Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Diagram Examples
A gallery of worked examples: modeling a recipe as a dataflow diagram, building sorting networks from permutations, round-tripping between diagrams and symbolic tensors, and viewing trees and graphs as diagram grids.
In[1]:=
<<Wolfram`DiagrammaticComputation`
A Recipe as a Dataflow
Any process whose steps consume and produce named resources is a diagram. The classic tiramisu cream:
In[2]:=
egg=
["Crack Egg","egg",{"white","yolk"}],beat=
["Beat",{"yolk","yolk","sugar"},"yolky paste"],whisk=
["Whisk",{"white","white"},"whisked whites"],stir=
["Stir",{"yolky paste","mascarpone"},"thick paste"],fold=
["Fold",{"whisked whites","thick paste"},"crema di mascarpone"]
 | Diagram |
| Diagram |
| Diagram |
| Diagram |
| Diagram |
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,
,
,
,
In[3]:=
 | ColumnDiagram |
| RowDiagram |
 | IdentityDiagram |
| RowDiagram |
Out[3]=
Sorting Networks
A bubble sort is a stack of adjacent transpositions. Start from an unsorted row of labelled wires:
In[4]:=
init=
MapIndexed
[#2〚1〛,#1]&,{C,B,A}
 | RowDiagram |
| Diagram |
Out[4]=
In[5]:=
| PermutationDiagram |
Out[5]=
Stacking the three swaps sorts the wires:
In[6]:=
sortNetwork=
init,
[{B,A}{A,B}],
[{C,A}{A,C}],
[{C,B}{B,C}],"Rotate"Pi2
| ColumnDiagram |
| PermutationDiagram |
| PermutationDiagram |
| PermutationDiagram |
Out[6]=
In[7]:=
| SimplifyDiagram |
| ColumnDiagram |
 | PermutationDiagram |
| PermutationDiagram |
| PermutationDiagram |
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Diagrams and Tensors
A composition of symbolic processes reads directly as matrix algebra. The property of a diagram extracts the contraction:
"Tensor"
In[8]:=
| ColumnDiagram |
| Diagram |
| Diagram |
| Diagram |
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ArrayDotArrayDot,,1,,1
⥎
C
⥎
B
⥎
A
In the other direction, turns a tensor expression into a diagram. A contraction of two arrays over two indices:
In[9]:=
| TensorDiagram |
Out[9]=
The round trip preserves the network:
In[10]:=
d1=
[A,a,b],
[B,b,a]
| DiagramNetwork |
| Diagram |
| Diagram |
Out[10]=
Diagrams whose labels carry concrete arrays evaluate numerically:
Trees and Graphs as Grids
A graph becomes a network of vertex diagrams joined along its edges:
The network's grid arrangement introduces the necessary caps, cups and crossings automatically:
Executable Dataflow with Parallelism
Annotated diagrams run as functions (see the introduction tech note). Functions in independent branches can run on parallel kernels: