From: du yu <doof...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: How to define w types in agda?
Date: Thu, 25 Jan 2018 08:26:41 -0800 (PST) [thread overview]
Message-ID: <2d2edbc3-10f6-4c85-a88d-f810acf6789a@googlegroups.com> (raw)
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I have the following initial thoughts but can't work out to define zero as
a w type
data Zro : Set where
data One : Set where
O1 : One
data Two : Set where
O2 : Two
I2 : Two
-- w types
rec2 : (x y : Set) -> Two -> Set
rec2 x _ O2 = x
rec2 _ y I2 = y
data W (A : Set) (B : A -> Set) : Set where -- well founded trees
w : (s : A) -> B s -> W A B
sup : (a : A) -> ((B a) -> ((x : A) -> W A B )) -> W A B
natw : Set
natw = W Two (rec2 Zro One) -- nat type as w type
zero_w : natw
zero_w = sup O2 (λ x y → {!!})
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next reply other threads:[~2018-01-25 16:26 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-01-25 16:26 du yu [this message]
2018-01-26 2:38 ` [HoTT] " Favonia
2018-01-26 8:50 ` du yu
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