166 lines
3.3 KiB
Text
166 lines
3.3 KiB
Text
set_option trace.inductive_compiler.nested.define.failure true
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set_option max_memory 1000000
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inductive {u} vec (A : Type u) : nat -> Type u
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| vnil : vec 0
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| vcons : Pi (n : nat), A -> vec n -> vec (n+1)
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namespace X1
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print "simple"
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inductive foo : Type
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| mk : list foo -> foo
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end X1
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namespace X2
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print "with param"
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inductive {u} foo (A : Type u) : Type u
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| mk : A -> list foo -> foo
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end X2
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namespace X3
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print "with indices"
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inductive {u} foo (A B : Type u) : Type u
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| mk : A -> B -> vec foo 0 -> foo
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end X3
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namespace X4
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print "with locals in indices"
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inductive {u} foo (A : Type u) : Type u
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| mk : Pi (n : nat), A -> vec foo n -> foo
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end X4
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namespace X5
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print "nested-reflexive"
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inductive {u} foo (A : Type u) : Type u
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| mk : A -> (Pi (m : nat), vec foo m) -> foo
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end X5
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namespace X6
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print "locals + nested-reflexive locals in indices"
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inductive {u} foo (A : Type u) : Type u
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| mk : Pi (n : nat), A -> (Pi (m : nat), vec foo (n + m)) -> foo
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end X6
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namespace X7
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print "many different nestings"
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inductive {u} foo (A : Type u) : Type u
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| mk : Pi (n : nat), A -> list A -> prod A A -> (Pi (m : nat), vec foo (n + m)) -> vec foo n -> foo
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end X7
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namespace X8
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print "many different nestings, some sharing"
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inductive {u} foo (A : Type u) : Type u
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| mk₁ : Pi (n : nat), A -> (Pi (m : nat), vec (list foo) (n + m)) -> vec foo n -> foo
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| mk₂ : Pi (n : nat), A -> list A -> prod A A -> (Pi (m : nat), vec foo (n + m)) -> vec foo n -> foo
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end X8
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namespace X9b
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print "mutual + nesting"
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mutual inductive {u} foo, bar
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with foo : Type u
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| mk : list (list foo) -> foo
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with bar : Type u
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| mk : list foo -> bar
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end X9b
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namespace X10
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print "many layers of nesting nested inductive types"
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inductive wrap (A : Sort*)
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| mk : A -> wrap
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inductive box (A : Sort*)
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| mk : A -> wrap box -> box
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inductive foo (A : Sort*)
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| mk : A -> box foo -> foo
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inductive bar
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| mk : foo bar -> bar
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end X10
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namespace X11
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print "intro rule that introduces additional nesting"
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inductive {u} wrap (A : Type u) : Type u
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| mk : list A -> wrap
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inductive {u} foo : Type u
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| mk : wrap foo -> foo
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end X11
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namespace X12
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print "intro rule that introduces a lot of additional nesting"
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inductive wrap (A : Sort*) : Sort*
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| mk : list (list A) -> wrap
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inductive {u} box (A : Type u) : Type u
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| mk : A -> wrap box -> box
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end X12
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namespace X13
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print "with reducible definitions"
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attribute [reducible] definition list' := @list
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inductive wrap (A : Sort*) : Sort*
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| mk : A -> list' A -> wrap
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attribute [reducible] definition wrap' := @wrap
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inductive {u} foo (A : Type u) : Type u
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| mk : A -> wrap' (list' foo) -> foo
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end X13
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namespace X14
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print "with indices in original"
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inductive Foo : bool -> Type
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| mk : list (Foo ff) -> Foo tt
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end X14
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namespace X15
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print "nested inductive propositions eliminating to Prop"
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universe variable l
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inductive plist (A : Sort l) : Sort l
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| nil : plist
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| cons : A → plist → plist
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inductive foo (A : Type l) : ℕ → Prop
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| mk : A → plist (plist (foo 0)) → or (foo 1) (foo 2) → foo 1
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end X15
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namespace X16
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print "multiply nested inductive propositions"
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universe variable l
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inductive wrap (A : Sort l) : Sort l
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| mk : A -> wrap
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inductive box (A : Prop) : Prop
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| mk : A -> wrap box -> box
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inductive foo (A : Sort*) : Prop
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| mk : A -> box foo -> foo
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inductive bar : Prop
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| mk : foo bar -> bar
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end X16
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