{-# OPTIONS --rewriting --guardedness --sized-types #-} module README where ------------------------------------------------------------------------ -- The Agda standard library, version 2.1.1 -- -- Authors: Nils Anders Danielsson, Matthew Daggitt, Guillaume Allais -- with contributions from Andreas Abel, Stevan Andjelkovic, -- Jean-Philippe Bernardy, Peter Berry, Bradley Hardy, Joachim Breitner, -- Samuel Bronson, Daniel Brown, Jacques Carette, James Chapman, -- Liang-Ting Chen, Dominique Devriese, Dan Doel, Érdi Gergő, -- Zack Grannan, Helmut Grohne, Simon Foster, Liyang Hu, Jason Hu, -- Patrik Jansson, Alan Jeffrey, Wen Kokke, Evgeny Kotelnikov, -- James McKinna, Sergei Meshveliani, Eric Mertens, Darin Morrison, -- Guilhem Moulin, Shin-Cheng Mu, Ulf Norell, Noriyuki Ohkawa, -- Nicolas Pouillard, Andrés Sicard-Ramírez, Lex van der Stoep, -- Sandro Stucki, Milo Turner, Noam Zeilberger, Shu-Hung You -- and other anonymous contributors. ------------------------------------------------------------------------ -- This version of the library has been tested using Agda 2.7.0 -- The library comes with a .agda-lib file, for use with the library -- management system. -- Currently the library does not support the JavaScript compiler -- backend. ------------------------------------------------------------------------ -- Stability guarantees ------------------------------------------------------------------------ -- We do our best to adhere to the spirit of semantic versioning in that -- minor versions should not break people's code. This applies to the -- the entire library with one exception: modules with names that end in -- either ".Core" or ".Primitive". -- The former have (mostly) been created to avoid mutual recursion -- between modules and the latter to bind primitive operations to the -- more efficient operations supplied by the relevant backend. -- These modules may undergo backwards incompatible changes between -- minor versions and therefore are imported directly at your own risk. -- Instead their contents should be accessed by their parent module, -- whose interface will remain stable. ------------------------------------------------------------------------ -- High-level overview of contents ------------------------------------------------------------------------ -- 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. -- • Axiom -- Types and consequences of various additional axioms not -- necessarily included in Agda, e.g. uniqueness of identity -- proofs, function extensionality and excluded middle. import README.Axiom -- • Codata -- Coinductive data types and properties. There are two different -- approaches taken. The `Codata.Sized` folder contains the new more -- standard approach using sized types. The `Codata.Musical` -- folder contains modules using the old musical notation. -- • Data -- Data types and properties. -- • Effect -- Category theory-inspired idioms used to structure functional -- programs (functors and monads, for instance). import README.Data -- • Function -- Combinators and properties related to functions. -- • Foreign -- Related to the foreign function interface. -- • Induction -- A general framework for induction (includes lexicographic and -- well-founded induction). -- • IO -- Input/output-related functions. import README.IO -- • Level -- Universe levels. -- • Reflection -- Support for reflection. -- • Relation -- Properties of and proofs about relations. -- • Size -- Sizes used by the sized types mechanism. -- • Strict -- Provides access to the builtins relating to strictness. -- • Tactic -- Tactics for automatic proof generation -- ∙ Text -- Format-based printing, Pretty-printing, and regular expressions ------------------------------------------------------------------------ -- Library design ------------------------------------------------------------------------ -- The following modules contain a discussion of some of the choices -- that have been made whilst designing the library. -- • How mathematical hierarchies (e.g. preorder, partial order, total -- order) are handled in the library. import README.Design.Hierarchies -- • How decidability is handled in the library. import README.Design.Decidability ------------------------------------------------------------------------ -- 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.String -- Strings. import Data.Sum -- Disjoint sums. import Data.Unit -- The unit type. import Data.Vec -- Fixed-length vectors. -- • Some co-inductive data types import Codata.Sized.Stream -- Streams. import Codata.Sized.Colist -- Colists. -- • Some types used to structure computations import Effect.Functor -- Functors. import Effect.Applicative -- Applicative functors. import Effect.Monad -- Monads. -- • Equality -- Propositional equality: import Relation.Binary.PropositionalEquality -- Convenient syntax for "equational reasoning" using a preorder: import Relation.Binary.Reasoning.Preorder -- Solver for commutative ring or semiring equalities: import Algebra.Solver.Ring -- • 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 Data.Nat.Induction -- • Support for coinduction import Codata.Musical.Notation import Codata.Sized.Thunk -- • IO import IO -- ∙ Text -- Dependently typed formatted printing import Text.Printf ------------------------------------------------------------------------ -- More documentation ------------------------------------------------------------------------ -- Some examples showing how the case expression can be used. import README.Case -- Showcasing the framework for well-scoped substitutions import README.Data.Fin.Substitution.UntypedLambda -- Some examples showing how combinators can be used to emulate -- "functional reasoning" import README.Function.Reasoning -- An example showing how to use the debug tracing mechanism to inspect -- the behaviour of compiled Agda programs. import README.Debug.Trace -- An exploration of the generic programs acting on n-ary functions and -- n-ary heterogeneous products import README.Nary -- Explaining the inspect idiom: use case, equivalent handwritten -- auxiliary definitions, and implementation details. import README.Inspect -- Explaining how to use the automatic solvers import README.Tactic.MonoidSolver import README.Tactic.RingSolver -- Explaining how the Haskell FFI works import README.Foreign.Haskell -- Explaining string formats and the behaviour of printf import README.Text.Printf -- Showcasing the pretty printing module import README.Text.Pretty -- Demonstrating the regular expression matching import README.Text.Regex -- Explaining how to display tables of strings: import README.Text.Tabular ------------------------------------------------------------------------ -- All library modules ------------------------------------------------------------------------ -- For short descriptions of every library module, see Everything; -- to exclude unsafe modules, see EverythingSafe: import Everything import EverythingSafe -- Note that the Everything* modules are generated automatically. If -- you have downloaded the library from its Git repository and want -- to type check README then you can (try to) construct Everything by -- running "cabal install && GenerateEverything". -- Note that all library sources are located under src or ffi. The -- modules README, README.* and Everything are not really part of the -- library, so these modules are located in the top-level directory -- instead.