Function

class discopy.python.multiplicative.Function(inside, dom, cod)

Bases: discopy.python.function.Function

Python function with tuple as tensor.

Parameters:

• inside (Callable) – The callable Python object inside the function.

• dom (type) – The domain of the function, i.e. its list of input types.

• cod (type) – The codomain of the function, i.e. its list of output types.

Summary

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 multiplicative trace of a function.

ty_factory

alias of tuple[type, …]

tensor(other)

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)

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)

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)

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)

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)

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)

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)

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)

The multiplicative trace of a function.

Parameters:

n – The number of types to trace over.