ClosedDSL

Linear function as data, that is, one that can be part of an input or output of a linear function (-⚬). While A -⚬ B is a morphism in a category, A =⚬ B is an object called the internal hom of A and B in a closed monoidal category.

Libretto arrow, also called a ''component'' or a ''linear function''.

┏━━━━━━━━━━┓
┞───┐      ┞───┐
╎ A │      ╎ B │
┟───┘      ┟───┘
┗━━━━━━━━━━┛

In A -⚬ B, we say that the ''in-port'' is of type A and the ''out-port'' is of type B. Note that the distinction between the in-port and the out-port is only formal. Information or resources may flow in and out through both the in-port and the out-port.

"Linear" means that each input is ''consumed'' exactly once, in particular, it cannot be ignored or used twice.

Signal that travels in the direction of -⚬, i.e. the positive direction. It may signal completion of a (potentially effectful) computation. It cannot be ignored. (If this signal was the only handle to an (effectful) computation, ignoring it would mean losing track of that computation, which is considered to be a resource leak.)

A black hole that can absorb (i.e. take over the responsibility to await) Need signals, but from which there is no escape.

Signal that travels in the direction opposite to -⚬, i.e. the negative direction. It may signal completion of a (potentially effectful) computation. It cannot be ignored. (If this signal was the only handle to an (effectful) computation, ignoring it would mean losing track of that computation, which is considered to be a resource leak.)

No resource. It is the identity element for |*|. There is no flow of information through a One-typed port.

Signal that travels in the direction of -⚬, i.e. the positive direction. [Unlike Done, it cannot be the only handle to an effectful computation. As such, it can be ignored, e.g. as the losing contestant in racePair.

Signal that travels in the direction opposite to -⚬, i.e. the negative direction. Unlike Need, it cannot be the only handle to an effectful computation. As such, it can be ignored, e.g. as the losing contestant in selectPair.

A black hole that can absorb (i.e. take over the responsibility to await) Done signals, but from which there is no escape.

Impossible resource. Analogous to Nothing. It is the identity element for |+|.

Choice between A and B. The consumer chooses whether to get A or B (but can get only one of them). The producer has to be ready to provide either of them.

Concurrent pair. Also called a ''tensor product'' or simply ''times''.

Either A or B. Analogous to scala.Either. Whether it is going to be A or B is decided by the producer. The consumer has to be ready to handle either of the two cases.

Alias for |+|.

Alias for |*|.

Inverse of coFactorL.

Inverse of coFactorR.

Distribute the factor on the left into the summands on the right. Inverse of factorL.

Distribute the factor on the right into the summands on the left. Inverse of factorR.

Factor out the factor A on the left of both summands.

Factor out the factor C on the right of both summands.

Reverses the Need signal (flowing in the negative direciton, i.e. against the -⚬ arrow) into a Done signal (flowing in the positive direction, i.e. along the -⚬ arrow).

 ┏━━━━━━┓
 ┃      ┞────┐
 ┃   ┌┄┄╎Need│
 ┃   ┆  ┟────┘
 ┃   ┆  ┃
 ┃   ┆  ┞────┐
 ┃   └┄→╎Done│
 ┃      ┟────┘
 ┗━━━━━━┛

Signals (in the negative direction) when it is known which side of the choice (A |&| B) has been chosen.

Signals when it is decided whether A |+| B actually contains the left side or the right side.

Hides one level of a recursive type definition.

Reverses the Done signal (flowing in the positive direction, i.e. along the -⚬ arrow) into a Need signal (flowing in the negative direciton, i.e. against the -⚬ arrow).

 ┏━━━━━━━━━━━┓
 ┞────┐      ┃
 ╎Done│┄┄┐   ┃
 ┟────┘  ┆   ┃
 ┃       ┆   ┃
 ┞────┐  ┆   ┃
 ╎Need│←┄┘   ┃
 ┟────┘      ┃
 ┗━━━━━━━━━━━┛

Races the two Ping signals. Produces left if the first signal wins and right if the second signal wins. It is biased to the left: if both signals have arrived by the time of inquiry, returns left.

Races the two Pong signals (traveling from right to left). Chooses left if the first signal wins and right if the second signal wins. It is biased to the left: if both signals have arrived by the time of inquiry, chooses left.

Unpacks one level of a recursive type definition.