Index of /~nad/listings/lib-0.3

[ICO]NameLast modifiedSizeDescription

[PARENTDIR]Parent Directory   -  
[TXT]Data.Bool.Properties..>2009-12-23 11:06 148K 
[TXT]Data.Unit.html 2009-12-23 11:06 23K 
[TXT]Foreign.Haskell.html 2009-12-23 11:06 17K 
[TXT]Algebra.Props.Lattic..>2009-12-23 11:06 20K 
[TXT]Data.Nat.Divisibilit..>2009-12-23 11:06 134K 
[TXT]Relation.Nullary.Neg..>2009-12-23 11:06 114K 
[TXT]Relation.Nullary.Pro..>2009-12-23 11:06 8.4K 
[TXT]Relation.Binary.Prod..>2009-12-23 11:06 156K 
[TXT]Relation.Binary.Refl..>2009-12-23 11:06 47K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:06 10K 
[TXT]Relation.Binary.NonS..>2009-12-23 11:06 67K 
[TXT]Data.Nat.InfinitelyO..>2009-12-23 11:06 57K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:06 11K 
[TXT]Data.Maybe.Core.html 2009-12-23 11:06 4.6K 
[TXT]Data.Nat.GCD.Lemmas...>2009-12-23 11:06 225K 
[TXT]Data.List.All.Proper..>2009-12-23 11:06 45K 
[TXT]Relation.Binary.Preo..>2009-12-23 11:06 21K 
[TXT]Relation.Binary.Stri..>2009-12-23 11:06 6.3K 
[TXT]Relation.Nullary.Uni..>2009-12-23 11:06 119K 
[TXT]Relation.Binary.On.html2009-12-23 11:06 108K 
[TXT]Data.AVL.html 2009-12-23 11:06 215K 
[TXT]Data.Bin.html 2009-12-23 11:06 173K 
[TXT]Algebra.Props.Abelia..>2009-12-23 11:07 34K 
[TXT]Data.AVL.IndexedMap...>2009-12-23 11:07 46K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:07 10K 
[TXT]Data.DifferenceVec.html2009-12-23 11:07 36K 
[TXT]Data.Star.Pointer.html 2009-12-23 11:07 73K 
[TXT]Data.Nat.LCM.html 2009-12-23 11:07 90K 
[TXT]Relation.Binary.Cons..>2009-12-23 11:07 88K 
[TXT]Data.Sign.html 2009-12-23 11:07 11K 
[TXT]Algebra.Props.Ring.html2009-12-23 11:07 41K 
[TXT]Category.Applicative..>2009-12-23 11:07 28K 
[TXT]Data.Fin.Substitutio..>2009-12-23 11:07 83K 
[TXT]Data.Vec.html 2009-12-23 11:07 181K 
[TXT]Algebra.Props.Distri..>2009-12-23 11:07 46K 
[TXT]Data.Bool.Show.html 2009-12-23 11:07 3.4K 
[TXT]Data.Nat.html 2009-12-23 11:07 121K 
[TXT]Data.AVL.Sets.html 2009-12-23 11:07 26K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:07 18K 
[TXT]Relation.Nullary.html 2009-12-23 11:07 8.3K 
[TXT]Relation.Binary.Part..>2009-12-23 11:07 5.3K 
[TXT]Data.Fin.Substitutio..>2009-12-23 11:07 24K 
[TXT]Category.Monad.html 2009-12-23 11:07 14K 
[TXT]Data.Char.html 2009-12-23 11:07 15K 
[TXT]Relation.Binary.Indu..>2009-12-23 11:07 26K 
[TXT]Data.Fin.Substitutio..>2009-12-23 11:07 73K 
[TXT]Data.List.Countdown...>2009-12-23 11:07 198K 
[TXT]Data.Function.Equali..>2009-12-23 11:07 81K 
[TXT]Data.Bool.html 2009-12-23 11:07 26K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:07 6.5K 
[TXT]Data.Star.Environmen..>2009-12-23 11:07 19K 
[TXT]Data.BoundedVec.html 2009-12-23 11:07 38K 
[TXT]Everything.html 2009-12-23 11:07 86K 
[TXT]Size.html 2009-12-23 11:07 3.4K 
[TXT]Algebra.Props.Group...>2009-12-23 11:07 58K 
[TXT]Level.html 2009-12-23 11:07 10K 
[TXT]Data.Stream.html 2009-12-23 11:07 75K 
[TXT]Data.Nat.Show.html 2009-12-23 11:07 11K 
[TXT]Data.Empty.html 2009-12-23 11:07 3.8K 
[TXT]Data.Product.html 2009-12-23 11:07 94K 
[TXT]Relation.Binary.List..>2009-12-23 11:08 241K 
[TXT]Relation.Binary.Orde..>2009-12-23 11:08 31K 
[TXT]Data.Maybe.html 2009-12-23 11:08 75K 
[TXT]Data.Nat.DivMod.html 2009-12-23 11:08 77K 
[TXT]Data.DifferenceNat.html2009-12-23 11:08 12K 
[TXT]Relation.Binary.Cons..>2009-12-23 11:08 11K 
[TXT]Data.Star.html 2009-12-23 11:08 84K 
[TXT]Data.Fin.Subset.html 2009-12-23 11:08 27K 
[TXT]Data.Function.html 2009-12-23 11:08 55K 
[TXT]Data.List.Any.Proper..>2009-12-23 11:08 720K 
[TXT]Algebra.RingSolver.S..>2009-12-23 11:08 4.3K 
[TXT]Category.Monad.Ident..>2009-12-23 11:08 5.1K 
[TXT]Data.Function.LeftIn..>2009-12-23 11:08 48K 
[TXT]Category.Monad.Conti..>2009-12-23 11:08 38K 
[TXT]Data.List.Reverse.html 2009-12-23 11:08 28K 
[TXT]Category.Functor.html 2009-12-23 11:08 7.1K 
[TXT]Algebra.Props.Boolea..>2009-12-23 11:08 494K 
[TXT]Algebra.FunctionProp..>2009-12-23 11:08 4.8K 
[TXT]Relation.Binary.html 2009-12-23 11:09 113K 
[TXT]Induction.Nat.html 2009-12-23 11:09 46K 
[TXT]Relation.Binary.Stri..>2009-12-23 11:09 69K 
[TXT]Data.List.Properties..>2009-12-23 11:09 243K 
[TXT]Data.String.html 2009-12-23 11:09 27K 
[TXT]Data.Vec.Properties...>2009-12-23 11:09 134K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:09 8.2K 
[TXT]Data.List.NonEmpty.P..>2009-12-23 11:09 42K 
[TXT]Data.Sum.html 2009-12-23 11:09 36K 
[TXT]Data.List.Any.html 2009-12-23 11:09 103K 
[TXT]Relation.Binary.Core..>2009-12-23 11:09 125K 
[TXT]Relation.Nullary.Cor..>2009-12-23 11:09 7.9K 
[TXT]Category.Applicative..>2009-12-23 11:09 6.3K 
[TXT]Relation.Binary.List..>2009-12-23 11:09 103K 
[TXT]Algebra.Morphism.html 2009-12-23 11:09 41K 
[TXT]Data.Rational.html 2009-12-23 11:09 63K 
[TXT]Data.List.NonEmpty.html2009-12-23 11:09 123K 
[TXT]Data.Star.Properties..>2009-12-23 11:09 94K 
[TXT]Relation.Binary.EqRe..>2009-12-23 11:09 7.2K 
[TXT]Data.Fin.Subset.Prop..>2009-12-23 11:09 48K 
[TXT]Data.Integer.Divisib..>2009-12-23 11:09 13K 
[TXT]Data.Star.Decoration..>2009-12-23 11:09 74K 
[TXT]Data.Colist.html 2009-12-23 11:09 173K 
[TXT]Data.Nat.Properties...>2009-12-23 11:09 432K 
[TXT]Algebra.RingSolver.L..>2009-12-23 11:09 144K 
[TXT]Data.Digit.html 2009-12-23 11:09 61K 
[TXT]Data.Function.Inject..>2009-12-23 11:09 27K 
[TXT]Data.Star.Vec.html 2009-12-23 11:09 30K 
[TXT]Relation.Binary.Sum...>2009-12-23 11:09 270K 
[TXT]Algebra.Operations.html2009-12-23 11:09 31K 
[TXT]Algebra.html 2009-12-23 11:09 135K 
[TXT]Data.Star.Fin.html 2009-12-23 11:09 8.8K 
[TXT]IO.Primitive.html 2009-12-23 11:09 14K 
[TXT]Induction.WellFounde..>2009-12-23 11:09 17K 
[TXT]Algebra.RingSolver.A..>2009-12-23 11:09 54K 
[TXT]Relation.Nullary.Dec..>2009-12-23 11:09 36K 
[TXT]Data.Fin.html 2009-12-23 11:09 103K 
[TXT]Relation.Binary.Prod..>2009-12-23 11:09 121K 
[TXT]Data.Star.Nat.html 2009-12-23 11:09 19K 
[TXT]Relation.Binary.Hete..>2009-12-23 11:09 140K 
[TXT]Data.Fin.Substitutio..>2009-12-23 11:09 497K 
[TXT]Data.Map.html 2009-12-23 11:09 58K 
[TXT]Data.Integer.html 2009-12-23 11:09 158K 
[TXT]Data.Product.Record...>2009-12-23 11:09 55K 
[TXT]Relation.Unary.html 2009-12-23 11:09 68K 
[TXT]Data.Sets.html 2009-12-23 11:09 57K 
[TXT]Relation.Binary.List..>2009-12-23 11:09 107K 
[TXT]Data.List.html 2009-12-23 11:09 215K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:09 9.4K 
[TXT]Data.Covec.html 2009-12-23 11:09 123K 
[TXT]Induction.Lexicograp..>2009-12-23 11:09 39K 
[TXT]Relation.Binary.Simp..>2009-12-23 11:09 13K 
[TXT]Agda.css 2009-12-23 11:09 1.1K 
[TXT]Data.BoundedVec.Inef..>2009-12-23 11:09 18K 
[TXT]Data.Fin.Props.html 2009-12-23 11:09 120K 
[TXT]Data.Nat.GCD.html 2009-12-23 11:09 126K 
[TXT]Data.Nat.Coprimality..>2009-12-23 11:09 96K 
[TXT]Data.Star.BoundedVec..>2009-12-23 11:09 28K 
[TXT]Algebra.Structures.html2009-12-23 11:09 162K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:09 69K 
[TXT]Relation.Binary.Prop..>2009-12-23 11:09 11K 
[TXT]Data.List.All.html 2009-12-23 11:09 43K 
[TXT]Relation.Binary.Prod..>2009-12-23 11:09 198K 
[TXT]Data.Vec.N-ary.html 2009-12-23 11:09 99K 
[TXT]IO.html 2009-12-23 11:09 49K 
[TXT]Category.Monad.Index..>2009-12-23 11:09 32K 
[TXT]Category.Monad.Parti..>2009-12-23 11:09 49K 
[TXT]Data.Conat.html 2009-12-23 11:09 25K 
[TXT]Category.Monad.State..>2009-12-23 11:09 71K 
[TXT]Data.Integer.Propert..>2009-12-23 11:09 80K 
[TXT]Induction.html 2009-12-23 11:09 28K 
[TXT]Algebra.FunctionProp..>2009-12-23 11:09 58K 
[TXT]Data.Cofin.html 2009-12-23 11:09 19K 
[TXT]Data.DifferenceList...>2009-12-23 11:09 33K 
[TXT]Data.Sign.Properties..>2009-12-23 11:09 11K 
[TXT]Coinduction.html 2009-12-23 11:09 6.5K 
[TXT]Data.Fin.Dec.html 2009-12-23 11:09 129K 
[TXT]Data.Star.List.html 2009-12-23 11:09 9.3K 
[TXT]Algebra.RingSolver.html2009-12-23 11:09 194K 
[TXT]Relation.Nullary.Sum..>2009-12-23 11:09 17K 
[TXT]Relation.Binary.Flip..>2009-12-23 11:09 156K 
[TXT]Data.Graph.Acyclic.html2009-12-23 11:10 195K 
[TXT]Data.Vec.Equality.html 2009-12-23 11:10 74K 

README
module README where

------------------------------------------------------------------------
-- The Agda standard library, version 0.3
--
-- Author: Nils Anders Danielsson, with contributions from
-- Jean-Philippe Bernardy, Samuel Bronson, Liang-Ting Chen, Dan Doel,
-- Patrik Jansson, Darin Morrison, Shin-Cheng Mu, Ulf Norell, Nicolas
-- Pouillard and Andrés Sicard-Ramírez
------------------------------------------------------------------------

-- This version of the library has been tested using Agda 2.2.6.

-- Note that no guarantees are currently made about forwards or
-- backwards compatibility, the library is still at an experimental
-- stage.

-- To make use of the library, add the path to the library’s root
-- directory (src) to the Agda search path, either using the
-- --include-path flag or by customising the Emacs mode variable
-- agda2-include-dirs (M-x customize-group RET agda2 RET).

-- Contributions to this library are welcome (but to avoid wasted work
-- it is suggested that you discuss large changes before implementing
-- them). Please send contributions in the form of darcs patches (run
-- darcs send --output <patch file> and attach the patch file to an
-- email), and include a statement saying that you agree to release
-- your library patches under the library's licence. It is appreciated
-- if every patch contains a single, complete change, and if the
-- coding style used in the library is adhered to.

------------------------------------------------------------------------
-- Module hierarchy
------------------------------------------------------------------------

-- The top-level module names of the library are currently allocated
-- as follows:
--
-- • Algebra
--     Abstract algebra (monoids, groups, rings etc.), along with
--     properties needed to specify these structures (associativity,
--     commutativity, etc.), and operations on and proofs about the
--     structures.
-- • Category
--     Category theory-inspired idioms used to structure functional
--     programs (functors and monads, for instance).
-- • Coinduction
--     Support for coinduction.
-- • Data
--     Data types and properties about data types. (Also some
--     combinators working solely on and with functions; see
--     Data.Function.)
-- • Foreign
--     Related to the foreign function interface.
-- • Induction
--     A general framework for induction (includes lexicographic and
--     well-founded induction).
-- • IO
--     Input/output-related functions.
-- • Level
--     Universe levels.
-- • Relation
--     Properties of and proofs about relations (mostly homogeneous
--     binary relations).
-- • Size
--     Sizes used by the sized types mechanism.

------------------------------------------------------------------------
-- A selection of useful library modules
------------------------------------------------------------------------

-- Note that module names in source code are often hyperlinked to the
-- corresponding module. In the Emacs mode you can follow these
-- hyperlinks by typing M-. or clicking with the middle mouse button.

-- • Some data types

import Data.Bool     -- Booleans.
import Data.Char     -- Characters.
import Data.Empty    -- The empty type.
import Data.Fin      -- Finite sets.
import Data.List     -- Lists.
import Data.Maybe    -- The maybe type.
import Data.Nat      -- Natural numbers.
import Data.Product  -- Products.
import Data.Stream   -- Streams.
import Data.String   -- Strings.
import Data.Sum      -- Disjoint sums.
import Data.Unit     -- The unit type.
import Data.Vec      -- Fixed-length vectors.

-- • Some types used to structure computations

import Category.Functor      -- Functors.
import Category.Applicative  -- Applicative functors.
import Category.Monad        -- Monads.

-- • Equality

-- Propositional equality:
import Relation.Binary.PropositionalEquality

-- Convenient syntax for "equational reasoning" using a preorder:
import Relation.Binary.PreorderReasoning

-- Solver for commutative ring or semiring equalities:
import Algebra.RingSolver

-- • Properties of functions, sets and relations

-- Monoids, rings and similar algebraic structures:
import Algebra

-- Negation, decidability, and similar operations on sets:
import Relation.Nullary

-- Properties of homogeneous binary relations:
import Relation.Binary

-- • Induction

-- An abstraction of various forms of recursion/induction:
import Induction

-- Well-founded induction:
import Induction.WellFounded

-- Various forms of induction for natural numbers:
import Induction.Nat

-- • Support for coinduction

import Coinduction

-- • IO

import IO

------------------------------------------------------------------------
-- Record hierarchies
------------------------------------------------------------------------

-- When an abstract hierarchy of some sort (for instance semigroup →
-- monoid → group) is included in the library the basic approach is to
-- specify the properties of every concept in terms of a record
-- containing just properties, parameterised on the underlying
-- operations, sets etc.:
--
--   record IsSemigroup {A} (≈ : Rel A) (∙ : Op₂ A) : Set where
--     open FunctionProperties ≈
--     field
--       isEquivalence : IsEquivalence ≈
--       assoc         : Associative ∙
--       ∙-cong        : ∙ Preserves₂ ≈ ⟶ ≈ ⟶ ≈
--
-- More specific concepts are then specified in terms of the simpler
-- ones:
--
--     record IsMonoid {A} (≈ : Rel A) (∙ : Op₂ A) (ε : A) : Set where
--       open FunctionProperties ≈
--       field
--         isSemigroup : IsSemigroup ≈ ∙
--         identity    : Identity ε ∙
--
--     open IsSemigroup isSemigroup public
--
-- Note here that open IsSemigroup isSemigroup public ensures that the
-- fields of the isSemigroup record can be accessed directly; this
-- technique enables the user of an IsMonoid record to use underlying
-- records without having to manually open an entire record hierarchy.
-- This is not always possible, though. Consider the following definition
-- of preorders:
--
--   record IsPreorder {A : Set}
--                     (_≈_ : Rel A) -- The underlying equality.
--                     (_∼_ : Rel A) -- The relation.
--                     : Set where
--     field
--       isEquivalence : IsEquivalence _≈_
--       -- Reflexivity is expressed in terms of an underlying equality:
--       reflexive     : _≈_ ⇒ _∼_
--       trans         : Transitive _∼_
--       ∼-resp-≈      : _∼_ Respects₂ _≈_
--
--     module Eq = IsEquivalence isEquivalence
--
--     refl : Reflexive _∼_
--     refl = reflexive Eq.refl
--
-- The Eq module in IsPreorder is not opened publicly, because it
-- contains some fields which clash with fields or other definitions
-- in IsPreorder.

-- Records packing up properties with the corresponding operations,
-- sets, etc. are sometimes also defined:
--
--   record Semigroup : Set₁ where
--     infixl 7 _∙_
--     infix  4 _≈_
--     field
--       Carrier     : Set
--       _≈_         : Rel Carrier
--       _∙_         : Op₂ Carrier
--       isSemigroup : IsSemigroup _≈_ _∙_
--
--     open IsSemigroup isSemigroup public
--
--     setoid : Setoid
--     setoid = record { isEquivalence = isEquivalence }
--
--   record Monoid : Set₁ where
--     infixl 7 _∙_
--     infix  4 _≈_
--     field
--       Carrier  : Set
--       _≈_      : Rel Carrier
--       _∙_      : Op₂ Carrier
--       ε        : Carrier
--       isMonoid : IsMonoid _≈_ _∙_ ε
--
--     open IsMonoid isMonoid public
--
--     semigroup : Semigroup
--     semigroup = record { isSemigroup = isSemigroup }
--
--     open Semigroup semigroup public using (setoid)
--
-- Note that the Monoid record does not include a Semigroup field.
-- Instead the Monoid /module/ includes a "repackaging function"
-- semigroup which converts a Monoid to a Semigroup.

-- The above setup may seem a bit complicated, but we think it makes the
-- library quite easy to work with, while also providing enough
-- flexibility.

------------------------------------------------------------------------
-- More documentation
------------------------------------------------------------------------

-- Some examples showing where the natural numbers and some related
-- operations and properties are defined, and how they can be used:

import README.Nat

------------------------------------------------------------------------
-- Core modules
------------------------------------------------------------------------

-- Some modules have names ending in ".Core". These modules are
-- internal, and have (mostly) been created to avoid mutual recursion
-- between modules. They should not be imported directly; their
-- contents are reexported by other modules.

------------------------------------------------------------------------
-- All library modules
------------------------------------------------------------------------

-- For short descriptions of every library module, see Everything:

import Everything