #-} {-# OPTIONS --show-implicit #-} module HeapProperties where open import HeapPropertiesDefs public open import HeapLemmasForSplitting public
{-# OPTIONS --without-K #-} open import HoTT {- A proof that (A * B) * C ≃ (C * B) * A, which combined with commutativity - proves associativity. - - Agda has a hard time compiling this but sometimes it succeeds. - - Favonia (2016 May): I have consistent success in compiling this file. - -} open import homoto...
-- {-# OPTIONS -v tc.meta:25 #-} -- Andreas, 2013-05-23 module DontPruneBlocked where open import Common.Equality open import Common.Product data Bool : Set where true false : Bool if : {A : Set} → Bool → A → A → A if true a b = a if false a b = b test1 : let Fst : Bool → Bool → Bool Fst = _ I : Bo...
-- The following file contains various examples of highlighting. -- It does not necessarily typecheck (but it should parse) a : A → Set a b : A → Set postulate a : A → Set abstract a b : A → Set abstracta : A → Set postulate abstract a : A → Set private a b : A → Set abstract a : A → Set pattern-a : A → Set abstra...
-- Andreas, 2014-02-11 issue raised by Niccolo Veltri -- {-# OPTIONS -v term.matrices:40 #-} open import Common.Equality data _=⟨_⟩⇒*_ {X : Set}(x : X)(f : X → X) : X → Set where done : x =⟨ f ⟩⇒* x next : ∀{y z} → f y ≡ z → x =⟨ f ⟩⇒* y → x =⟨ f ⟩⇒* z trans* : ∀{X}{x y z}{f : X → X} → x =⟨ f ⟩⇒* y → y =⟨ f ⟩⇒* ...
-- This file comes from the agda class taught by Peter Selinger at -- Dalhousie University. It contains a bonus question that -- propostional logic is complete. We will show this in -- Kalmar.agda. -- The course link: -- https://www.mathstat.dal.ca/~selinger/agda-lectures/ {-# OPTIONS --without-K --safe #-} module Pr...
{-# OPTIONS --safe #-} module Cubical.Data.Queue where open import Cubical.Data.Queue.Base public open import Cubical.Data.Queue.Finite public
-------------------------------------------------------------------------------- -- This is part of Agda Inference Systems {-# OPTIONS --sized-types #-} open import Agda.Builtin.Equality open import Data.Product open import Data.Sum open import Size open import Codata.Thunk open import Level open import Relation.Una...
module ShadowModule where module A where module B where data D : Set where open A module B where
module Metalogic.Classical.Propositional.ProofSystem {ℓₚ} (Proposition : Set(ℓₚ)) where import Lvl open import Data hiding (empty) import Data.List open Data.List using (List ; ∅ ; _⊰_ ; _++_ ; [_ ; _]) open Data.List.Notation import Data.List.Relation.Membership import Data.List.Rela...
module nodcap.NF.Axiom where open import Data.Nat as ℕ using (ℕ; suc; zero) open import Data.Pos as ℕ⁺ open import Data.List as L using (List; []; _∷_; _++_) open import Function using (_$_) open import Relation.Binary.PropositionalEquality as P using (_≡_; _≢_) open import Data.Environment open import nodcap.Base ope...
module Levitation where open import Data.Product record ⊤ : Set1 where constructor tt data Desc : Set2 where `1 : Desc `Σ : (S : Set1)(D : S → Desc) → Desc `ind× : (D : Desc) → Desc `hind× : (H : Set)(D : Desc) → Desc ⟦_⟧ : Desc → Set1 → Set1 ⟦ `1 ⟧ X = ⊤ ⟦ `Σ S D ⟧ X = Σ S (\s → ⟦ D s ⟧ X)...
-- -- Created by Dependently-Typed Lambda Calculus on 2020-10-08 -- Connective -- Author: dplaindoux -- {-# OPTIONS --without-K #-} module Connective where import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl) open Eq.≡-Reasoning open import Data.Nat using (ℕ) open import Function using (_∘_) ...
module Generic.Test.Elim where open import Generic.Core open import Generic.Function.Elim open import Generic.Test.Data.Vec -- Is it possible to get rid of these `lift`s? elimVec′ : ∀ {n α π} {A : Set α} -> (P : ∀ {n} -> Vec A n -> Set π) -> (∀ {n} {xs : Vec A n} x -> P xs -> P (x ∷ᵥ xs)) -...
------------------------------------------------------------------------ -- Some corollaries ------------------------------------------------------------------------ module TotalParserCombinators.Derivative.Corollaries where open import Data.List open import Function.Base open import Function.Inverse using (_↔_) impo...
{-# OPTIONS --safe --sized-types #-} module STLC.Operational where open import STLC.Operational.Base
{-# OPTIONS --cubical-compatible #-} module WithoutK-PatternSynonyms2 where -- Equality defined with two indices. data _≡_ {A : Set} : A → A → Set where refl : ∀ x → x ≡ x pattern r x = refl x -- The --cubical-compatible option works with pattern synonyms. K : (A : Set) (x : A) (P : x ≡ x → Set) → P (refl x) → (p...
open import Relation.Binary.Core module BBHeap.Insert {A : Set} (_≤_ : A → A → Set) (tot≤ : Total _≤_) (trans≤ : Transitive _≤_) where open import BBHeap _≤_ open import BBHeap.Properties _≤_ open import BBHeap.Subtyping.Properties _≤_ trans≤ open import Bound....
------------------------------------------------------------------------ -- Some definitions related to the binary sum type former ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Equality module Sum {c⁺} (eq : ∀ {a p} → Equality-with-J a p c⁺) w...
module StdLibStuff where {- -- Data.Empty data ⊥ : Set where -- Relation.Nullary.Core infix 3 ¬_ ¬_ : Set → Set ¬ P = P → ⊥ data Dec (P : Set) : Set where yes : ( p : P) → Dec P no : (¬p : ¬ P) → Dec P -} -- Relation.Binary.Core infix 4 _≡_ -- _≢_ data _≡_ {A : Set} (x : A) : A → Set where refl : x ≡...
-- Andreas, 2021-04-14, #1154 -- Andreas, 2021-04-12, BNFC/bnfc#354 -- Make sure we confirm tentative layout columns on first newline. private private private A : Set B : Set -- all three blocks (8,16,24) should be confirmed here private -- the column for this block ne...
module LC.Base where open import Data.Nat -------------------------------------------------------------------------------- -- de Bruijn indexed lambda calculus infix 5 ƛ_ infixl 7 _∙_ infix 9 var_ data Term : Set where var_ : (x : ℕ) → Term ƛ_ : (M : Term) → Term _∙_ : (M : Term) → (N : Term) → Term
module posts.agda.typed-protocols where open import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl) open import Relation.Nullary using (¬_) open import Data.Empty using (⊥; ⊥-elim) open import Data.List open import Data.Nat open import Data.Unit using (⊤; tt) open import Function.Base using (_$_;...
------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use -- Data.Vec.Relation.Binary.Pointwise.Extensional directly. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} modu...
open import MJ.Types import MJ.Classtable.Core as Core module MJ.Classtable.Code {c}(Ct : Core.Classtable c) where open import Prelude open import Data.Maybe as Maybe using (Maybe; just; nothing) open import Data.Star as Star open import Data.List open import Data.List.Relation.Unary.All hiding (construct) open impor...
-- Andreas, Jesper, 2017-05-13, issue #2578 reported by nad -- Jesper, 2017-07-06, absurd clauses are no longer highlighted as catchall, -- so the test case had to be changed to reproduce the intended behaviour. data _⊎_ (A B : Set) : Set where inj₁ : A → A ⊎ B inj₂ : B → A ⊎ B record ⊤ : Set where constructor ...
-- Check that errors from tactics are displayed properly. module _ where open import Common.Prelude hiding (_>>=_) open import Common.Equality open import Common.Reflection failTactic : Term → TC ⊤ failTactic hole = inferType hole >>= λ goal → typeError (strErr "Surprisingly the" ∷ nameErr (quote failTactic) ∷ ...
------------------------------------------------------------------------ -- The Agda standard library -- -- The Maybe type ------------------------------------------------------------------------ -- The definitions in this file are reexported by Data.Maybe. module Data.Maybe.Core where open import Level data Maybe ...
module Type.Identity.Proofs where import Lvl open import Structure.Function open import Structure.Relator.Properties open import Structure.Relator open import Structure.Type.Identity open import Type.Identity open import Type private variable ℓ ℓ₁ ℓ₂ ℓₑ ℓₑ₁ ℓₑ₂ ℓₚ : Lvl.Level private variable T A B : Type{ℓ} pri...
-- Abstract constructors module Issue476c where module M where data D : Set abstract data D where c : D x : M.D x = M.c
module Array.APL where open import Array.Base open import Array.Properties open import Data.Nat open import Data.Nat.DivMod hiding (_/_) open import Data.Nat.Properties open import Data.Fin using (Fin; zero; suc; raise; toℕ; fromℕ≤) open import Data.Fin.Properties using (toℕ<n) open import Data.Vec open import Data.Ve...
module Numeral.Natural.Coprime.Proofs where open import Functional open import Logic open import Logic.Classical open import Logic.Propositional open import Logic.Propositional.Theorems import Lvl open import Numeral.Finite open import Numeral.Natural open import Numeral.Natural.Coprime open import Numeral.Natura...
{-# OPTIONS --universe-polymorphism #-} -- {-# OPTIONS --verbose tc.records.ifs:15 #-} -- {-# OPTIONS --verbose tc.constr.findInScope:15 #-} -- {-# OPTIONS --verbose tc.term.args.ifs:15 #-} -- {-# OPTIONS --verbose cta.record.ifs:15 #-} -- {-# OPTIONS --verbose tc.section.apply:25 #-} -- {-# OPTIONS --verbose tc.mod.ap...
------------------------------------------------------------------------ -- The Agda standard library -- -- The Stream type and some operations ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe --sized-types #-} module Codata.Stream where open import Size open im...
------------------------------------------------------------------------------ -- ABP auxiliary lemma ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# OPTIO...
-- Andreas, 2019-02-24, issue #3457 -- Error messages for illegal as-clause import Agda.Builtin.Nat Fresh-name as _ -- Previously, this complained about a duplicate module definition -- with unspeakable name. -- Expected error: -- Not in scope: Fresh-name
module Classes where open import Agda.Primitive open import Agda.Builtin.Equality open import Relation.Binary.PropositionalEquality.Core open ≡-Reasoning id : ∀ {ℓ} {A : Set ℓ} → A → A id x = x _$_ : ∀ {ℓ} {A B : Set ℓ} → (A → B) → A → B _$_ = id _∘_ : ∀ {ℓ} {A B C : Set ℓ} → (B → C) → (A → B) → A → C f ∘ g = λ ...
data Bool : Set where true false : Bool record Top : Set where foo : Top foo with true ... | true = _ ... | false = top where top = record{ } -- the only purpose of this was to force -- evaluation of the with function clauses -- which were in an __IMPOSSIBLE__ stat...
open import Prelude open import Nat open import dynamics-core open import contexts module lemmas-disjointness where -- disjointness is commutative ##-comm : {A : Set} {Δ1 Δ2 : A ctx} → Δ1 ## Δ2 → Δ2 ## Δ1 ##-comm (π1 , π2) = π2 , π1 -- the empty context is disjoint from any context empty-disj : {A : Set} (Γ...
{-# OPTIONS --safe #-} module Cubical.Algebra.Group.Properties where open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels open import Cubical.Foundations.Structure open import Cubical.Foundations.GroupoidLaws hiding (assoc) open import Cubical.Data.Sigma open import Cubical.Algebra.Semigrou...
{-# OPTIONS --safe #-} module Cubical.HITs.Cost where open import Cubical.HITs.Cost.Base
{- 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 -} open import Level using (0ℓ) open import Util.Prelude -- This module i...
module Cats.Category.Setoids.Facts where open import Cats.Category open import Cats.Category.Setoids using (Setoids) open import Cats.Category.Setoids.Facts.Exponentials using (hasExponentials) open import Cats.Category.Setoids.Facts.Initial using (hasInitial) open import Cats.Category.Setoids.Facts.Products using ...
module AML where open import Level open import Data.Product data satisfied (a : Set) (m : Set → Set) : Set where s : m a → satisfied a m data reachability (m₀ : Set → Set) (m : Set → Set) : Set where tt : reachability m₀ m data necessarity (m₀ : Set → Set) (a : Set) : Set₁ where n : ∀ m → (reachability m₀ m) ...
module Array.Properties where open import Array.Base open import Data.Fin using (Fin; zero; suc; raise; fromℕ≤; fromℕ<; fromℕ) open import Data.Nat open import Data.Nat.Properties open import Data.Vec open import Data.Vec.Properties open import Relation.Binary.PropositionalEquality open import Function using (_$_; _∘...
module Oscar.Class.Symmetry where open import Oscar.Class.Extensionality open import Oscar.Function open import Oscar.Level record Symmetry {a} {A : Set a} {ℓ} (_≤_ : A → A → Set ℓ) : Set (a ⊔ ℓ) where field ⦃ ′extensionality ⦄ : Extensionality _≤_ (λ ⋆ → flip _≤_ ⋆) id id symmetry : ∀ {x y} → x ≤ y → y ≤ x...
import cedille-options module elaboration (options : cedille-options.options) where open import lib options' = record options {during-elaboration = tt; erase-types = ff; show-qualified-vars = ff} open import general-util open import monad-instances open import cedille-types open import classify options' {id}...