Annotation.

Value variable or primitive operation.

Data constructor or literal.

Type abstraction (level-1).

Value and Witness abstraction (level-0).

Application.

Possibly recursive bindings.

Case branching.

Type cast.

Type can appear as the argument of an application.

Witness can appear as the argument of an application.

Weaken the effect of an expression. The given effect is added to the effect of the body.

Weaken the closure of an expression. The closures of these expressions are added to the closure of the body.

Purify the effect (action) of an expression.

Forget about the closure (sharing) of an expression.

Box up a computation, capturing its effects in the S computation type.

Run a computation, releasing its effects into the environment.

Non-recursive expression binding.

Recursive binding of lambda abstractions.

Bind a local region variable, and witnesses to its properties.

Holds a region handle during evaluation.

The default pattern always succeeds.

Match a data constructor and bind its arguments.

Witness variable.

Witness constructor.

Witness application.

Joining of witnesses.

Type can appear as the argument of an application.

Baked in unit data constructor.

Primitive data constructor used for literals and baked-in constructors.

The type of the constructor needs to be attached to handle the case where there are too many constructors in the data type to list, like for Int literals. In this case we determine what data type it belongs to from the attached type of the data constructor.

Data constructor that has a data type declaration.

Witness constructors baked into the language.

Witness constructors defined in the environment. In the interpreter we use this to hold runtime capabilities. The attached type must be closed.

(axiom) The pure effect is pure.

pure     :: Pure !0

(axiom) The empty closure is empty.

empty    :: Empty $0

Convert a capability guaranteeing that a region is in the global heap, into a witness that a closure using this region is empty. This lets us rely on the garbage collector to reclaim objects in the region. It is needed when we suspend the evaluation of expressions that have a region in their closure, because the type of the returned thunk may not reveal that it references objects in that region.

use      :: [r : %]. Global r => Empty (Use r)

Convert a capability guaranteeing the constancy of a region, into a witness that a read from that region is pure. This lets us suspend applications that read constant objects, because it doesn't matter if the read is delayed, we'll always get the same result.

read     :: [r : %]. Const r  => Pure (Read r)

Convert a capability guaranteeing the constancy of a region, into a witness that allocation into that region is pure. This lets us increase the sharing of constant objects, because we can't tell constant objects of the same value apart.

alloc    :: [r : %]. Const r  => Pure (Alloc r)