lean2/tests/lean/univ_vars.lean

import logic
set_option pp.universes true

universe u
variable A : Type.{u}

definition id1 (a : A) : A := a
check @id1

variable B : Type

definition id2 (a : B) : B := a
check @id2

universe variable k
variable C : Type.{k}

definition id3 (a : C) := a

check @id3

universe variables l m
variable A₁ : Type.{l}
variable A₂ : Type.{l}
definition foo (a₁ : A₁) (a₂ : A₂) := a₁ == a₂
check @foo

check Type.{m}
feat(frontends/lean): add 'universe variable' command We can declare variables anywhere. So, we must also be able do declare "universe" variables anywhere. Here is a minimal example that requires this feature ``` -- We want A and B to be in the same universe universe variable l variable A : Type.{l} variable B : Type.{l} definition tst := A = B ``` The following doesn't work because A and B are in different universes ``` variable A : Type variable B : Type definition tst := A = B ``` The following works, but tst is not universe polymorphic, since l is one fixed global universe ``` universe l variable A : Type.{l} variable B : Type.{l} definition tst := A = B ``` 2014-10-11 17:58:15 +00:00			`import logic`
			`set_option pp.universes true`

			`universe u`
			`variable A : Type.{u}`

			`definition id1 (a : A) : A := a`
			`check @id1`

			`variable B : Type`

			`definition id2 (a : B) : B := a`
			`check @id2`

			`universe variable k`
			`variable C : Type.{k}`

			`definition id3 (a : C) := a`

			`check @id3`

			`universe variables l m`
			`variable A₁ : Type.{l}`
			`variable A₂ : Type.{l}`
			`definition foo (a₁ : A₁) (a₂ : A₂) := a₁ == a₂`
			`check @foo`

			`check Type.{m}`