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module ShouldBeAppliedToTheDatatypeParameters where data Nat : Set where zero : Nat suc : Nat -> Nat mutual F : Nat -> Set F zero = Nat F (suc n) = Foo (F n) data Foo (A : Set) : Set where fooI1 : F (suc zero)
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record ⊤ : Set where constructor tt data ⊥ : Set where open import Agda.Builtin.Size record Delay (F : Size → Set) (i : Size) : Set where coinductive field force : {j : Size< i} → F j open Delay public data Stream (A : Set) (i : Size) : Set where _∷_ : A → Delay (Stream A) i → Stream A i concat : Stream ⊤ ∞ →...
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-- Andreas, 2015-07-01 polarity needs to be computed for abstract defs. -- See also issue 1599 for the same problem with positivity. -- {-# OPTIONS -v tc.pos:10 -v tc.polarity:20 #-} open import Common.Size open import Common.Prelude data D (i : Size) : Set where c : ∀ (j : Size< i) → D i abstract E : Bool → Si...
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module List.Permutation.Pair.Properties (A : Set) where open import List.Permutation.Base A open import List.Permutation.Base.Concatenation A open import List.Permutation.Base.Equivalence A open import List.Permutation.Base.Preorder A open import List.Permutation.Pair A open import Data.List open import Data.Product o...
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{-# OPTIONS --allow-unsolved-metas #-} module _ where open import Agda.Builtin.Bool postulate P : Set → Set record R : Set1 where constructor con field A : Set B : Set data D : Set1 where con : Set → Set → D snd : D → Set snd (con A B) = B -- Eliminating from an under-applied constructor shouldn't...
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{-# OPTIONS --without-K --erased-cubical --no-import-sorts #-} module Soundness where open import Prelude open import Instruments open import MakeTracks using (makeTrackList) open import Motif using (motif; levels) open import SUtil ---------------- macro getDef : Name → Term → TC ⊤ getDef n h = do d ← get...
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{-# OPTIONS --no-termination-check #-} ------------------------------------------------------------------------ -- A terminating parser data type and the accompanying interpreter ------------------------------------------------------------------------ -- This code is based on "Parallel Parsing Processes" by Koen --...
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{-# OPTIONS --no-qualified-instances #-} module NoQualifiedInstances-AnonymousInstance where postulate A : Set f : {{A}} → A postulate instance _ : A test : A test = f
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open import Structure.Setoid open import Structure.Category open import Type module Structure.Category.Monoid {ℓₒ ℓₘ ℓₑ} {Obj : Type{ℓₒ}} {Morphism : Obj → Obj → Type{ℓₘ}} ⦃ morphism-equiv : ∀{x y} → Equiv{ℓₑ}(Morphism x y) ⦄ (cat : Category(Morphism)) where open import Logic.Predicate open import Structu...
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{-# OPTIONS --without-K #-} open import lib.Basics open import lib.NConnected open import lib.types.Bool open import lib.types.Lift open import lib.types.Nat open import lib.types.Pointed open import lib.types.TLevel open import lib.types.Suspension module lib.types.IteratedSuspension where ⊙Susp^ : ∀ {i} (n : ℕ) → ...
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{-# OPTIONS --without-K #-} module HoTT.Exercises.Chapter2 where open import HoTT.Base module Exercise1 {i} {A : 𝒰 i} where module _ {x y z : A} (p : x == y) (q : y == z) where -- Induction over p _∙₁_ : x == z _∙₁_ = =-ind D d p z q where D : (x y : A) → x == y → 𝒰 i D x y p = (z : A) → (...
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------------------------------------------------------------------------------ -- Well-founded relation on trees ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-...
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-- This file contains several ways to define localisation -- and proves them all to be equivalent {-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Experiments.LocalisationDefs where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Foundations.Equiv ...
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-- Andreas, 2018-06-09, issue #2513, parsing attributes postulate fail : ∀ @0 A → A → A -- Should fail.
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-- Andreas, 2018-10-27, issue #3327 -- -- Test that {-# NO_UNIVERSE_CHECK #-} pragma only applies to the following definition. module _ where -- The following pragma should only apply to the following definition, -- but due to a bug is actually applying to the rest of the module. {-# NO_UNIVERSE_CHECK #-} data ⊥ : S...
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-- Properties of Fibonacci nunmbers {-# OPTIONS --without-K --safe #-} module Math.NumberTheory.Fibonacci.Nat.Properties where -- agda-stdlib open import Data.Unit using (tt) open import Data.Sum open import Data.Nat open import Data.Nat.Properties open import Relation.Binary.PropositionalEquality open import Relati...
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open import Nat open import Prelude open import core open import contexts open import lemmas-consistency open import lemmas-disjointness open import weakening module typed-elaboration where mutual typed-elaboration-synth : {Γ : tctx} {e : hexp} {τ : htyp} {d : ihexp} {Δ : hctx} → Γ ⊢ ...
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module Ag07 where open import IO data W (A : Set) (B : A → Set) : Set where sup : (a : A) → (b : B a → W A B) → W A B module WBinTree where data Tree : Set where Leaf : Tree Node : Tree data Direction : Set where Left : Direction Right : Direction data Bottom : Set where void : ∀ {A :...
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module Implicits.Resolution.Ambiguous.SystemFEquiv where open import Prelude open import Function.Equivalence using (_⇔_; equivalence) open import Data.List.Properties open import Relation.Binary.HeterogeneousEquality as H using () open import Data.Vec.Properties as VP using () open import Data.Vec hiding ([_]) open ...
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------------------------------------------------------------------------ -- Pointed and non-pointed ω-cpos ------------------------------------------------------------------------ {-# OPTIONS --erased-cubical --safe #-} module Omega-cpo where open import Equality.Propositional.Cubical open import Logical-equivalence...
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open import Nat open import Prelude open import dynamics-core open import contexts open import lemmas-consistency open import type-assignment-unicity open import lemmas-progress-checks -- taken together, the theorems in this file argue that for any expression -- d, at most one summand of the labeled sum that results f...
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module Metalogic.Constructive.Provability where open import Sets.BoolSet open import Functional import Lvl open import Type -- Structural rules record Structural {ℓ ℓₘ} {Formula : Type{ℓ}} (_⊢_ : BoolSet(Formula) → Formula → Type{ℓₘ}) : Type{ℓₘ Lvl.⊔ ℓ} where field assumption : ∀{Γ}{φ} → (φ ∈ Γ) → (Γ ⊢ φ...
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module Function.Iteration.Order where open import Data open import Data.Boolean.Stmt open import Functional renaming (id to id-fn) open import Function.Iteration hiding (_^_) open import Function.Iteration.Proofs open import Logic open import Logic.IntroInstances open import Logic.Propositional open import Logic.Propo...
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module Issue2487-4 where open import Agda.Primitive -- this should not be consistency-checked open import Agda.Builtin.Bool f : Bool → Bool f true = true f _ = false
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{-# OPTIONS --cubical --safe --postfix-projections #-} module Relation.Nullary.Decidable.Logic where open import Prelude open import Data.Sum infixl 7 _&&_ _&&_ : Dec A → Dec B → Dec (A × B) (x && y) .does = x .does and y .does (yes x && yes y) .why = ofʸ (x , y) (yes x && no y) .why = ofⁿ (y ∘ snd) (no x && y) ...
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{-# OPTIONS --cubical --safe --postfix-projections #-} module Data.Bool.Properties where open import HLevels open import Path open import Data.Bool.Base open import Data.Bool.Truth open import Data.Unit.Properties open import Data.Unit open import Data.Empty open import Data.Empty.Properties using (isProp⊥) open impo...
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{-# OPTIONS --without-K #-} --open import HoTT open import homotopy.3x3.PushoutPushout open import homotopy.3x3.Transpose open import homotopy.3x3.Common module homotopy.3x3.From {i} (d : Span^2 {i}) where open Span^2 d open M d hiding (Pushout^2) open M (transpose d) using () renaming (A₀∙ to A∙₀; A₂∙ to A∙₂; A₄∙ t...
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module general-util where open import instances public get-file-contents : (filename : string) → IO (maybe string) get-file-contents e = doesFileExist e >>= λ b → if b then (readFiniteFile e >>= λ s → return (just s)) else return nothing maybe-else : ∀{ℓ}{A B : Set ℓ} → B → (A → B) → maybe ...
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------------------------------------------------------------------------ -- M-types for indexed containers, defined coinductively (in Cubical -- Agda) ------------------------------------------------------------------------ {-# OPTIONS --erased-cubical --safe --guardedness #-} import Equality.Path as P module Contai...
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{-# OPTIONS --without-K --exact-split #-} module rings where import abelian-groups open abelian-groups public has-mul-Ab : { l1 : Level} (A : Ab l1) → UU l1 has-mul-Ab A = Σ ( has-associative-bin-op (set-Ab A)) ( λ μ → ( is-unital (pair (set-Ab A) μ)) × ( ( (a b c : type-Ab A) → Id (pr1...
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module Everything where import Tuple import Inductive import Inductive.Examples.Empty import Inductive.Examples.Unit import Inductive.Examples.Sum import Inductive.Examples.Product import Inductive.Examples.Nat import Inductive.Examples.Ord import Inductive.Examples.List import Inductive.Examples.BinTree
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{-# OPTIONS --without-K --rewriting #-} open import HoTT open import cohomology.Theory open import groups.ExactSequence open import groups.HomSequence module cw.cohomology.GridLongExactSequence {i} (CT : CohomologyTheory i) {X Y Z : Ptd i} (n : ℤ) (f : X ⊙→ Y) (g : Y ⊙→ Z) where open CohomologyTheory CT open impor...
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------------------------------------------------------------------------ -- A compiler ------------------------------------------------------------------------ open import Prelude import Lambda.Syntax module Lambda.Compiler {Name : Type} (open Lambda.Syntax Name) (def : Name → Tm 1) where open import Equali...
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module Bin-laws where import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; sym; cong) open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; step-≡; _∎) open import Data.Nat using (ℕ; zero; suc; _+_; _*_) open import Induction′ using (+-suc; +-identityʳ; +-comm; +-assoc) -- 2進数の表現 data Bin : Set where ⟨⟩ : Bi...
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-- Previously Agda accepted invalid module names when no module header -- was given.
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module RandomAccessList.General.Redundant where open import RandomAccessList.General.Core open import Data.Nat Redundant : Set → ℕ → Set Redundant A = General A 0 2 cons : ∀ {n A} → A → Redundant A n → Redundant A n cons a [] = ? cons a (∺ x x₁ x₂ xs) = ?
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module RMonads.RMonadMorphs where open import Library open import Functors open import Categories open import RMonads open Fun open RMonad record RMonadMorph {a b c d}{C : Cat {a}{b}}{D : Cat {c}{d}}{J : Fun C D} (M M' : RMonad J) : Set (a ⊔ b ⊔ c ⊔ d) where constructor rmonadmorph open Cat D ...
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--------------------------------------------------------------------------- -- The gcd is greatest that any common divisor --------------------------------------------------------------------------- {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorp...
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{-# OPTIONS --without-K --safe #-} module Algebra.Linear where open import Algebra.Linear.Core public open import Algebra.Linear.Construct public open import Algebra.Linear.Morphism public open import Algebra.Linear.Structures public
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{-# OPTIONS --without-K #-} module SymmetricMonoidalCategory where open import Level open import Categories.Category using (Category) open import Categories.Monoidal using (Monoidal) open import Categories.Monoidal.Braided using (Braided; module Braided) open import Categories.NaturalIsomorphism using (module Natur...
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module Generic.Lib.Data.Sum where open import Data.Sum hiding (swap) renaming (map to smap) hiding (map₁; map₂) public
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-- Display whether or not the timeout was hit when using auto -l. module Issue945 where data ⊥ : Set where ¬_ : Set → Set ¬ A = A → ⊥ record ∃ {A : Set} (P : A → Set) : Set where constructor _,_ field witness : A proof : P witness -- Exhaustive lem₁ : ∀ {A : Set} (P : A → Set) (x : A) → (∀ x → ¬ P x) ...
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open import Everything module Test.Class where record ℭlass {ℓ} {𝔢} {CONSTRAINTS : Ø 𝔢} (constraints : CONSTRAINTS) : Ø ↑̂ ℓ where constructor ∁ field type : Ø ℓ private record SET-CLASS ⦃ _ : Constraint constraints ⦄ : Ø ℓ where constructor ∁ field ⋆ : type ...
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{-# OPTIONS --without-K --safe #-} -- The category of Sets is Monoidal module Categories.Category.Monoidal.Instance.Sets where open import Level open import Data.Product using (Σ; _×_; _,_; proj₁; proj₂; uncurry; map; <_,_>) open import Data.Sum using (_⊎_; inj₁; inj₂; [_,_]′) open import Data.Unit using (⊤) open im...
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-- Andreas, 2016-12-15, issue #2341 -- `with` needs to abstract also in sort of target type. -- {-# OPTIONS -v tc.with:100 #-} open import Agda.Primitive test : ∀ a → Set (lsuc a) test a with a ... | w = Set w
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------------------------------------------------------------------------ -- The Agda standard library -- -- Propositional equality ------------------------------------------------------------------------ -- This file contains some core definitions which are reexported by -- Relation.Binary.PropositionalEquality. modu...
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{-# OPTIONS --without-K #-} open import lib.Basics open import lib.types.Bool open import lib.types.Lift open import lib.types.Paths open import lib.types.Pointed open import lib.types.Wedge open import lib.cubical.Square module lib.types.BigWedge where module _ {i j} {A : Type i} where private data #BigWedge...
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{-# OPTIONS --allow-incomplete-matches #-} module Issue3295.Incomplete where open import Agda.Builtin.Nat f : Nat → Nat f zero = zero
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{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Algebra.RingSolver.EvaluationHomomorphism where open import Cubical.Foundations.Prelude open import Cubical.Data.Nat using (ℕ) open import Cubical.Data.FinData open import Cubical.Data.Vec open import Cubical.Algebra.RingSolver.RawRing open import Cub...
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module z where -- http://www.cse.chalmers.se/~ulfn/papers/afp08/tutorial.pdf {- Dependently Typed Programming in Agda Ulf Norell1 : Chalmers University, Gothenburg : ulfn@chalmers.se James Chapman : Institute of Cybernetics, Tallinn : james@cs.ioc.ee ---------------------------------------------------------------...
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{-# OPTIONS --cubical --safe #-} module Cubical.HITs.Localization.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Foundations.PathSplitEquiv open isPathSplitEquiv module _ {ℓα ℓs ℓt} {A : Type ℓα} {S : A → Type ℓs} {T : A → Type ℓt} where isLocal : ∀ ...
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module Oscar.Category.SemigroupoidAction where open import Oscar.Category.Action open import Oscar.Category.Setoid open import Oscar.Category.Semigroupoid open import Oscar.Function open import Oscar.Level module _ {𝔊𝔬 𝔊𝔪 𝔊𝔮} (semigroupoid : Semigroupoid 𝔊𝔬 𝔊𝔪 𝔊𝔮) where open Semigroupoid semigroupoid ...
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{-# NON_TERMINATING #-} mutual record R : Set where inductive field x : T T : Set T = T → R
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open import Everything module Test.SurjidentityI where module _ {𝔬₁} {𝔒₁ : Ø 𝔬₁} {𝔯₁} (_∼₁_ : 𝔒₁ → 𝔒₁ → Ø 𝔯₁) {𝔬₂} {𝔒₂ : Ø 𝔬₂} {𝔯₂} (_∼₂_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂) (_∼₂2_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂) {𝔯₂'} (_∼₂'_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂') {ℓ₂} (_∼̇₂_ : ∀ {x y} → x ∼₂ y → x ∼₂ y → Ø ℓ₂) ...
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data Nat : Set where zero : Nat suc : Nat → Nat data ⊥ : Set where ⊥-elim : {A : Set} → ⊥ → A ⊥-elim = λ where () ⊥-elim₂ : {A : Set} → ⊥ → A → A ⊥-elim₂ = λ where () _ ⊥-elim₃ : {A : Set} → A → ⊥ → A ⊥-elim₃ = λ where _ () data D : Set where c₁ : ⊥ → D c₂ : D Parses : D → Set₁ Parses = λ where c₂ ...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Natural number types and operations requiring the axiom K. ------------------------------------------------------------------------ {-# OPTIONS --with-K --safe #-} module Data.Nat.WithK where open import Data....
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{-# OPTIONS --safe --warning=error #-} open import Agda.Primitive using (Level; lzero; lsuc; _⊔_) open import LogicalFormulae open import Logic.PropositionalLogic open import Functions.Definition open import Numbers.Naturals.Naturals open import Vectors open import Boolean.Definition module Logic.PropositionalAxiomsT...
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-- Andreas, 2016-11-18, issue #2174 -- report and test case by Nisse postulate F : Set → Set → Set G : Set G = {!!} -- WAS: giving first F ? and then F ? ? lead to one of the metas not goalified. -- Should succeed now, see script Issue2174a.sh
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{-# OPTIONS --without-K #-} module algebra.group.classifying where open import level open import algebra.group.core open import algebra.group.morphism open import equality.core open import function.isomorphism open import pointed.core open import sets.unit open import sum open import hott.level.core open import hott....
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{-# OPTIONS -v treeless.opt:20 #-} module _ where open import Agda.Builtin.Nat using (_<_) open import Common.Prelude open import Common.Integer -- Should compile to -- λ a b → case a of -- "neg" → 0 - b -- _ → b match-on-lit : String → Integer → Integer match-on-lit "neg" x with x ......
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{-# OPTIONS --cubical --no-import-sorts #-} module Spaces where open import Agda.Primitive renaming (_⊔_ to ℓ-max; lsuc to ℓ-suc; lzero to ℓ-zero) private variable ℓ ℓ' ℓ'' : Level open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc) open import Cubical.Structures.CommRing open ...
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{-# OPTIONS --cubical --no-import-sorts #-} open import Bundles module Properties.AlmostOrderedField {ℓ ℓ'} (AOF : AlmostOrderedField {ℓ} {ℓ'}) where open import Agda.Primitive renaming (_⊔_ to ℓ-max; lsuc to ℓ-suc; lzero to ℓ-zero) private variable ℓ'' : Level open import Cubical.Foundations.Everything rena...
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module Oscar.Property.Transitivity where open import Oscar.Level record Transitivity {𝔬} {⋆ : Set 𝔬} {𝔮} (_↦_ : ⋆ → ⋆ → Set 𝔮) : Set (𝔬 ⊔ 𝔮) where field transitivity : ∀ {x y} → x ↦ y → ∀ {z} → y ↦ z → x ↦ z open Transitivity ⦃ … ⦄ public
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------------------------------------------------------------------------ -- Sums (disjoint unions) ------------------------------------------------------------------------ module Data.Sum where open import Data.Function open import Data.Maybe.Core ---------------------------------------------------------------------...
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-- Andreas, 2019-04-10, issue #3683 reported by akaposi. -- Regression in the termination checker introduced together -- with collecting function calls also in the type signatures -- (fix of #1556). data A : Set data B : A → Set data A where a : A f : B a → A data B where module _ (A' : Set)(B' : A' → Set) ...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Properties of operations on the Colist type ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe --sized-types #-} module Codata.Colist.Properties where open ...
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module BadCon where data D : Set where d : D data E : Set where d : E postulate F : D -> Set test : (x : D) -> F x test = d -- Bad error (unbound de Bruijn index): -- the constructor d does not construct an element of F @0 -- when checking that the expression d has type (x : D) → F x
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{-# OPTIONS --copatterns --sized-types #-} module Streams where open import Size open import Function open import Relation.Binary open import Relation.Binary.PropositionalEquality as P open ≡-Reasoning open import Data.List using (List; module List; []; _∷_; _++_; length) open import Data.Nat using (ℕ; zero; suc) op...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Greatest common divisor ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Nat.GCD where open import Data.Nat open import Data.Nat.Divisibil...
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------------------------------------------------------------------------------ -- Properties of the Collatz function ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphis...
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{-# OPTIONS --without-K #-} module sets.unit where record ⊤ : Set where constructor tt ⊤-elim : (P : ⊤ → Set) → P tt → (x : ⊤) → P x ⊤-elim P ptt tt = ptt
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-- Andreas, 2015-09-12 open import Common.Product open import Common.Equality module _ (A : Set) where mutual X : A × A → A X = _ test : (x y : A × A) → X (proj₁ x , proj₁ y) ≡ proj₁ x test _ _ = refl -- This worked even before the fix of #1316, -- since _ record variables are expanded (see #473).
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------------------------------------------------------------------------ -- Some substitution lemmas ------------------------------------------------------------------------ open import Atom module Substitution (atoms : χ-atoms) where open import Equality.Propositional open import Prelude hiding (const) open import...
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module Base where postulate String : Set Char : Set {-# BUILTIN STRING String #-} {-# BUILTIN CHAR Char #-} data Unit : Set where unit : Unit {-# COMPILED_DATA Unit () #-} data Bool : Set where true : Bool false : Bool data False : Set where record True : Set where IsTrue : Bool -> Set Is...
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module Base.Partial where open import Data.String using (String) open import Base.Free using (Free) record Partial (S : Set) (P : S → Set) : Set₁ where field undefined : {A : Set} → Free S P A error : {A : Set} → String → Free S P A open Partial ⦃ ... ⦄ public
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------------------------------------------------------------------------ -- The Agda standard library -- -- A bunch of properties ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Bool.Properties where open import Algebra.Bundles open import Data....
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------------------------------------------------------------------------ -- A definitional interpreter ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} module Lambda.Simplified.Delay-monad.Interpreter where open import Equality.Propositional open import Prelude ...
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module Serializer.VecBool where open import Data.Fin hiding (_+_) open import Data.Nat open import Data.Vec open import Data.Bool open import Function using (_∘_ ; _$_ ; _∋_ ; id ; const) open import Function.Bijection open import Function.Injection open import Function.Surjection open import Function.Equality using (...
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{-# OPTIONS --without-K #-} open import HoTT module homotopy.PushoutComm where -- How do I prevent [to] from being exported? private module _ {i j k} (s : Span {i} {j} {k}) where open Span s flip : Span flip = span B A C g f to : Pushout s → Pushout flip to = To.f module M where module To = Pusho...
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module Extensions.ListFirstFunctional where open import Prelude hiding (_⊔_) open import Level private lemma : ∀ {a b} {A : Set a} {P : A → Set b} (decP : ∀ a → (Dec $ P a)) v {x y} → any decP (x List.∷ v) ≡ yes (there {x = x} y) → ¬ P x lemma decP v {x} {y} eq p with decP x lemma decP v () p ...
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------------------------------------------------------------------------------ -- Testing the translation of definitions ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymor...
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{-# OPTIONS --without-K --rewriting #-} open import HoTT open import homotopy.FinWedge module homotopy.Bouquet where Rose : ∀ {i} (I : Type i) → Type i Rose I = BigWedge {A = I} (λ _ → ⊙S¹) Bouquet-family : ∀ {i} (I : Type i) (m : ℕ) → (I → Ptd₀) Bouquet-family I m _ = ⊙Sphere m Bouquet : ∀ {i} (I : Type i) (m : ℕ...
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module Data.Nat.Extra where open import Data.Nat open import Data.Bool isZero : ℕ → Bool isZero 0 = true isZero (suc _) = false
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module Tactic.Nat.Exp where open import Prelude Var = Nat Env : Set → Set Env Atom = Atom → Nat infixl 6 _⟨+⟩_ infixl 7 _⟨*⟩_ data Exp (Atom : Set) : Set where var : (x : Atom) → Exp Atom lit : (n : Nat) → Exp Atom _⟨+⟩_ _⟨*⟩_ : (e e₁ : Exp Atom) → Exp Atom ⟦_⟧e : ∀ {Atom} → Exp Atom → Env Atom → Nat ⟦ var ...
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module DTGP.State where open import Data.Product infixl 1 _>>=_ _=<<_ data State (S A : Set) : Set where state : (S → A × S) → State S A runState : ∀ {S A} → State S A → S → A × S runState (state f) = f return : ∀ {S A} → A → State S A return a = state (λ s → a , s) _>>=_ : {S A B : Set} → State S A → (A → State...
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open import Nat open import Prelude open import List open import Hazelnut-core module Hazelnut-checks where ----------------------------------------------------------------------------- -- these theorems aren't listed in the draft, but have been discussed -- since submission. broadly speaking, they act as sanit...
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-- Typing contexts and environments module Syntax.Context where open import Syntax.Types open import Relation.Binary using (IsPreorder) open import Relation.Binary.PropositionalEquality hiding ([_]) open import Data.Sum -- | Data types -- A type judgement with temporal qualifiers: -- a type is either inhabited now...
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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 -} open import LibraBFT.Prelude open import LibraBFT.Base.Types import ...
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open import Data.Bool hiding (if_then_else_) open import Data.Empty open import Data.List open import Data.List.Properties open import Data.Maybe open import Data.Product open import Data.Sum open import Data.Unit open import Relation.Binary.PropositionalEquality hiding (Extensionality ; [_]) open import Relation.Null...
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{-# OPTIONS --postfix-projections #-} {-# OPTIONS --rewriting #-} -- A Beth model for normalization by evaluation open import Library module NbeModel (Base : Set) (B⦅_⦆ : Base → Set) where import Formulas ; open module Form = Formulas Base hiding (Mon) import Derivations ; open module Der = Derivations B...
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-------------------------------------------------------------------------------- -- This is part of Agda Inference Systems {-# OPTIONS --sized-types #-} open import Relation.Nullary open import Relation.Nullary.Decidable open import Data.Nat open import Data.Vec open import Data.Fin open import Data.Product open impo...
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{-# OPTIONS --cubical --safe #-} module Container.Polynomial where open import Prelude hiding (id; const; _×_; Π; _⊎_; Σ; _∘_; ⊤; ⊥) open import Data.Unit.UniversePolymorphic open import Data.Empty.UniversePolymorphic import Prelude as P open import Container module _ {s p : Level} where id : Container s p id...
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module Data.Collection.Core.Properties where -- open import Data.List public using (List; []; _∷_) -- open import Data.String public using (String; _≟_) -- open import Level using (zero) -- -- open import Function using (flip) -- open import Relation.Nullary -- open import Relation.Nullary.Negation -- open import Rela...
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{- Mathematical Foundations of Programming (G54FOP) Nicolai Kraus Lecture 3, 7 Feb 2018 ==================== INTRODUCTION TO AGDA ==================== Your G54FPP project could involve Agda. If you want. Btw, text in {- -} is a comment. So is text after --. links to help you install and learn Agd...
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------------------------------------------------------------------------------ -- Common definitions ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# OPTION...
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{-# OPTIONS --without-K #-} module Model.Stream where open import Model.Size as MS using ( Size ; Sizes ; _≤_ ; _<_ ; ≤-IsProp ; ≤-trans ; nat ) open import Model.Type.Core open import Util.HoTT.FunctionalExtensionality open import Util.HoTT.HLevel open import Util.Prelude import Data.Nat.Properties as ℕ open Size...
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------------------------------------------------------------------------ -- Some cancellation lemmas ------------------------------------------------------------------------ open import Atom module Cancellation (atoms : χ-atoms) where open import Equality.Propositional open import Prelude hiding (const) open import...
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{-# OPTIONS --safe #-} {- This file models "ZF - powerset" in cubical agda, via a cumulative hierarchy, in the sense given in the HoTT book §10.5 "The cumulative hierarchy". A great amount of inspiration is taken from the Coq implementations found in Jérémy Ledent, Modeling set theory in homotopy type theory, code of ...
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{-# OPTIONS --safe #-} {- This is inspired by/copied from: https://github.com/agda/agda-stdlib/blob/master/src/Tactic/MonoidSolver.agda Boilerplate code for calling the ring solver is constructed automatically with agda's reflection features. -} module Cubical.Algebra.RingSolver.ReflectionSolving where open i...
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open import Nat open import Prelude open import List open import judgemental-erase open import moveerase open import statics-checks open import statics-core module aasubsume-min where -- this predicate on derivations of actions bans the cases that induce -- non-determinism. mutual aasubmin-synth : ∀{Γ e t α ...
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