Safe Haskell	None
Language	GHC2024

Circuit.Diagram

Description

Generic, untyped string-diagram syntax.

This is the surface that renderers consume. It discards the Haskell types but keeps the layout structure: boxes, wires, bends, swaps, composition and tensor. Constructors live here independently of any particular semantic interpretation (polynomial lenses, matrices, etc.).

Synopsis

data SDiagram
- = SWire
- | SBox String Int Int
- | SSpider Int Int
- | SPrismBox
- | SBeside SDiagram SDiagram
- | SThenD SDiagram SDiagram
- | SBend
- | SBend'
- | STurn SDiagram
- | SUnitL
- | SUnitL'
- | SUnitR
- | SUnitR'
- | SAssoc
- | SAssoc'
- | SSwap
- | STrace SDiagram
sCopy :: SDiagram
sMerge :: SDiagram
sDelete :: SDiagram
sCreate :: SDiagram

Documentation

data SDiagram Source #

Untyped drawing syntax for a string diagram.

This is what a renderer consumes. It discards the Haskell types but keeps the layout structure: boxes, wires, bends, swaps, composition and tensor.

Constructors

SWire	Straight identity wire.
SBox String Int Int	Box with a label, a number of input ports and a number of output ports.
SSpider Int Int	Spider node with an input arity and an output arity (hypergraph junction: all its ports share one wire class).
SPrismBox	Prism box.
SBeside SDiagram SDiagram	Two diagrams side by side (tensor product).
SThenD SDiagram SDiagram	Two diagrams chained (composition).
SBend	Cup (counit): bends two wires back to the unit.
SBend'	Cap (unit): introduces two wires from the unit.
STurn SDiagram	Dual (rotate 180°).
SUnitL	Left unitor `I ⊗ A -> A`.
SUnitL'	Inverse left unitor `A -> I ⊗ A`.
SUnitR	Right unitor `A ⊗ I -> A`.
SUnitR'	Inverse right unitor `A -> A ⊗ I`.
SAssoc	Associator `A ⊗ (B ⊗ C) -> (A ⊗ B) ⊗ C`.
SAssoc'	Inverse associator `(A ⊗ B) ⊗ C -> A ⊗ (B ⊗ C)`.
SSwap	Symmetric braiding `A ⊗ B -> B ⊗ A`.
STrace SDiagram	Trace: hide the last input/output pair as a feedback loop. A value `STrace d` represents a diagram `d` whose last input and last output are connected, removing one port from each boundary.

Instances

Instances details

Eq SDiagram Source #
Instance details Defined in Circuit.Diagram Methods (==) :: SDiagram -> SDiagram -> Bool # (/=) :: SDiagram -> SDiagram -> Bool #
Show SDiagram Source #
Instance details Defined in Circuit.Diagram Methods showsPrec :: Int -> SDiagram -> ShowS # show :: SDiagram -> String # showList :: [SDiagram] -> ShowS #

sCopy :: SDiagram Source #

Copy spider: one input forked to two outputs.

sMerge :: SDiagram Source #

Merge spider: two inputs joined to one output.

sDelete :: SDiagram Source #

Delete spider: erases one input.

sCreate :: SDiagram Source #

Create spider: produces one output from nothing.