Wolfram/ DiagrammaticComputation

Abstract compositional diagrammatic calculus

Contributed by: Nik Murzin, Ian Ford

The paclet provides Diagram and Port with constructors ToDiagram, TensorDiagram, IdentityDiagram, PermutationDiagram, CapDiagram, CupDiagram, CopyDiagram, SpiderDiagram; compositions DiagramComposition, DiagramProduct, DiagramSum, DiagramNetwork, RowDiagram, ColumnDiagram; transformations DiagramDual, DiagramFlip, DiagramReverse, DiagramArrange, SimplifyDiagram; conversions DiagramFunction, DiagramTensor; surgery DiagramCases, DiagramMap, DiagramMapAt, DiagramExtract, DiagramInsert, DiagramDelete; and rewriting DiagramReplace, DiagramReplaceList, DiagramNestReplace, DiagramRule.

Installation Instructions

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

To load the code after installation, evaluate this code:
Needs["Wolfram`DiagrammaticComputation`"]

Details

A Diagram is a symbolic process with typed input and output Ports — a morphism in a symmetric monoidal category. Diagrams compose sequentially (DiagramComposition), in parallel (DiagramProduct), additively (DiagramSum), or orderlessly by port name (DiagramNetwork).

Composite diagrams render as 2D grids (DiagramGrid) or single nodes (DiagramGraphics); arbitrary networks arrange into grids automatically by inserting identities, permutations, caps, cups and spiders (DiagramArrange).

Diagrams convert to and from other compositional structures: graphs, trees, hypergraphs, neural networks and system models via ToDiagram, symbolic tensor contractions via DiagramTensor and TensorDiagram, and executable dataflow functions via DiagramFunction.

Subdiagrams can be located, mapped over and edited (DiagramCases, DiagramMap, DiagramReplacePart) and rewritten by hypergraph-matched rules (DiagramReplace, DiagramRule), including the standard interaction-net rule schemas.

The paclet depends on the WolframInstitute/Hypergraph paclet for rule matching.

Paclet Guide

Examples

Basic Examples (3)

Create a simple diagram with one input and two output ports:

In[1]:=

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