# polycirc.operation

The primitive circuits from which arithmetic circuits are built.

Each `Operation` can have multiple inputs and outputs. For example, if we call the `Copy` operation as a function, we can see it repeats its input:

```>>> from polycirc.ast import diagram_to_ast
>>> f = diagram_to_ast(Copy().diagram(), 'copy').to_function()
>>> f(314)
[314, 314]
```

Since `Copy` has one input and two outputs, its type is `1 → 2`

```>>> Copy().type
(1, 2)
```

Similarly, the `Add` operation adds its inputs:

```>>> from polycirc.ast import diagram_to_ast
>>> f(314, 1)

```

A diagram built from these primitives is like a circuit whose wires carry values in some semiring S. Note that the set of primitives included is also functionally complete. For further mathematical details, refer to Wilson and Zanasi [WZ22].

Polycirc currently supports the following primitive operations:

Operation

Type

Function

2→1

[x₁+x₂]

Negate

1→1

[-x₁]

Constant(c)

0→1

[c]

Copy

1→2

[x₁, x₁]

1→0

[]

Sub

2→1

[x₁-x₂]

Mul

2→1

[x₁*x₂]

Shr

2→1

[x₁ >> x₂]

Eq

2→1

[int(x₁ == x₂)]

Gt

2→1

[int(x₁ > x₂)]

Geq

2→1

[int(x₁ >= x₂)]

Lt

2→1

[int(x₁ < x₂)]

Leq

2→1

[int(x₁ <= x₂)]

class polycirc.operation.Operation
abstract property type: Tuple[int, int]

The number of inputs and outputs

property source
property target
abstract property fwd: Diagram

the forward map of this operation as a Diagram

abstract property rev: Diagram

the reverse map of this operation as a Diagram. This generally corresponds to its reverse derivative.

abstract property residual: Diagram
diagram()

Return the operation as a singleton diagram

class polycirc.operation.LinearOperation

An Operation with an empty residual

fwd() Diagram

the forward map of this operation as a Diagram

rev() Diagram

the reverse map of this operation as a Diagram. This generally corresponds to its reverse derivative.

residual()
abstract dagger() Diagram

For an operation `op` of type A → B, its dagger `op.dagger()` must have type `B → A`.

property type
dagger()
class polycirc.operation.Negate
property type
dagger()
class polycirc.operation.Constant(value: int)
value: int
property type
dagger()
class polycirc.operation.Copy
property type
dagger()
property type
dagger()
class polycirc.operation.Sub
property type
dagger()
class polycirc.operation.Mul
property type
residual()
fwd()
rev()
class polycirc.operation.Shr
property type
dagger()
class polycirc.operation.Eq
property type
dagger()
class polycirc.operation.Gt
property type
dagger()
class polycirc.operation.Geq
property type
dagger()
class polycirc.operation.Lt
property type
dagger()
class polycirc.operation.Leq
property type
dagger()