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View Code? Open in Web Editor NEWA dependent type theory with user defined data types
A dependent type theory with user defined data types
I am not able to write tt
and ff
in a REPL session. Is this on purpose? It is unexpected for me at least.
~/git/datatt/library (main)$ ../_build/default/src/repl.exe
-- data Bool => | tt | ff
data Bool
-- tt
Type Error: 1.1-1.3 - Unbound var `tt`
-- ff
Type Error: 1.1-1.3 - Unbound var `ff`
Lifting is removed (or is it hidden?) in the normalized output in the REPL. Here the output is ill-typed.
-- List Type
Type Error: 1.6-1.10 - Type too large to be contained in Type
-- List^1 Type
_ : Type^1
_ = List Type
Currently lift
only increase the level of universes, but this results in the following ill-typed lifting:
-- map^1
_ : (A : Type^1) → (B : Type^1) → (f : A → B) → List A → List B
_ = λ A ⇒ λ B ⇒ λ f ⇒ λ \95 ⇒ elim \95 with | cons x (xs / ih) ⇒ cons (f x) ih | nil ⇒ nil
Here List
is applied to A
, but A
is in Type^1
while List
expects a Type
, so this is ill-typed.
I would expect:
(A : Type^1) → (B : Type^1) → (f : A → B) → List^1 A → List^1 B
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