AntonAntonov/ MonadMakers

Functions for making software monads

Contributed by: Anton Antonov

Functions for making software monads. Monad programming provides an interface design method that allows interactive, dynamic creation and change of sequentially structured computations with polymorphic and context-aware behavior.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["AntonAntonov/MonadMakers"]

To load the code after installation, evaluate this code:
Needs["AntonAntonov`MonadMakers`"]

Details

In this paclet the concept "software monad" is seen as a design pattern, suitable for rapid and dynamic building of computational workflows.

WL code of software monads is generated (and evaluated) with GenerateStateMonadCode.

The monadic pipelines can be constructed with the douple right arrow symbol, "⟹".

The generated monads have context that is an Association, accessible with functions with the suffixes "EchoContext" and "EchoFunctionContext".

Each generated monad has a "pipeline value", accessible with functions with the suffixes "EchoValue" and "EchoFunctionValue".

The "monad tracer", TraceMonad, allows tracking of pipeline executions of other monads.

The generated monads adhere to the monad axioms.

There no need to deal with monad types explicitly, the generated monad code is "sufficient."

One reason for this is that in WL the notion of algebraic data type is not needed -- pattern matching can be used instead. (And pattern matching comes from WL's core "book of replacement rules" principle.)

Paclet Guide

Examples

Basic Examples (2)

Generate a software monad with prefix "MState":

In[1]:=

$InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["GenerateStateMonadCode", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"AntonAntonov/MonadMakers\"", ",", "\"AntonAntonov`MonadMakers`GenerateStateMonadCode\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["AntonAntonov/MonadMakers", 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Execute monadic pipeline with MState:

In[2]:=

$SeedRandom[34]; MStateUnit[ RandomReal[{0, 1}, {3, 2}], <|"mark" -> "None", "threshold" -> 0.5|>] \[DoubleLongRightArrow] MStateEchoValue \[DoubleLongRightArrow] MStateEchoContext \[DoubleLongRightArrow] MStateAddToContext["data"] \[DoubleLongRightArrow] (MStateUnit[#1 /. (x_ /; x < #2["threshold"] :> #2[ "mark"]), #2] &) \[DoubleLongRightArrow] MStateEchoValue \[DoubleLongRightArrow] MStateModifyContext[ Join[#1, <|"mark" -> "Lesser", "threshold" -> 0.8|>] &] \[DoubleLongRightArrow] MStateEchoContext \[DoubleLongRightArrow] (MStateUnit[#2[ "data"] /. (x_ /; x < #2["threshold"] :> #2[ "mark"]), #2] &) \[DoubleLongRightArrow] MStateEchoValue;$

Generate a software monad with the prefix "Perhaps":

In[3]:=

Make a monadic pipeline with the monad tracer that shows the changes of pipeline's value and tabulates pipeline's operations with corresponding descriptions:

In[4]:=