Function#

class discopy.python.Function(inside, dom, cod)[source]#

Bases: Composable[tuple[type, …]], Whiskerable

A function is a callable inside with a pair of types dom and cod.

Parameters:

inside (Callable) – The callable Python object inside the function.
dom (tuple[type, ...]) – The domain of the function, i.e. its input type.
cod (tuple[type, ...]) – The codomain of the function, i.e. its output type.

Summary

`id`()	The identity function on a given tuple of types `dom`.
`then`(other)	The sequential composition of two functions, called with `>>`.
`tensor`(other)	The parallel composition of two functions, called with `@`.
`swap`(x, y)	The function for swapping two tuples of types `x` and `y`.
`copy`(x[, n])	The function for making `n` copies of a tuple of types `x`.
`discard`(dom)	The function discarding a tuple of types, i.e. making zero copies.
`ev`(base, exponent[, left])	The evaluation function, i.e. take a function and apply it to an argument.
`curry`([n, left])	Currying, i.e. turn a binary function into a function-valued function.
`uncurry`([left])	Uncurrying, i.e. turn a function-valued function into a binary function.
`fix`([n])	The parameterised fixed point of a function.
`trace`([n, left])	The trace of a function.

id()[source]#

The identity function on a given tuple of types dom.

Parameters:: dom (python.Ty) – The typle of types on which to take the identity.
Return type:: Function

then(other)[source]#

The sequential composition of two functions, called with >>.

Parameters:: other (Function) – The other function to compose in sequence.
Return type:: Function

tensor(other)[source]#

The parallel composition of two functions, called with @.

Parameters:: other (Function) – The other function to compose in sequence.
Return type:: Function

static swap(x, y)[source]#

The function for swapping two tuples of types x and y.

Parameters:

x (tuple[type, ...]) – The tuple of types on the left.
y (tuple[type, ...]) – The tuple of types on the right.

Return type:

Function

static braid(x, y)#

The function for swapping two tuples of types x and y.

Parameters:

x (tuple[type, ...]) – The tuple of types on the left.
y (tuple[type, ...]) – The tuple of types on the right.

Return type:

Function

static copy(x, n=2)[source]#

The function for making n copies of a tuple of types x.

Parameters:

x (tuple[type, ...]) – The tuple of types to copy.
n – The number of copies.

Return type:

Function

static discard(dom)[source]#

The function discarding a tuple of types, i.e. making zero copies.

Parameters:: dom (tuple[type, ...]) – The tuple of types to discard.
Return type:: Function

static ev(base, exponent, left=True)[source]#

The evaluation function, i.e. take a function and apply it to an argument.

Parameters:

base (tuple[type, ...]) – The output type.
exponent (tuple[type, ...]) – The input type.
left – Whether to take the function on the left or right.

Return type:

Function

curry(n=1, left=True)[source]#

Currying, i.e. turn a binary function into a function-valued function.

Parameters:

n – The number of types to curry.
left – Whether to curry on the left or right.

Return type:

Function

uncurry(left=True)[source]#

Uncurrying, i.e. turn a function-valued function into a binary function.

Parameters:: left – Whether to uncurry on the left or right.
Return type:: Function

fix(n=1)[source]#

The parameterised fixed point of a function.

Parameters:: n – The number of types to take the fixed point over.
Return type:: Function

trace(n=1, left=False)[source]#

The trace of a function.

Parameters:: n – The number of types to trace over.

Function

Contents

Function#