Pi type notation

Provides the Π x : α, β x notation as an alternative to Lean 4's built-in (x : α) → β x notation. To get all non-∀ pi types to pretty print this way then do open scoped PiNotation.

The notation also accepts extended binders, like Π x ∈ s, β x for Π x, x ∈ s → β x.

def PiNotation.piNotation : Lean.Parser.Parser

Dependent function type (a "pi type"). The notation Π x : α, β x can also be written as (x : α) → β x.

def PiNotation.«termΠ__,_» : Lean.ParserDescr

Dependent function type (a "pi type"). The notation Π x ∈ s, β x is short for Π x, x ∈ s → β x.

def PiNotation.replacePiNotation : Lean.Macro

Since pi notation and forall notation are interchangeable, we can parse it by simply using the pre-existing forall parser.

def PiNotation.delabPi : Lean.PrettyPrinter.Delaborator.Delab

Override the Lean 4 pi notation delaborator with one that uses Π. Note that this takes advantage of the fact that (x : α) → p x notation is never used for propositions, so we can match on this result and rewrite it.