Unbound.LocallyNameless.Types

Special type combinators for specifying binding structure.

Documentation

data GenBind order card p t

The most fundamental combinator for expressing binding structure is Bind. The term type Bind p t represents a pattern p paired with a term t, where names in p are bound within t.

Like Name, Bind is also abstract. You can create bindings using bind and take them apart with unbind and friends.

Constructors

B p t

Instances

(Rep order0, Rep card0, Rep p0, Rep t0, Sat (ctx0 p0), Sat (ctx0 t0)) => Rep1 ctx (GenBind order card p t)

(Rep order, Rep card, Subst c b, Subst c a, Alpha a, Alpha b) => Subst c (GenBind order card a b)

(Show a, Show b) => Show (GenBind order card a b)

(Rep order0, Rep card0, Rep p0, Rep t0) => Rep (GenBind order card p t)

(Binary p, Binary t) => Binary (GenBind order card p t)

(Rep order, Rep card, Alpha p, Alpha t) => Alpha (GenBind order card p t)

type Bind p t = GenBind StrictOrder StrictCard p t

type SetBind p t = GenBind RelaxedOrder StrictCard p t

type SetPlusBind p t = GenBind RelaxedOrder RelaxedCard p t

data Rebind p1 p2

Rebind allows for nested bindings. If p1 and p2 are pattern types, then Rebind p1 p2 is also a pattern type, similar to the pattern type (p1,p2) except that p1 scopes over p2. That is, names within terms embedded in p2 may refer to binders in p1.

Constructors

R p1 p2

Instances

(Rep p10, Rep p20, Sat (ctx0 p10), Sat (ctx0 p20)) => Rep1 ctx (Rebind p1 p2)

(Subst c b, Subst c a, Alpha a, Alpha b) => Subst c (Rebind a b)

(Show a, Show b) => Show (Rebind a b)

(Rep p10, Rep p20) => Rep (Rebind p1 p2)

(Binary p1, Binary p2) => Binary (Rebind p1 p2)

(Alpha p, Alpha q) => Alpha (Rebind p q)

data Rec p

If p is a pattern type, then Rec p is also a pattern type, which is recursive in the sense that p may bind names in terms embedded within itself. Useful for encoding e.g. lectrec and Agda's dot notation.

Constructors

Rec p

Instances

(Rep p0, Sat (ctx0 p0)) => Rep1 ctx (Rec p)

(Alpha a, Subst c a) => Subst c (Rec a)

Show a => Show (Rec a)

Rep p0 => Rep (Rec p)

Alpha p => Alpha (Rec p)

newtype TRec p

TRec is a standalone variant of Rec: the only difference is that whereas Rec p is a pattern type, TRec p is a term type. It is isomorphic to Bind (Rec p) ().

Note that TRec corresponds to Pottier's abstraction construct from alpha-Caml. In this context, Embed t corresponds to alpha-Caml's inner t, and Shift (Embed t) corresponds to alpha-Caml's outer t.

Constructors

TRec (Bind (Rec p) ())

Instances

Show a => Show (TRec a)

newtype Embed t

Embed allows for terms to be embedded within patterns. Such embedded terms do not bind names along with the rest of the pattern. For examples, see the tutorial or examples directories.

If t is a term type, then Embed t is a pattern type.

Embed is not abstract since it involves no binding, and hence it is safe to manipulate directly. To create and destruct Embed terms, you may use the Embed constructor directly. (You may also use the functions embed and unembed, which additionally can construct or destruct any number of enclosing Shifts at the same time.)

Constructors

Embed t

Instances

(Rep t0, Sat (ctx0 t0)) => Rep1 ctx (Embed t)

Subst c a => Subst c (Embed a)

Eq t => Eq (Embed t)

Show a => Show (Embed a)

Rep t0 => Rep (Embed t)

Binary p => Binary (Embed p)

IsEmbed (Embed t)

Alpha t => Alpha (Embed t)

type Embedded (Embed t) = t

newtype Shift p

Shift the scope of an embedded term one level outwards.

Constructors

Shift p

Instances

(Rep p0, Sat (ctx0 p0)) => Rep1 ctx (Shift p)

Subst c a => Subst c (Shift a)

Eq p => Eq (Shift p)

Show a => Show (Shift a)

Rep p0 => Rep (Shift p)

IsEmbed e => IsEmbed (Shift e)

Alpha a => Alpha (Shift a)

type Embedded (Shift e) = Embedded e

module Unbound.LocallyNameless.Name

Pay no attention to the man behind the curtain

These type representation objects are exported so they can be referenced by auto-generated code. Please pretend they do not exist.

rGenBind :: forall order card p t. (Rep order, Rep card, Rep p, Rep t) => R (GenBind order card p t)

rRebind :: forall p1 p2. (Rep p1, Rep p2) => R (Rebind p1 p2)

rEmbed :: forall t. Rep t => R (Embed t)

rRec :: forall p. Rep p => R (Rec p)

rShift :: forall p. Rep p => R (Shift p)