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. This can be disabled with the pp.mathlib.binderPredicates option.

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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.

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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.

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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.

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PiNotation.replacePiNotation (Lean.Syntax.node info kind args) = pure (Lean.Syntax.node info `Lean.Parser.Term.forall args)
PiNotation.replacePiNotation x✝ = Lean.Macro.throwUnsupported

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def PiNotation.delabPi :

Lean.PrettyPrinter.Delaborator.Delab

Override the Lean 4 pi notation delaborator with one that prints cute binders such as ∀ ε > 0.

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def PiNotation.delabPi' :

Lean.PrettyPrinter.Delaborator.Delab

Override the Lean 4 pi notation delaborator with one that uses Π and prints cute binders such as ∀ ε > 0. 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.

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