commit 8212f5d8195180e784ae0cbe89a77b937dcc2e4b
parent 5243dee218fcb7507a9eb5749e91d58269746fe4
Author: Jared Tobin <jared@jtobin.ca>
Date: Tue, 30 May 2017 22:30:02 +1200
General cleanup.
Diffstat:
8 files changed, 380 insertions(+), 1202 deletions(-)
diff --git a/README.md b/README.md
@@ -18,9 +18,8 @@ do-notation.
Query measures by integrating meaurable functions against them. Extract
moments, cumulative density functions, or probabilities.
-Check out the module comments or *examples* folder for sample use. You can
-also check out a few blog posts I wrote about the theoretical foundations and
-implementation of the library here:
+You can check out a few blog posts I wrote about the theoretical foundations
+and implementation of the library here:
* [Foundations of the Giry Monad][foun]
* [Implementing the Giry Monad][impl]
diff --git a/cabal.config b/cabal.config
@@ -1,866 +0,0 @@
--- Stackage snapshot from: http://www.stackage.org/snapshot/lts-1.11
--- Please place this file next to your .cabal file as cabal.config
--- To only use tested packages, uncomment the following line:
--- remote-repo: stackage-lts-1.11:http://www.stackage.org/snapshot/lts-1.11
-constraints: abstract-deque ==0.3,
- abstract-par ==0.3.3,
- accelerate ==0.15.0.0,
- ace ==0.6,
- action-permutations ==0.0.0.1,
- active ==0.1.0.18,
- AC-Vector ==2.3.2,
- ad ==4.2.1.1,
- adjunctions ==4.2,
- aeson ==0.8.0.2,
- aeson-pretty ==0.7.2,
- aeson-qq ==0.7.4,
- aeson-utils ==0.2.2.1,
- alarmclock ==0.2.0.5,
- alex ==3.1.4,
- amqp ==0.10.1,
- ansi-terminal ==0.6.2.1,
- ansi-wl-pprint ==0.6.7.1,
- appar ==0.1.4,
- approximate ==0.2.1.1,
- arbtt ==0.8.1.4,
- arithmoi ==0.4.1.1,
- array installed,
- arrow-list ==0.6.1.5,
- asn1-data ==0.7.1,
- asn1-encoding ==0.9.0,
- asn1-parse ==0.9.0,
- asn1-types ==0.3.0,
- async ==2.0.2,
- atto-lisp ==0.2.2,
- attoparsec ==0.12.1.3,
- attoparsec-conduit ==1.1.0,
- attoparsec-enumerator ==0.3.3,
- attoparsec-expr ==0.1.1.1,
- authenticate ==1.3.2.11,
- auto-update ==0.1.2.1,
- aws ==0.11.2,
- bake ==0.2,
- bank-holidays-england ==0.1.0.2,
- barecheck ==0.2.0.6,
- base installed,
- base16-bytestring ==0.1.1.6,
- base64-bytestring ==1.0.0.1,
- base-compat ==0.5.0,
- base-prelude ==0.1.16,
- base-unicode-symbols ==0.2.2.4,
- basic-prelude ==0.3.11.1,
- bifunctors ==4.2.1,
- binary installed,
- binary-conduit ==1.2.3,
- binary-list ==1.0.1.0,
- bindings-DSL ==1.0.22,
- bioace ==0.0.1,
- bioalign ==0.0.5,
- biocore ==0.3.1,
- biofasta ==0.0.3,
- biofastq ==0.1,
- biophd ==0.0.5,
- biopsl ==0.4,
- biosff ==0.3.7.1,
- bits ==0.4,
- BlastHTTP ==1.0.1,
- blastxml ==0.3.2,
- blaze-builder ==0.3.3.4,
- blaze-builder-enumerator ==0.2.0.6,
- blaze-html ==0.7.1.0,
- blaze-markup ==0.6.3.0,
- blaze-svg ==0.3.4.1,
- blaze-textual ==0.2.0.9,
- BlogLiterately ==0.7.1.7,
- BlogLiterately-diagrams ==0.1.4.3,
- bloodhound ==0.5.0.1,
- bmp ==1.2.5.2,
- Boolean ==0.2.3,
- bool-extras ==0.4.0,
- bound ==1.0.4,
- BoundedChan ==1.0.3.0,
- broadcast-chan ==0.1.0,
- bson ==0.3.1,
- bumper ==0.6.0.3,
- byteable ==0.1.1,
- bytedump ==1.0,
- byteorder ==1.0.4,
- bytes ==0.14.1.3,
- bytestring installed,
- bytestring-builder ==0.10.4.1.2,
- bytestring-lexing ==0.4.3.2,
- bytestring-mmap ==0.2.2,
- bytestring-progress ==1.0.3,
- bytestring-show ==0.3.5.6,
- bytestring-trie ==0.2.4,
- bzlib ==0.5.0.5,
- bzlib-conduit ==0.2.1.3,
- c2hs ==0.20.1,
- Cabal installed,
- cabal-install ==1.18.0.8,
- cabal-src ==0.2.5,
- cairo ==0.13.1.0,
- case-insensitive ==1.2.0.4,
- cases ==0.1.2,
- cassava ==0.4.2.1,
- cautious-file ==1.0.2,
- cereal ==0.4.1.1,
- cereal-conduit ==0.7.2.3,
- certificate ==1.3.9,
- charset ==0.3.7,
- Chart ==1.3.3,
- Chart-diagrams ==1.3.3,
- ChasingBottoms ==1.3.0.11,
- check-email ==1.0,
- checkers ==0.4.1,
- chell ==0.4.0.1,
- chell-quickcheck ==0.2.4,
- chunked-data ==0.1.0.1,
- cipher-aes ==0.2.10,
- cipher-blowfish ==0.0.3,
- cipher-camellia ==0.0.2,
- cipher-des ==0.0.6,
- cipher-rc4 ==0.1.4,
- circle-packing ==0.1.0.4,
- classy-prelude ==0.10.5,
- classy-prelude-conduit ==0.10.5,
- classy-prelude-yesod ==0.10.5,
- clientsession ==0.9.1.1,
- clock ==0.4.1.3,
- cmdargs ==0.10.12,
- code-builder ==0.1.3,
- colour ==2.3.3,
- comonad ==4.2.3,
- comonads-fd ==4.0,
- comonad-transformers ==4.0,
- compdata ==0.9,
- compensated ==0.6.1,
- composition ==1.0.1.0,
- compressed ==3.10,
- concatenative ==1.0.1,
- concurrent-extra ==0.7.0.9,
- concurrent-supply ==0.1.7,
- cond ==0.4.1.1,
- conduit ==1.2.4,
- conduit-combinators ==0.3.0.6,
- conduit-extra ==1.1.7.0,
- configurator ==0.3.0.0,
- connection ==0.2.4,
- constraints ==0.4.1.3,
- containers installed,
- containers-unicode-symbols ==0.3.1.1,
- contravariant ==1.2.2,
- control-monad-free ==0.5.3,
- control-monad-loop ==0.1,
- convertible ==1.1.0.0,
- cookie ==0.4.1.4,
- courier ==0.1.0.15,
- cpphs ==1.18.9,
- cprng-aes ==0.6.1,
- cpu ==0.1.2,
- criterion ==1.0.2.0,
- crypto-api ==0.13.2,
- cryptocipher ==0.6.2,
- crypto-cipher-tests ==0.0.11,
- crypto-cipher-types ==0.0.9,
- cryptohash ==0.11.6,
- cryptohash-conduit ==0.1.1,
- cryptohash-cryptoapi ==0.1.3,
- crypto-numbers ==0.2.7,
- crypto-pubkey ==0.2.8,
- crypto-pubkey-types ==0.4.3,
- crypto-random ==0.0.8,
- crypto-random-api ==0.2.0,
- css-text ==0.1.2.1,
- csv ==0.1.2,
- csv-conduit ==0.6.3,
- curl ==1.3.8,
- data-accessor ==0.2.2.6,
- data-accessor-mtl ==0.2.0.4,
- data-binary-ieee754 ==0.4.4,
- data-default ==0.5.3,
- data-default-class ==0.0.1,
- data-default-instances-base ==0.0.1,
- data-default-instances-containers ==0.0.1,
- data-default-instances-dlist ==0.0.1,
- data-default-instances-old-locale ==0.0.1,
- data-inttrie ==0.1.0,
- data-lens-light ==0.1.2.1,
- data-memocombinators ==0.5.1,
- data-reify ==0.6,
- DAV ==1.0.3,
- Decimal ==0.4.2,
- deepseq installed,
- deepseq-generics ==0.1.1.2,
- derive ==2.5.21,
- diagrams ==1.2,
- diagrams-builder ==0.6.0.3,
- diagrams-cairo ==1.2.0.6,
- diagrams-contrib ==1.1.2.5,
- diagrams-core ==1.2.0.5,
- diagrams-haddock ==0.2.2.13,
- diagrams-lib ==1.2.0.8,
- diagrams-postscript ==1.1.0.4,
- diagrams-svg ==1.1.0.4,
- Diff ==0.3.0,
- digest ==0.0.1.2,
- digestive-functors ==0.7.1.4,
- dimensional ==0.13.0.1,
- directory installed,
- directory-tree ==0.12.0,
- direct-sqlite ==2.3.15,
- distributed-process ==0.5.3,
- distributed-process-async ==0.2.1,
- distributed-process-client-server ==0.1.2,
- distributed-process-execution ==0.1.1,
- distributed-process-extras ==0.2.0,
- distributed-process-simplelocalnet ==0.2.2.0,
- distributed-process-supervisor ==0.1.2,
- distributed-process-task ==0.1.1,
- distributed-static ==0.3.1.0,
- distributive ==0.4.4,
- djinn-ghc ==0.0.2.3,
- djinn-lib ==0.0.1.2,
- dlist ==0.7.1,
- dlist-instances ==0.1,
- doctest ==0.9.13,
- double-conversion ==2.0.1.0,
- dual-tree ==0.2.0.5,
- easy-file ==0.2.0,
- either ==4.3.3.2,
- elm-build-lib ==0.14.0.0,
- elm-compiler ==0.14.1,
- elm-core-sources ==1.0.0,
- elm-package ==0.2.2,
- email-validate ==2.0.1,
- enclosed-exceptions ==1.0.1,
- entropy ==0.3.6,
- enumerator ==0.4.20,
- eq ==4.0.3,
- erf ==2.0.0.0,
- errorcall-eq-instance ==0.1.0,
- errors ==1.4.7,
- ersatz ==0.2.6.1,
- esqueleto ==2.1.2.1,
- exceptions ==0.6.1,
- exception-transformers ==0.3.0.4,
- executable-path ==0.0.3,
- extensible-exceptions ==0.1.1.4,
- extra ==1.0.1,
- failure ==0.2.0.3,
- fast-logger ==2.2.3,
- fay ==0.21.2.1,
- fay-base ==0.19.4.2,
- fay-builder ==0.2.0.3,
- fay-dom ==0.5.0.1,
- fay-jquery ==0.6.0.3,
- fay-text ==0.3.2.2,
- fay-uri ==0.2.0.0,
- fb ==1.0.8,
- fb-persistent ==0.3.4,
- fclabels ==2.0.2.2,
- FenwickTree ==0.1.2,
- fgl ==5.5.0.1,
- file-embed ==0.0.8.2,
- file-location ==0.4.6,
- filemanip ==0.3.6.3,
- filepath installed,
- fingertree ==0.1.0.1,
- fixed ==0.2.1.1,
- fixed-list ==0.1.5,
- flexible-defaults ==0.0.1.1,
- focus ==0.1.3,
- foldl ==1.0.7,
- FontyFruity ==0.4.1,
- force-layout ==0.3.0.9,
- foreign-store ==0.1,
- foreign-var ==0.0.0.1,
- formatting ==6.0.0,
- fpco-api ==1.2.0.5,
- free ==4.10.0.1,
- freenect ==1.2,
- frisby ==0.2,
- fsnotify ==0.1.0.3,
- fuzzcheck ==0.1.1,
- gd ==3000.7.3,
- generic-aeson ==0.2.0.2,
- generic-deriving ==1.6.3,
- GenericPretty ==1.2.1,
- generics-sop ==0.1.1,
- ghc-heap-view ==0.5.3,
- ghcid ==0.3.4,
- ghc-mod ==5.2.1.2,
- ghc-mtl ==1.2.1.0,
- ghc-paths ==0.1.0.9,
- ghc-prim installed,
- ghc-syb-utils ==0.2.3,
- gio ==0.13.0.4,
- git-embed ==0.1.0,
- gl ==0.6.3,
- glib ==0.13.1.0,
- Glob ==0.7.5,
- GLURaw ==1.4.0.2,
- GLUT ==2.5.1.1,
- graph-core ==0.2.1.0,
- graphs ==0.5.0.1,
- gravatar ==0.6,
- groundhog ==0.7.0.2,
- groundhog-mysql ==0.7.0.1,
- groundhog-postgresql ==0.7.0.2,
- groundhog-sqlite ==0.7.0.1,
- groundhog-th ==0.7.0,
- groupoids ==4.0,
- groups ==0.4.0.0,
- gtk ==0.13.4,
- gtk2hs-buildtools ==0.13.0.3,
- haddock-api ==2.15.0.2,
- haddock-library ==1.1.1,
- half ==0.2.0.1,
- HandsomeSoup ==0.3.5,
- happstack-server ==7.3.9,
- happy ==1.19.5,
- hashable ==1.2.3.1,
- hashable-extras ==0.2.0.1,
- hashmap ==1.3.0.1,
- hashtables ==1.2.0.2,
- haskeline installed,
- haskell2010 installed,
- haskell98 installed,
- haskell-lexer ==1.0,
- haskell-names ==0.4.1,
- haskell-packages ==0.2.4.4,
- haskell-src ==1.0.2.0,
- haskell-src-exts ==1.16.0.1,
- haskell-src-meta ==0.6.0.8,
- hasql ==0.7.2,
- hasql-backend ==0.4.0,
- hasql-postgres ==0.10.2,
- hastache ==0.6.1,
- HaTeX ==3.16.0.0,
- HaXml ==1.25.3,
- haxr ==3000.10.3.1,
- HCodecs ==0.5,
- hdaemonize ==0.5.0.0,
- hdevtools ==0.1.0.6,
- heaps ==0.3.1,
- hebrew-time ==0.1.1,
- heist ==0.14.1,
- here ==1.2.6,
- heredoc ==0.2.0.0,
- hflags ==0.4,
- highlighting-kate ==0.5.11.1,
- hinotify ==0.3.7,
- hint ==0.4.2.2,
- histogram-fill ==0.8.4.1,
- hit ==0.6.3,
- hjsmin ==0.1.4.7,
- hledger ==0.24,
- hledger-lib ==0.24,
- hlibgit2 ==0.18.0.14,
- hlint ==1.9.16,
- hmatrix ==0.16.1.4,
- hmatrix-gsl ==0.16.0.3,
- hoauth2 ==0.4.3,
- holy-project ==0.1.1.1,
- hoogle ==4.2.38,
- hoopl installed,
- hOpenPGP ==1.11,
- hostname ==1.0,
- hostname-validate ==1.0.0,
- hourglass ==0.2.8,
- hpc installed,
- hPDB ==1.2.0.2,
- hPDB-examples ==1.2.0.1,
- hs-bibutils ==5.5,
- hscolour ==1.20.3,
- hse-cpp ==0.1,
- hslogger ==1.2.8,
- hslua ==0.3.13,
- hspec ==2.1.4,
- hspec2 ==0.6.1,
- hspec-core ==2.1.4,
- hspec-discover ==2.1.4,
- hspec-expectations ==0.6.1.1,
- hspec-meta ==2.0.0,
- hspec-wai ==0.6.3,
- hspec-wai-json ==0.6.0,
- HStringTemplate ==0.7.3,
- hsyslog ==2.0,
- HTF ==0.12.2.3,
- html ==1.0.1.2,
- html-conduit ==1.1.1.1,
- HTTP ==4000.2.19,
- http-client ==0.4.8,
- http-client-tls ==0.2.2,
- http-conduit ==2.1.5,
- http-date ==0.0.5,
- http-reverse-proxy ==0.4.1.2,
- http-types ==0.8.6,
- HUnit ==1.2.5.2,
- hweblib ==0.6.3,
- hxt ==9.3.1.15,
- hxt-charproperties ==9.2.0.1,
- hxt-http ==9.1.5.2,
- hxt-pickle-utils ==0.1.0.2,
- hxt-regex-xmlschema ==9.2.0.2,
- hxt-relaxng ==9.1.5.5,
- hxt-unicode ==9.0.2.4,
- hybrid-vectors ==0.1.2.1,
- hyphenation ==0.4.2,
- idna ==0.3.0,
- ieee754 ==0.7.6,
- IfElse ==0.85,
- imagesize-conduit ==1.0.0.4,
- immortal ==0.2,
- incremental-parser ==0.2.3.4,
- indents ==0.3.3,
- ini ==0.3.1,
- integer-gmp installed,
- integration ==0.2.1,
- interpolate ==0.1.0,
- interpolatedstring-perl6 ==0.9.0,
- intervals ==0.7.1,
- io-choice ==0.0.5,
- io-manager ==0.1.0.2,
- io-memoize ==1.1.1.0,
- iproute ==1.3.1,
- iterable ==3.0,
- ixset ==1.0.6,
- js-flot ==0.8.3,
- js-jquery ==1.11.2,
- json-autotype ==0.2.5.4,
- json-schema ==0.7.3.1,
- JuicyPixels ==3.2.3,
- JuicyPixels-repa ==0.7,
- kan-extensions ==4.2.1,
- kdt ==0.2.2,
- keter ==1.3.8,
- keys ==3.10.1,
- kure ==2.16.6,
- language-c ==0.4.7,
- language-ecmascript ==0.16.2,
- language-glsl ==0.1.1,
- language-haskell-extract ==0.2.4,
- language-java ==0.2.7,
- language-javascript ==0.5.13.3,
- lazy-csv ==0.5,
- lca ==0.2.4,
- lens ==4.6.0.1,
- lens-aeson ==1.0.0.3,
- lens-family-th ==0.4.1.0,
- lhs2tex ==1.18.1,
- libgit ==0.3.0,
- libnotify ==0.1.1.0,
- lifted-async ==0.2.0.2,
- lifted-base ==0.2.3.6,
- linear ==1.15.5,
- linear-accelerate ==0.2,
- list-t ==0.4.3,
- loch-th ==0.2.1,
- log-domain ==0.9.3,
- logfloat ==0.12.1,
- logict ==0.6.0.2,
- loop ==0.2.0,
- lucid ==2.5,
- lzma-conduit ==1.1.3,
- machines ==0.4.1,
- mandrill ==0.1.1.0,
- map-syntax ==0.2,
- markdown ==0.1.13.1,
- markdown-unlit ==0.2.0.1,
- math-functions ==0.1.5.2,
- matrix ==0.3.4.2,
- MaybeT ==0.1.2,
- MemoTrie ==0.6.2,
- mersenne-random-pure64 ==0.2.0.4,
- messagepack ==0.3.0,
- messagepack-rpc ==0.1.0.3,
- mime-mail ==0.4.8.1,
- mime-mail-ses ==0.3.2.2,
- mime-types ==0.1.0.5,
- missing-foreign ==0.1.1,
- MissingH ==1.3.0.1,
- mmap ==0.5.9,
- mmorph ==1.0.4,
- MonadCatchIO-transformers ==0.3.1.3,
- monad-control ==0.3.3.1,
- monad-coroutine ==0.8.0.1,
- monadcryptorandom ==0.6.1,
- monad-extras ==0.5.9,
- monadic-arrays ==0.2.1.3,
- monad-journal ==0.6.0.2,
- monad-logger ==0.3.13.1,
- monad-loops ==0.4.2.1,
- monad-par ==0.3.4.7,
- monad-parallel ==0.7.1.4,
- monad-par-extras ==0.3.3,
- monad-primitive ==0.1,
- monad-products ==4.0.0.1,
- MonadPrompt ==1.0.0.5,
- MonadRandom ==0.3.0.1,
- monad-st ==0.2.4,
- monads-tf ==0.1.0.2,
- mongoDB ==2.0.3,
- monoid-extras ==0.3.3.5,
- monoid-subclasses ==0.3.6.2,
- mono-traversable ==0.7.0,
- mtl ==2.1.3.1,
- mtlparse ==0.1.4.0,
- mtl-prelude ==1.0.3,
- multimap ==1.2.1,
- multipart ==0.1.2,
- MusicBrainz ==0.2.3,
- mutable-containers ==0.2.1.2,
- mwc-random ==0.13.3.0,
- mysql ==0.1.1.7,
- mysql-simple ==0.2.2.4,
- nanospec ==0.2.0,
- nats ==1,
- neat-interpolation ==0.2.2,
- nettle ==0.1.0,
- network ==2.6.0.2,
- network-conduit-tls ==1.1.0.2,
- network-info ==0.2.0.5,
- network-multicast ==0.0.11,
- network-simple ==0.4.0.4,
- network-transport ==0.4.1.0,
- network-transport-tcp ==0.4.1,
- network-transport-tests ==0.2.2.0,
- network-uri ==2.6.0.1,
- newtype ==0.2,
- nsis ==0.2.4,
- numbers ==3000.2.0.1,
- numeric-extras ==0.0.3,
- NumInstances ==1.4,
- numtype ==1.1,
- Octree ==0.5.4.2,
- old-locale installed,
- old-time installed,
- OneTuple ==0.2.1,
- opaleye ==0.3.1,
- OpenGL ==2.9.2.0,
- OpenGLRaw ==1.5.0.1,
- openpgp-asciiarmor ==0.1,
- operational ==0.2.3.2,
- options ==1.2.1.1,
- optparse-applicative ==0.11.0.2,
- osdkeys ==0.0,
- pandoc ==1.13.2,
- pandoc-citeproc ==0.6,
- pandoc-types ==1.12.4.1,
- pango ==0.13.0.5,
- parallel ==3.2.0.6,
- parallel-io ==0.3.3,
- parseargs ==0.1.5.2,
- parsec ==3.1.8,
- parsers ==0.12.1.1,
- partial-handler ==0.1.0,
- path-pieces ==0.1.5,
- patience ==0.1.1,
- pcre-light ==0.4.0.3,
- pdfinfo ==1.5.2,
- pem ==0.2.2,
- persistent ==2.1.1.7,
- persistent-mongoDB ==2.1.2.1,
- persistent-mysql ==2.1.2.1,
- persistent-postgresql ==2.1.2.2,
- persistent-sqlite ==2.1.1.2,
- persistent-template ==2.1.0.1,
- phantom-state ==0.2.0.2,
- pipes ==4.1.4,
- pipes-concurrency ==2.0.3,
- pipes-parse ==3.0.2,
- placeholders ==0.1,
- pointed ==4.2,
- polyparse ==1.10,
- pool-conduit ==0.1.2.3,
- postgresql-binary ==0.5.1,
- postgresql-libpq ==0.9.0.2,
- postgresql-simple ==0.4.10.0,
- pqueue ==1.2.1,
- prefix-units ==0.1.0.2,
- prelude-extras ==0.4,
- present ==2.2,
- pretty installed,
- prettyclass ==1.0.0.0,
- pretty-class ==1.0.1.1,
- pretty-show ==1.6.8.2,
- primes ==0.2.1.0,
- primitive ==0.5.4.0,
- process installed,
- process-conduit ==1.2.0.1,
- process-extras ==0.2.0,
- product-profunctors ==0.6,
- profunctor-extras ==4.0,
- profunctors ==4.3.2,
- project-template ==0.1.4.2,
- publicsuffixlist ==0.1,
- punycode ==2.0,
- pure-io ==0.2.1,
- pureMD5 ==2.1.2.1,
- pwstore-fast ==2.4.4,
- quandl-api ==0.2.0.0,
- QuasiText ==0.1.2.5,
- QuickCheck ==2.7.6,
- quickcheck-assertions ==0.1.1,
- quickcheck-instances ==0.3.10,
- quickcheck-io ==0.1.1,
- quickcheck-unicode ==1.0.0.0,
- quickpull ==0.4.0.0,
- rainbow ==0.20.0.4,
- rainbow-tests ==0.20.0.4,
- random ==1.0.1.1,
- random-fu ==0.2.6.2,
- random-shuffle ==0.0.4,
- random-source ==0.3.0.6,
- rank1dynamic ==0.2.0.1,
- Rasterific ==0.4.2,
- raw-strings-qq ==1.0.2,
- ReadArgs ==1.2.2,
- reducers ==3.10.3.1,
- reflection ==1.5.1.1,
- regex-applicative ==0.3.1,
- regex-base ==0.93.2,
- regex-compat ==0.95.1,
- regex-pcre-builtin ==0.94.4.8.8.35,
- regex-posix ==0.95.2,
- regexpr ==0.5.4,
- regex-tdfa ==1.2.0,
- regex-tdfa-rc ==1.1.8.3,
- regular ==0.3.4.4,
- regular-xmlpickler ==0.2,
- rematch ==0.2.0.0,
- repa ==3.3.1.2,
- repa-algorithms ==3.3.1.2,
- repa-devil ==0.3.2.2,
- repa-io ==3.3.1.2,
- reroute ==0.2.2.1,
- resource-pool ==0.2.3.2,
- resourcet ==1.1.4.1,
- rest-client ==0.4.0.5,
- rest-core ==0.33.1.2,
- rest-gen ==0.16.1.8,
- rest-happstack ==0.2.10.4,
- rest-snap ==0.1.17.14,
- rest-stringmap ==0.2.0.3,
- rest-types ==1.11.1.1,
- rest-wai ==0.1.0.4,
- rev-state ==0.1,
- rfc5051 ==0.1.0.3,
- runmemo ==1.0.0.1,
- rvar ==0.2.0.2,
- safe ==0.3.8,
- safecopy ==0.8.4,
- scientific ==0.3.3.7,
- scotty ==0.9.0,
- scrobble ==0.2.1.1,
- securemem ==0.1.7,
- semigroupoid-extras ==4.0,
- semigroupoids ==4.2,
- semigroups ==0.16.2.2,
- sendfile ==0.7.9,
- seqloc ==0.6.1.1,
- setenv ==0.1.1.3,
- SHA ==1.6.4.1,
- shake ==0.14.3,
- shake-language-c ==0.6.4,
- shakespeare ==2.0.4.1,
- shakespeare-i18n ==1.1.0,
- shakespeare-text ==1.1.0,
- shell-conduit ==4.5.2,
- shelly ==1.5.7,
- silently ==1.2.4.1,
- simple-reflect ==0.3.2,
- simple-sendfile ==0.2.18,
- singletons ==1.0,
- siphash ==1.0.3,
- skein ==1.0.9.2,
- slave-thread ==0.1.5,
- smallcheck ==1.1.1,
- smtLib ==1.0.7,
- snap ==0.13.3.2,
- snap-core ==0.9.6.4,
- snaplet-fay ==0.3.3.10,
- snap-server ==0.9.4.6,
- socks ==0.5.4,
- sodium ==0.11.0.3,
- sourcemap ==0.1.3.0,
- speculation ==1.5.0.1,
- sphinx ==0.6.0.1,
- split ==0.2.2,
- Spock ==0.7.7.0,
- Spock-digestive ==0.1.0.0,
- Spock-worker ==0.2.1.3,
- spoon ==0.3.1,
- sqlite-simple ==0.4.8.0,
- stackage ==0.3.1,
- stateref ==0.3,
- statestack ==0.2.0.3,
- statistics ==0.13.2.1,
- statistics-linreg ==0.3,
- stm ==2.4.4,
- stm-chans ==3.0.0.2,
- stm-conduit ==2.5.4,
- stm-containers ==0.2.8,
- stm-stats ==0.2.0.0,
- storable-complex ==0.2.2,
- storable-endian ==0.2.5,
- streaming-commons ==0.1.10.0,
- streams ==3.2,
- strict ==0.3.2,
- stringable ==0.1.3,
- stringbuilder ==0.5.0,
- stringprep ==1.0.0,
- stringsearch ==0.3.6.5,
- stylish-haskell ==0.5.11.1,
- SVGFonts ==1.4.0.3,
- syb ==0.4.4,
- syb-with-class ==0.6.1.5,
- system-canonicalpath ==0.2.3.0,
- system-fileio ==0.3.16.1,
- system-filepath ==0.4.13.2,
- system-posix-redirect ==1.1.0.1,
- tabular ==0.2.2.7,
- tagged ==0.7.3,
- tagshare ==0.0,
- tagsoup ==0.13.3,
- tagstream-conduit ==0.5.5.3,
- tar ==0.4.1.0,
- tardis ==0.3.0.0,
- tasty ==0.10.1,
- tasty-ant-xml ==1.0.1,
- tasty-golden ==2.2.2.4,
- tasty-hunit ==0.9.1,
- tasty-kat ==0.0.3,
- tasty-quickcheck ==0.8.3.2,
- tasty-smallcheck ==0.8.0.1,
- tasty-th ==0.1.3,
- template-haskell installed,
- temporary ==1.2.0.3,
- temporary-rc ==1.2.0.3,
- terminal-progress-bar ==0.0.1.4,
- terminal-size ==0.3.0,
- terminfo installed,
- test-framework ==0.8.1.1,
- test-framework-hunit ==0.3.0.1,
- test-framework-quickcheck2 ==0.3.0.3,
- test-framework-th ==0.2.4,
- testing-feat ==0.4.0.2,
- testpack ==2.1.3.0,
- texmath ==0.8.0.1,
- text ==1.2.0.4,
- text-binary ==0.1.0,
- text-format ==0.3.1.1,
- text-icu ==0.7.0.1,
- tf-random ==0.5,
- th-desugar ==1.4.2.1,
- th-expand-syns ==0.3.0.5,
- th-extras ==0.0.0.2,
- th-lift ==0.7.2,
- th-orphans ==0.8.3,
- threads ==0.5.1.3,
- th-reify-many ==0.1.3,
- thyme ==0.3.5.5,
- time installed,
- time-compat ==0.1.0.3,
- time-lens ==0.4.0.1,
- timezone-olson ==0.1.6,
- timezone-series ==0.1.4,
- tls ==1.2.16,
- tls-debug ==0.3.4,
- tostring ==0.2.1.1,
- transformers installed,
- transformers-base ==0.4.4,
- transformers-compat ==0.3.3.3,
- traverse-with-class ==0.2.0.3,
- tree-view ==0.4,
- tuple ==0.3.0.2,
- type-eq ==0.4.2,
- type-list ==0.0.0.1,
- udbus ==0.2.1,
- unbounded-delays ==0.1.0.9,
- union-find ==0.2,
- uniplate ==1.6.12,
- unix installed,
- unix-compat ==0.4.1.4,
- unix-time ==0.3.5,
- unordered-containers ==0.2.5.1,
- uri-encode ==1.5.0.4,
- url ==2.1.3,
- utf8-light ==0.4.2,
- utf8-string ==0.3.8,
- uuid ==1.3.8,
- vault ==0.3.0.4,
- vector ==0.10.12.2,
- vector-algorithms ==0.6.0.3,
- vector-binary-instances ==0.2.1.0,
- vector-instances ==3.3.0.1,
- vector-space ==0.8.7,
- vector-space-points ==0.2.1,
- vector-th-unbox ==0.2.1.2,
- vhd ==0.2.2,
- void ==0.7,
- wai ==3.0.2.3,
- wai-app-static ==3.0.0.6,
- wai-conduit ==3.0.0.2,
- wai-eventsource ==3.0.0,
- wai-extra ==3.0.4.5,
- wai-logger ==2.2.3,
- wai-middleware-static ==0.6.0.1,
- wai-websockets ==3.0.0.5,
- warp ==3.0.9.3,
- warp-tls ==3.0.2,
- webdriver ==0.6.1,
- web-fpco ==0.1.1.0,
- websockets ==0.9.3.0,
- wizards ==1.0.1,
- wl-pprint ==1.1,
- wl-pprint-extras ==3.5.0.4,
- wl-pprint-terminfo ==3.7.1.3,
- wl-pprint-text ==1.1.0.3,
- word8 ==0.1.2,
- wordpass ==1.0.0.2,
- X11 ==1.6.1.2,
- x509 ==1.5.0.1,
- x509-store ==1.5.0,
- x509-system ==1.5.0,
- x509-validation ==1.5.1,
- xenstore ==0.1.1,
- xhtml installed,
- xml ==1.3.14,
- xml-conduit ==1.2.3.3,
- xmlgen ==0.6.2.1,
- xml-hamlet ==0.4.0.10,
- xmlhtml ==0.2.3.4,
- xml-types ==0.3.4,
- xss-sanitize ==0.3.5.5,
- yackage ==0.7.0.7,
- yaml ==0.8.10.1,
- Yampa ==0.9.6,
- YampaSynth ==0.2,
- yesod ==1.4.1.4,
- yesod-auth ==1.4.3.1,
- yesod-auth-deskcom ==1.4.0,
- yesod-auth-fb ==1.6.6,
- yesod-auth-hashdb ==1.4.1.2,
- yesod-auth-oauth2 ==0.0.12,
- yesod-bin ==1.4.4,
- yesod-core ==1.4.8.1,
- yesod-eventsource ==1.4.0.1,
- yesod-fay ==0.7.1,
- yesod-fb ==0.3.4,
- yesod-form ==1.4.4,
- yesod-gitrepo ==0.1.1.0,
- yesod-newsfeed ==1.4.0.1,
- yesod-persistent ==1.4.0.2,
- yesod-sitemap ==1.4.0.1,
- yesod-static ==1.4.0.4,
- yesod-test ==1.4.3.1,
- yesod-text-markdown ==0.1.7,
- yesod-websockets ==0.2.1.1,
- zeromq4-haskell ==0.6.3,
- zip-archive ==0.2.3.7,
- zlib ==0.5.4.2,
- zlib-bindings ==0.1.1.5,
- zlib-enum ==0.2.3.1,
- zlib-lens ==0.1.1.2
diff --git a/examples/CRP.hs b/examples/CRP.hs
@@ -1,98 +0,0 @@
-{-# LANGUAGE TemplateHaskell #-}
-
--- | An example defining measures for various finite realizations of a Chinese
--- Restaurant Process.
-
-import Control.Applicative
-import Control.Lens
-import Control.Monad.Trans
-import Data.IntMap.Strict (IntMap)
-import qualified Data.IntMap.Strict as IntMap
-import Measurable.Core
-
-data Table = Table {
- _number :: {-# UNPACK #-} !Int
- , _people :: {-# UNPACK #-} !Int
- } deriving (Eq, Show)
-
-instance Ord Table where
- t1 < t2 = _people t1 < _people t2
- t1 <= t2 = _people t1 <= _people t2
-
-makeLenses ''Table
-
--- | Mass function for a given table. It's dependent on the state of the
--- restaurant via @n@ and @newestTable@.
-tableMass :: (Fractional a, Integral b) => b -> a -> Table -> Table -> a
-tableMass n a newestTable table
- | table^.number == newestTable^.number = a / (fromIntegral n + a)
- | otherwise = fromIntegral (table^.people) / (fromIntegral n + a)
-
--- | A measure defined over tables.
-tableMeasure
- :: (Integral b, Applicative m, Monad m, Traversable t)
- => b
- -> Double
- -> Table
- -> t Table
- -> MeasureT m Table
-tableMeasure n a newestTable =
- fromDensityCountingT (tableMass n a newestTable)
-
--- | A probability measure over restaurants, represented by IntMaps.
-restaurantMeasure
- :: (Monad m, Applicative m)
- => Double
- -> IntMap Table
- -> MeasureT m (IntMap Table)
-restaurantMeasure a restaurant = do
- let numCustomers = sumOf (traverse.people) restaurant
- numTables = lengthOf traverse restaurant
- nextTableNum = succ numTables
- possibleTable = Table nextTableNum 1
- possibleRestaurant =
- IntMap.insert nextTableNum possibleTable restaurant
-
- table <- tableMeasure numCustomers a
- possibleTable possibleRestaurant
-
- let newTable
- | table^.number == possibleTable^.number = table
- | otherwise = table&people %~ succ
-
- return (IntMap.insert (newTable^.number) newTable restaurant)
-
--- | A measure for a finite realization of a CRP measure with a given number of
--- customers and concentration parameter.
-chineseRestaurantProcess
- :: (Enum a, Eq a, Monad m, Applicative m, Num a)
- => a
- -> Double
- -> MeasureT m (IntMap Table)
-chineseRestaurantProcess n a = go n IntMap.empty where
- go 0 restaurant = return restaurant
- go j restaurant = restaurantMeasure a restaurant >>= go (pred j)
-
-main :: IO ()
-main = do
- let numTables = fromIntegral . lengthOf traverse
- tinyRestaurant = chineseRestaurantProcess 2 1
- smallRestaurant = chineseRestaurantProcess 3 1
- bigRestaurant = chineseRestaurantProcess 9 1
- bigRestaurantAntisocial = chineseRestaurantProcess 9 3
-
- meanTinyRestaurant <- integrate numTables tinyRestaurant
- meanSmallRestaurant <- integrate numTables smallRestaurant
- meanBigRestaurant <- integrate numTables bigRestaurant
- meanBigRestaurantAntisocial <- integrate numTables bigRestaurantAntisocial
-
- let numCustomers = fromIntegral . sumOf (traverse.people)
-
- differentQuestion <- integrate numCustomers bigRestaurantAntisocial
-
- print meanTinyRestaurant
- print meanSmallRestaurant
- print meanBigRestaurant
- print meanBigRestaurantAntisocial
- print differentQuestion
-
diff --git a/measurable.cabal b/measurable.cabal
@@ -1,8 +1,7 @@
name: measurable
-version: 1.0.0.1
+version: 1.0.0
license: BSD3
license-file: LICENSE
-copyright: (c) Jared Tobin 2013 - 2015.
author: Jared Tobin
maintainer: jared@jtobin.ca
stability: Experimental
@@ -10,25 +9,26 @@ category: Math
homepage: http://github.com/jtobin/measurable
bug-reports: http://github.com/jtobin/measurable/issues
build-type: Simple
-cabal-version: >=1.18
+cabal-version: >= 1.18
synopsis: A shallowly-embedded DSL for basic measure wrangling.
description:
@measurable@ is a simple shallowly-embedded DSL for dealing with measures.
-
+ .
It adds a @Measure@ synonym for a standard continuation type with a
restricted output type and no @callCC@ implementation.
-
+ .
You can construct measures from samples, mass/density functions, or even
sampling functions.
-
+ .
Construct image measures by @fmap@-ing measurable functions over them, or
create new measures from existing ones by seamless measure arithmetic provided
by a simple @Num@ instance. Create measures from graphs of other measures
- using the @Monad@ instance and do-notation.
-
+ using the @Monad@ instance and do-notation. The @Applicative@ instance
+ gives you product measure.
+ .
Query measures by integrating meaurable functions against them. Extract
moments, cumulative density functions, or probabilities.
-
+ .
Caveat: while fun to play with, and rewarding to see how measures fit
together, measure operations as nested integrals are exponentially complex.
Don't expect them to scale very far!
@@ -41,16 +41,12 @@ library
hs-source-dirs: src
default-language: Haskell2010
exposed-modules:
- Measurable.Core
+ Measurable
+ , Measurable.Core
, Measurable.Measures
- , Measurable.Util
-
- other-extensions:
- BangPatterns
- FlexibleInstances
build-depends:
- base >= 4.7 && < 4.8
+ base
, foldl
, integration
, math-functions
@@ -58,23 +54,3 @@ library
, statistics
, transformers
-Test-suite measurable-examples
- type: exitcode-stdio-1.0
- hs-source-dirs: src, examples
- main-is: CRP.hs
- default-language: Haskell2010
- ghc-options:
- -threaded -rtsopts
- build-depends:
- base >= 4.7 && < 4.8
- , containers
- , foldl
- , integration
- , lens
- , measurable
- , mtl
- , mwc-random
- , primitive
- , statistics
- , transformers
-
diff --git a/src/Measurable.hs b/src/Measurable.hs
@@ -0,0 +1,5 @@
+
+module Measurable where
+
+import Measurable.Core
+import Measurable.Measures
diff --git a/src/Measurable/Core.hs b/src/Measurable/Core.hs
@@ -1,112 +1,92 @@
{-# OPTIONS_GHC -Wall #-}
-{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_GHC -fno-warn-type-defaults #-}
-{-# LANGUAGE BangPatterns #-}
-{-# LANGUAGE FlexibleInstances #-}
module Measurable.Core where
import Control.Applicative
-import Control.Monad
-import Control.Monad.Trans
-import Data.Foldable (Foldable)
-import qualified Data.Foldable as Foldable
-import Data.Functor.Identity
-import Data.Traversable
-import Measurable.Util
+import Control.Foldl (Fold)
+import qualified Control.Foldl as Foldl
+import Data.List (foldl')
import Numeric.Integration.TanhSinh
--- | A hand-rolled continuation type. Exactly like the standard one you'd find
--- in @Control.Monad.Trans.Cont@, but without the supporting functions like
--- @callCC@, etc. included in that module.
-newtype ContT r m a = ContT { runContT :: (a -> m r) -> m r }
-
-type Cont r = ContT r Identity
-
-runCont :: Cont r a -> (a -> r) -> r
-runCont m k = runIdentity $ runContT m (Identity . k)
-
-cont :: ((a -> r) -> r) -> Cont r a
-cont f = ContT $ \c -> Identity $ f (runIdentity . c)
-
-- | A measure can be represented by nothing more than a continuation with a
-- restricted output type corresponding to the reals.
--
-- A @Functor@ instance implements pushforward or image measures - merely
-- @fmap@ a measurable function over a measure to create one.
--
--- An @Applicative@ instance adds measure convolution, subtraction, and
--- multiplication by enabling a @Num@ instance via 'liftA2' and an implicit
--- marginalizing effect. A @Monad@ instance lumps the ability to create
--- measures from graphs of measures on top of that.
-type Measure a = Cont Double a
-type MeasureT m a = ContT Double m a
+-- An @Applicative@ instance adds product measure, and in turn measure
+-- convolution, subtraction, and multiplication by enabling a @Num@ instance.
+--
+-- A @Monad@ instance lumps the ability to create measures from graphs of
+-- measures on top of that.
+newtype Measure a = Measure ((a -> Double) -> Double)
-instance Functor (ContT r m) where
- fmap f m = ContT $ \c -> runContT m (c . f)
+instance Functor Measure where
+ fmap f nu = Measure $ \g ->
+ integrate (g . f) nu
-instance Applicative (ContT r m) where
- pure x = ContT ($ x)
- f <*> v = ContT $ \c ->
- runContT f $ \g ->
- runContT v (c . g)
+instance Applicative Measure where
+ pure x = Measure (\f -> f x)
+ Measure h <*> Measure g = Measure $ \f ->
+ h (\k -> g (f . k))
-instance Monad (ContT r m) where
- return x = ContT ($ x)
- m >>= k = ContT $ \c ->
- runContT m $ \x ->
- runContT (k x) c
+instance Monad Measure where
+ return x = Measure (\f -> f x)
+ rho >>= g = Measure $ \f ->
+ integrate (\nu -> integrate f (g nu)) rho
-instance MonadTrans (ContT r) where
- lift m = ContT (m >>=)
+instance Num a => Num (Measure a) where
+ (+) = liftA2 (+)
+ (-) = liftA2 (-)
+ (*) = liftA2 (*)
+ abs = fmap abs
+ signum = fmap signum
+ fromInteger = pure . fromInteger
-- | The 'integrate' function is just 'runCont' with its arguments reversed
-- in order to resemble the conventional mathematical notation, in which one
-- integrates a measurable function against a measure.
--
--- >>> let mu = fromSamples [-1, 0, 1]
+-- >>> let mu = fromSample [-1, 0, 1]
-- >>> expectation mu
-- 0.0
-- >>> variance mu
-- 0.6666666666666666
integrate :: (a -> Double) -> Measure a -> Double
-integrate = flip runCont
+integrate f (Measure nu) = nu f
-integrateT :: Applicative m => (a -> Double) -> MeasureT m a -> m Double
-integrateT f = (`runContT` (pure . f))
+-- | The expectation of a measure is typically understood to be its expected
+-- value, which is found by integrating it against the identity function.
+expectation :: Measure Double -> Double
+expectation = integrate id
-instance (Applicative m, Num a) => Num (ContT Double m a) where
- (+) = liftA2 (+)
- (-) = liftA2 (-)
- (*) = liftA2 (*)
- abs = fmap id
- signum = fmap signum
- fromInteger = pure . fromInteger
+-- | The variance of a measure, as per the usual formula
+-- @var X = E^2 X - EX^2@.
+variance :: Measure Double -> Double
+variance mu = integrate (^ 2) mu - expectation mu ^ 2
+
+-- | Calculates the volume of a 'Measure' over its entire space. Trivially 1
+-- for any probability measure.
+--
+-- >>> let mu = fromSample [1..10]
+-- >>> volume mu
+-- 1.0
+volume :: Measure a -> Double
+volume = integrate $ const 1
-- | Create a 'Measure' from a probability mass function and its support,
-- provided as a foldable container.
--
-- The requirement to supply the entire support is restrictive but necessary;
--- for approximations, consider using 'fromSamples' or
--- 'fromSamplingFunction'.
+-- for approximations, consider using 'fromSample'.
--
-- >>> let mu = fromMassFunction (binomialPmf 10 0.2) [0..10]
-- >>> integrate fromIntegral mu
-- 2.0
-fromMassFunction
- :: (Functor f, Foldable f)
- => (a -> Double)
- -> f a
- -> Measure a
-fromMassFunction f support = cont $ \g ->
- Foldable.sum $ (g /* f) <$> support
-
-fromMassFunctionT :: (Applicative m, Traversable t)
- => (a -> Double)
- -> t a
- -> MeasureT m a
-fromMassFunctionT f support = ContT $ \g ->
- fmap Foldable.sum . traverse (g //* (pure . f)) $ support
+fromMassFunction :: Foldable f => (a -> Double) -> f a -> Measure a
+fromMassFunction f support = Measure $ \g ->
+ foldl' (\acc x -> acc + f x * g x) 0 support
-- | Create a 'Measure' from a probability density function.
--
@@ -120,135 +100,71 @@ fromMassFunctionT f support = ContT $ \g ->
-- >>> variance mu
-- 1.0000000000000002
fromDensityFunction :: (Double -> Double) -> Measure Double
-fromDensityFunction d = cont $ \f -> quadratureTanhSinh $ f /* d where
- quadratureTanhSinh = result . last . everywhere trap
+fromDensityFunction d = Measure $ \f ->
+ quadratureTanhSinh (\x -> f x * d x)
+ where
+ quadratureTanhSinh = result . last . everywhere trap
-- | Create a measure from a collection of observations.
--
-- Useful for creating general purpose empirical measures.
--
--- >>> let mu = fromSamples [(1, 2), (3, 4)]
+-- >>> let mu = fromSample [(1, 2), (3, 4)]
-- >>> integrate (uncurry (+)) mu
-- 5.0
-fromSamples :: Foldable f => f a -> Measure a
-fromSamples = cont . flip weightedAverage
-
-fromSamplesT
- :: (Applicative m, Traversable f)
- => f a
- -> MeasureT m a
-fromSamplesT = ContT . flip weightedAverageM
-
--- | Create a measure from a sampling function. Runs the sampling function
--- the provided number of times and runs 'fromSamples' on the result.
-fromSamplingFunction
- :: (Monad m, Applicative m)
- => (t -> m b)
- -> Int
- -> t
- -> MeasureT m b
-fromSamplingFunction f n g = (lift $ replicateM n (f g)) >>= fromSamplesT
-
--- | A simple alias for @fmap@.
-push :: (a -> b) -> Measure a -> Measure b
-push = fmap
-
-pushT :: Monad m => (a -> b) -> MeasureT m a -> MeasureT m b
-pushT = fmap
+fromSample :: Foldable f => f a -> Measure a
+fromSample = Measure . flip weightedAverage where
+ weightedAverage :: (Foldable f, Fractional r) => (a -> r) -> f a -> r
+ weightedAverage f = Foldl.fold (weightedAverageFold f)
--- | The expectation of a measure is typically understood to be its expected
--- value, which is found by integrating it against the identity function.
-expectation :: Measure Double -> Double
-expectation = integrate id
+ weightedAverageFold :: Fractional r => (a -> r) -> Fold a r
+ weightedAverageFold f = Foldl.premap f averageFold
-expectationT :: Applicative m => MeasureT m Double -> m Double
-expectationT = integrateT id
-
--- | The variance of a measure, as per the usual formula
--- @var X = E^2 X - EX^2@.
-variance :: Measure Double -> Double
-variance mu = integrate (^ 2) mu - expectation mu ^ 2
-
-varianceT :: Applicative m => MeasureT m Double -> m Double
-varianceT mu = liftA2 (-) (integrateT (^ 2) mu) ((^ 2) <$> expectationT mu)
+ averageFold :: Fractional a => Fold a a
+ averageFold = (/) <$> Foldl.sum <*> Foldl.genericLength
-- | The @nth@ raw moment of a 'Measure'.
rawMoment :: Int -> Measure Double -> Double
rawMoment n = integrate (^ n)
-rawMomentT :: (Applicative m, Monad m) => Int -> MeasureT m Double -> m Double
-rawMomentT n = integrateT (^ n)
-
--- | All raw moments of a 'Measure'.
-rawMoments :: Measure Double -> [Double]
-rawMoments mu = (`rawMoment` mu) <$> [1..]
-
-rawMomentsT :: (Applicative m, Monad m) => MeasureT m Double -> Int -> m [Double]
-rawMomentsT mu n = traverse (`rawMomentT` mu) $ take n [1..]
-
-- | The @nth@ central moment of a 'Measure'.
centralMoment :: Int -> Measure Double -> Double
-centralMoment n mu = integrate (\x -> (x - rm) ^ n) $ mu
- where rm = rawMoment 1 mu
-
-centralMomentT :: (Applicative m, Monad m) => Int -> MeasureT m Double -> m Double
-centralMomentT n mu = integrateT (^ n) $ do
- rm <- lift $ rawMomentT 1 mu
- (subtract rm) <$> mu
-
--- | All central moments of a 'Measure'.
-centralMoments :: Measure Double -> [Double]
-centralMoments mu = (`centralMoment` mu) <$> [1..]
-
-centralMomentsT :: (Applicative m, Monad m) => MeasureT m Double -> Int -> m [Double]
-centralMomentsT mu n = traverse (`centralMomentT` mu) $ take n [1..]
+centralMoment n mu = integrate (\x -> (x - rm) ^ n) mu where
+ rm = rawMoment 1 mu
-- | The moment generating function corresponding to a 'Measure'.
--
--- >>> let mu = fromSamples [1..10]
--- >>> let mgfMu = momentGeneratingFunction mu
+-- >>> let mu = fromSample [1..10]
+-- >>> let mgfMu = mgf mu
-- >>> fmap mgfMu [0, 0.5, 1]
-- [1.0,37.4649671547254,3484.377384533132]
-momentGeneratingFunction :: Measure Double -> Double -> Double
-momentGeneratingFunction mu t = integrate (exp . (* t)) mu
+mgf :: Measure Double -> Double -> Double
+mgf mu t = integrate (\x -> exp (t * x)) mu
-- | The cumulant generating function corresponding to a 'Measure'.
--
--- >>> let mu = fromSamples [1..10]
--- >>> let cgfMu = cumulantGeneratingFunction mu
+-- >>> let mu = fromSample [1..10]
+-- >>> let cgfMu = cgf mu
-- >>> fmap cgfMu [0, 0.5, 1]
-- [0.0,3.6234062871236543,8.156044651432666]
-cumulantGeneratingFunction :: Measure Double -> Double -> Double
-cumulantGeneratingFunction mu = log . momentGeneratingFunction mu
-
--- | Calculates the volume of a 'Measure' over its entire space. Trivially 1
--- for any probability measure.
---
--- >>> let mu = fromSamples [1..10]
--- >>> volume mu
--- 1.0
-volume :: Measure a -> Double
-volume = integrate $ const 1
-
-volumeT :: Applicative m => MeasureT m a -> m Double
-volumeT = integrateT $ const 1
+cgf :: Measure Double -> Double -> Double
+cgf mu = log . mgf mu
-- | The cumulative distribution function corresponding to a 'Measure'
--
--- >>> let mu = fromSamples [1..10]
+-- >>> let mu = fromSample [1..10]
-- >>> let cdfMu = cdf mu
-- >>> fmap cdfMu [0..10]
-- [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
cdf :: Measure Double -> Double -> Double
-cdf mu x = expectation $ negativeInfinity `to` x <$> mu
+cdf nu x = integrate (negativeInfinity `to` x) nu where
+ negativeInfinity = negate (1 / 0)
-cdfT :: Applicative m => MeasureT m Double -> Double -> m Double
-cdfT mu x = expectationT $ negativeInfinity `to` x <$> mu
-- | A helpful utility for calculating the volume of a region in a measure
-- space.
--
--- >>> let mu = fromSamples [1..10]
+-- >>> let mu = fromSample [1..10]
-- >>> integrate (2 `to` 8) mu
-- 0.7
to :: (Num a, Ord a) => a -> a -> a -> a
@@ -259,7 +175,7 @@ to a b x
-- | An analogue of 'to' for measures defined over non-ordered domains.
--
-- >>> data Group = A | B | C deriving Eq
--- >>> let mu = fromSamples [A, A, A, B, A, B, C]
+-- >>> let mu = fromSample [A, A, A, B, A, B, C]
-- >>> integrate (containing [B]) mu
-- 0.2857142857142857
-- >>> integrate (containing [A,C]) mu
@@ -271,3 +187,285 @@ containing xs x
| x `elem` xs = 1
| otherwise = 0
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+-- -- | A hand-rolled continuation type. Exactly like the standard one you'd find
+-- -- in @Control.Monad.Trans.Cont@, but without the supporting functions like
+-- -- @callCC@, etc. included in that module.
+-- newtype ContT r m a = ContT { runContT :: (a -> m r) -> m r }
+--
+-- type Cont r = ContT r Identity
+--
+-- -- | A measure can be represented by nothing more than a continuation with a
+-- -- restricted output type corresponding to the reals.
+-- --
+-- -- A @Functor@ instance implements pushforward or image measures - merely
+-- -- @fmap@ a measurable function over a measure to create one.
+-- --
+-- -- An @Applicative@ instance adds measure convolution, subtraction, and
+-- -- multiplication by enabling a @Num@ instance via 'liftA2' and an implicit
+-- -- marginalizing effect. A @Monad@ instance lumps the ability to create
+-- -- measures from graphs of measures on top of that.
+-- type MeasureT m a = ContT Double m a
+-- type Measure a = Cont Double a
+--
+-- runCont :: Cont r a -> (a -> r) -> r
+-- runCont m k = runIdentity $
+-- runContT m (\x -> Identity (k x))
+--
+-- cont :: ((a -> r) -> r) -> Cont r a
+-- cont f = ContT $ \c ->
+-- Identity (f (\x -> runIdentity (c x)))
+--
+-- -- | The 'integrate' function is just 'runCont' with its arguments reversed
+-- -- in order to resemble the conventional mathematical notation, in which one
+-- -- integrates a measurable function against a measure.
+-- --
+-- -- >>> let mu = fromSamples [-1, 0, 1]
+-- -- >>> expectation mu
+-- -- 0.0
+-- -- >>> variance mu
+-- -- 0.6666666666666666
+-- integrate :: (a -> Double) -> Measure a -> Double
+-- integrate = flip runCont
+--
+-- integrateT :: Applicative m => (a -> Double) -> MeasureT m a -> m Double
+-- integrateT f m = runContT m (\x -> pure (f x))
+--
+-- -- FIXME (jtobin):
+-- -- Write these in terms of integrate / integrateT.
+-- instance Functor (ContT r m) where
+-- fmap f m = ContT $ \c ->
+-- runContT m (\x -> c (f x))
+--
+-- instance Applicative (ContT r m) where
+-- pure x = ContT $ \f -> f x
+-- f <*> v = ContT $ \c ->
+-- runContT f $ \g ->
+-- runContT v (c . g)
+--
+-- instance Monad (ContT r m) where
+-- return x = ContT ($ x)
+-- m >>= k = ContT $ \c ->
+-- runContT m $ \x ->
+-- runContT (k x) c
+--
+-- instance MonadTrans (ContT r) where
+-- lift m = ContT (m >>=)
+--
+-- instance Num a => Num (ContT Double m a) where
+-- (+) = liftA2 (+)
+-- (-) = liftA2 (-)
+-- (*) = liftA2 (*)
+-- abs = fmap id
+-- signum = fmap signum
+-- fromInteger = pure . fromInteger
+--
+-- -- | Create a 'Measure' from a probability mass function and its support,
+-- -- provided as a foldable container.
+-- --
+-- -- The requirement to supply the entire support is restrictive but necessary;
+-- -- for approximations, consider using 'fromSamples' or
+-- -- 'fromSamplingFunction'.
+-- --
+-- -- >>> let mu = fromMassFunction (binomialPmf 10 0.2) [0..10]
+-- -- >>> integrate fromIntegral mu
+-- -- 2.0
+-- fromMassFunction
+-- :: (Functor f, Foldable f)
+-- => (a -> Double)
+-- -> f a
+-- -> Measure a
+-- fromMassFunction f support = cont $ \g ->
+-- Foldable.sum $ (g /* f) <$> support
+--
+-- fromMassFunctionT :: (Applicative m, Traversable t)
+-- => (a -> Double)
+-- -> t a
+-- -> MeasureT m a
+-- fromMassFunctionT f support = ContT $ \g ->
+-- fmap Foldable.sum . traverse (g //* (pure . f)) $ support
+--
+-- -- | Create a 'Measure' from a probability density function.
+-- --
+-- -- Note that queries on measures constructed with @fromDensityFunction@ are
+-- -- subject to numerical error due to the underlying dependency on quadrature!
+-- --
+-- -- >>> let f x = 1 / (sqrt (2 * pi)) * exp (- (x ^ 2) / 2)
+-- -- >>> let mu = fromDensityFunction f
+-- -- >>> expectation mu
+-- -- 0.0
+-- -- >>> variance mu
+-- -- 1.0000000000000002
+-- fromDensityFunction :: (Double -> Double) -> Measure Double
+-- fromDensityFunction d = cont $ \f -> quadratureTanhSinh $ f /* d where
+-- quadratureTanhSinh = result . last . everywhere trap
+--
+-- -- | Create a measure from a collection of observations.
+-- --
+-- -- Useful for creating general purpose empirical measures.
+-- --
+-- -- >>> let mu = fromSamples [(1, 2), (3, 4)]
+-- -- >>> integrate (uncurry (+)) mu
+-- -- 5.0
+-- fromSamples :: Foldable f => f a -> Measure a
+-- fromSamples = cont . flip weightedAverage
+--
+-- fromSamplesT
+-- :: (Applicative m, Traversable f)
+-- => f a
+-- -> MeasureT m a
+-- fromSamplesT = ContT . flip weightedAverageM
+--
+-- -- | Create a measure from a sampling function. Runs the sampling function
+-- -- the provided number of times and runs 'fromSamples' on the result.
+-- fromSamplingFunction
+-- :: Monad m
+-- => (t -> m b)
+-- -> Int
+-- -> t
+-- -> MeasureT m b
+-- fromSamplingFunction f n g = (lift $ replicateM n (f g)) >>= fromSamplesT
+--
+-- -- | A simple alias for @fmap@.
+-- push :: (a -> b) -> Measure a -> Measure b
+-- push = fmap
+--
+-- pushT :: (a -> b) -> MeasureT m a -> MeasureT m b
+-- pushT = fmap
+--
+-- -- | The expectation of a measure is typically understood to be its expected
+-- -- value, which is found by integrating it against the identity function.
+-- expectation :: Measure Double -> Double
+-- expectation = integrate id
+--
+-- expectationT :: Applicative m => MeasureT m Double -> m Double
+-- expectationT = integrateT id
+--
+-- -- | The variance of a measure, as per the usual formula
+-- -- @var X = E^2 X - EX^2@.
+-- variance :: Measure Double -> Double
+-- variance mu = integrate (^ 2) mu - expectation mu ^ 2
+--
+-- varianceT :: Applicative m => MeasureT m Double -> m Double
+-- varianceT mu = liftA2 (-) (integrateT (^ 2) mu) ((^ 2) <$> expectationT mu)
+--
+-- -- | The @nth@ raw moment of a 'Measure'.
+-- rawMoment :: Int -> Measure Double -> Double
+-- rawMoment n = integrate (^ n)
+--
+-- rawMomentT :: Monad m => Int -> MeasureT m Double -> m Double
+-- rawMomentT n = integrateT (^ n)
+--
+-- -- | All raw moments of a 'Measure'.
+-- rawMoments :: Measure Double -> [Double]
+-- rawMoments mu = (`rawMoment` mu) <$> [1..]
+--
+-- rawMomentsT :: Monad m => MeasureT m Double -> Int -> m [Double]
+-- rawMomentsT mu n = traverse (`rawMomentT` mu) $ take n [1..]
+--
+-- -- | The @nth@ central moment of a 'Measure'.
+-- centralMoment :: Int -> Measure Double -> Double
+-- centralMoment n mu = integrate (\x -> (x - rm) ^ n) $ mu
+-- where rm = rawMoment 1 mu
+--
+-- centralMomentT :: Monad m => Int -> MeasureT m Double -> m Double
+-- centralMomentT n mu = integrateT (^ n) $ do
+-- rm <- lift $ rawMomentT 1 mu
+-- (subtract rm) <$> mu
+--
+-- -- | All central moments of a 'Measure'.
+-- centralMoments :: Measure Double -> [Double]
+-- centralMoments mu = (`centralMoment` mu) <$> [1..]
+--
+-- centralMomentsT :: Monad m => MeasureT m Double -> Int -> m [Double]
+-- centralMomentsT mu n = traverse (`centralMomentT` mu) $ take n [1..]
+--
+-- -- | The moment generating function corresponding to a 'Measure'.
+-- --
+-- -- >>> let mu = fromSamples [1..10]
+-- -- >>> let mgfMu = momentGeneratingFunction mu
+-- -- >>> fmap mgfMu [0, 0.5, 1]
+-- -- [1.0,37.4649671547254,3484.377384533132]
+-- momentGeneratingFunction :: Measure Double -> Double -> Double
+-- momentGeneratingFunction mu t = integrate (exp . (* t)) mu
+--
+-- -- | The cumulant generating function corresponding to a 'Measure'.
+-- --
+-- -- >>> let mu = fromSamples [1..10]
+-- -- >>> let cgfMu = cumulantGeneratingFunction mu
+-- -- >>> fmap cgfMu [0, 0.5, 1]
+-- -- [0.0,3.6234062871236543,8.156044651432666]
+-- cumulantGeneratingFunction :: Measure Double -> Double -> Double
+-- cumulantGeneratingFunction mu = log . momentGeneratingFunction mu
+--
+-- -- | Calculates the volume of a 'Measure' over its entire space. Trivially 1
+-- -- for any probability measure.
+-- --
+-- -- >>> let mu = fromSamples [1..10]
+-- -- >>> volume mu
+-- -- 1.0
+-- volume :: Measure a -> Double
+-- volume = integrate $ const 1
+--
+-- volumeT :: Applicative m => MeasureT m a -> m Double
+-- volumeT = integrateT $ const 1
+--
+-- -- | The cumulative distribution function corresponding to a 'Measure'
+-- --
+-- -- >>> let mu = fromSamples [1..10]
+-- -- >>> let cdfMu = cdf mu
+-- -- >>> fmap cdfMu [0..10]
+-- -- [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
+-- cdf :: Measure Double -> Double -> Double
+-- cdf mu x = expectation $ negativeInfinity `to` x <$> mu
+--
+-- cdfT :: Applicative m => MeasureT m Double -> Double -> m Double
+-- cdfT mu x = expectationT $ negativeInfinity `to` x <$> mu
+--
+-- -- | A helpful utility for calculating the volume of a region in a measure
+-- -- space.
+-- --
+-- -- >>> let mu = fromSamples [1..10]
+-- -- >>> integrate (2 `to` 8) mu
+-- -- 0.7
+-- to :: (Num a, Ord a) => a -> a -> a -> a
+-- to a b x
+-- | x >= a && x <= b = 1
+-- | otherwise = 0
+--
+-- -- | An analogue of 'to' for measures defined over non-ordered domains.
+-- --
+-- -- >>> data Group = A | B | C deriving Eq
+-- -- >>> let mu = fromSamples [A, A, A, B, A, B, C]
+-- -- >>> integrate (containing [B]) mu
+-- -- 0.2857142857142857
+-- -- >>> integrate (containing [A,C]) mu
+-- -- 0.7142857142857143
+-- -- >>> integrate (containing [A,B,C]) mu
+-- -- 1.0
+-- containing :: (Num a, Eq b) => [b] -> b -> a
+-- containing xs x
+-- | x `elem` xs = 1
+-- | otherwise = 0
+--
diff --git a/src/Measurable/Util.hs b/src/Measurable/Util.hs
@@ -1,36 +0,0 @@
-
-module Measurable.Util where
-
-import Control.Applicative
-import Control.Foldl
-import qualified Control.Foldl as Foldl
-import Data.Foldable (Foldable)
-import Data.Traversable
-
-negativeInfinity :: Fractional a => a
-negativeInfinity = negate $ 1 / 0
-
-weightedAverage :: (Foldable f, Fractional r) => (a -> r) -> f a -> r
-weightedAverage f = Foldl.fold (weightedAverageFold f)
-
-weightedAverageM
- :: (Traversable t, Applicative f, Fractional r)
- => (a -> f r)
- -> t a
- -> f r
-weightedAverageM f = fmap (Foldl.fold averageFold) . traverse f
-
-weightedAverageFold :: Fractional r => (a -> r) -> Fold a r
-weightedAverageFold f = Foldl.premap f averageFold
-
-averageFold :: Fractional a => Fold a a
-averageFold = (/) <$> Foldl.sum <*> Foldl.genericLength
-
--- | Lifted multiplication.
-(/*) :: (Num c, Applicative f) => f c -> f c -> f c
-(/*) = liftA2 (*)
-
--- | Doubly-lifted multiplication.
-(//*) :: (Num c, Applicative f, Applicative g) => f (g c) -> f (g c) -> f (g c)
-(//*) = liftA2 (/*)
-
diff --git a/stack.yaml b/stack.yaml
@@ -2,4 +2,4 @@ flags: {}
packages:
- '.'
extra-deps: []
-resolver: lts-2.21
+resolver: lts-8.15
