From b3cc646e96819518257630e7d3157d4b1e56c373 Mon Sep 17 00:00:00 2001 From: linusbo Date: Tue, 3 Jan 2017 12:22:22 +0100 Subject: [PATCH] Uncommented slow function. --- examples/univprop.ctt | 117 +++++++++++++++++++++--------------------- 1 file changed, 58 insertions(+), 59 deletions(-) diff --git a/examples/univprop.ctt b/examples/univprop.ctt index fb480eb..63e2e0b 100644 --- a/examples/univprop.ctt +++ b/examples/univprop.ctt @@ -620,65 +620,64 @@ Fgrothendieck : functor CMon Ab (Fmor x z (monoidhomcomp (x.1, x.2.1) (y.1, y.2.1) (z.1, z.2.1) g h)) (monoidhomcomp ((f x).1, (f x).2.1.1) ((f y).1, (f y).2.1.1) ((f z).1, (f z).2.1.1) (Fmor x y g) (Fmor y z h)) - = undefined --- = let --- a0 : cmonoidhom x z --- = monoidhomcomp (x.1, x.2.1) (y.1, y.2.1) (z.1, z.2.1) g h --- a1 : cmoncgrouphom x (f z) --- = monoidhomcomp (x.1, x.2.1) (z.1, z.2.1) ((f z).1, (f z).2.1.1) a0 (grothendieckhom z) --- a2 : cgrouphom (f x) (f z) --- = grothendiecklem4 x (f z) a1 --- b0 : cmoncgrouphom x (f y) --- = monoidhomcomp (x.1, x.2.1) (y.1, y.2.1) ((f y).1, (f y).2.1.1) g (grothendieckhom y) --- b1 : cgrouphom (f x) (f y) --- = grothendiecklem4 x (f y) b0 --- c0 : cmoncgrouphom y (f z) --- = monoidhomcomp (y.1, y.2.1) (z.1, z.2.1) ((f z).1, (f z).2.1.1) h (grothendieckhom z) --- c1 : cgrouphom (f y) (f z) --- = grothendiecklem4 y (f z) c0 --- d : cgrouphom (f x) (f z) --- = monoidhomcomp ((f x).1, (f x).2.1.1) ((f y).1, (f y).2.1.1) ((f z).1, (f z).2.1.1) --- (Fmor x y g) (Fmor y z h) --- P (k : (f x).1.1) : hProp --- = ( Path (f z).1.1 (a2.1 k) (d.1 k) --- , (f z).1.2 (a2.1 k) (d.1 k) ) --- ps (k : pair x) : (P (qpr x k)).1 --- = let --- q0 : Path (f z).1.1 (a2.1 (qpr x k)) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) --- = comp (<_> (f z).1.1) (qop z (qpr z (h.1 (g.1 k.1), id z)) (qinveq z (h.1 (g.1 k.2), id z) @ i)) --- [ (i = 0) -> grothendiecklem3 x (f z) a1 k @ -j --- , (i = 1) -> comp (<_> (f z).1.1) (qopeq z (h.1 (g.1 k.1), id z) (id z, h.1 (g.1 k.2)) @ j) --- [ (j = 0) -> <_> qop z (qpr z (h.1 (g.1 k.1), id z)) (qpr z (id z, h.1 (g.1 k.2))) --- , (j = 1) -> qpr z ((hid z).2 (h.1 (g.1 k.1)) @ l, (hid z).1 (h.1 (g.1 k.2)) @ l) ]] --- q1 : Path (f y).1.1 (b1.1 (qpr x k)) (qpr y (g.1 k.1, g.1 k.2)) --- = comp (<_> (f y).1.1) (qop y (qpr y (g.1 k.1, id y)) (qinveq y (g.1 k.2, id y) @ i)) --- [ (i = 0) -> grothendiecklem3 x (f y) b0 k @ -j --- , (i = 1) -> comp (<_> (f y).1.1) (qopeq y (g.1 k.1, id y) (id y, g.1 k.2) @ j) --- [ (j = 0) -> <_> qop y (qpr y (g.1 k.1, id y)) (qpr y (id y, g.1 k.2)) --- , (j = 1) -> qpr y ((hid y).2 (g.1 k.1) @ l, (hid y).1 (g.1 k.2) @ l) ]] --- q2 (k : pair y) : Path (f z).1.1 (c1.1 (qpr y k)) (qpr z (h.1 k.1, h.1 k.2)) --- = comp (<_> (f z).1.1) (qop z (qpr z (h.1 k.1, id z)) (qinveq z (h.1 k.2, id z) @ i)) --- [ (i = 0) -> grothendiecklem3 y (f z) c0 k @ -j --- , (i = 1) -> comp (<_> (f z).1.1) (qopeq z (h.1 k.1, id z) (id z, h.1 k.2) @ j) --- [ (j = 0) -> <_> qop z (qpr z (h.1 k.1, id z)) (qpr z (id z, h.1 k.2)) --- , (j = 1) -> qpr z ((hid z).2 (h.1 k.1) @ l, (hid z).1 (h.1 k.2) @ l) ]] --- q3 : Path (f z).1.1 (c1.1 (b1.1 (qpr x k))) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) --- = comp (<_> (f z).1.1) (c1.1 (q1 @ i)) --- [ (i = 0) -> <_> c1.1 (b1.1 (qpr x k)) --- , (i = 1) -> q2 (g.1 k.1, g.1 k.2) ] --- q4 : Path (f z).1.1 (c1.1 (b1.1 (qpr x k))) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) --- = comp (<_> (f z).1.1) (c1.1 (q1 @ i)) --- [ (i = 0) -> <_> c1.1 (b1.1 (qpr x k)) --- , (i = 1) -> q2 (g.1 k.1, g.1 k.2) ] --- in comp (<_> (f z).1.1) (q0 @ i) --- [ (i = 0) -> <_> a2.1 (qpr x k) --- , (i = 1) -> q3 @ -j ] --- p : Path ((f x).1.1 -> (f z).1.1) a2.1 d.1 --- = \ (k : (f x).1.1) -> (setquotprop (pair x) (peqrel x) P ps k @ i) --- in lemSig ((f x).1.1 -> (f z).1.1) --- (ismonoidhom ((f x).1, (f x).2.1.1) ((f z).1, (f z).2.1.1)) --- (propismonoidhom ((f x).1, (f x).2.1.1) ((f z).1, (f z).2.1.1)) --- a2 d p + = let + a0 : cmonoidhom x z + = monoidhomcomp (x.1, x.2.1) (y.1, y.2.1) (z.1, z.2.1) g h + a1 : cmoncgrouphom x (f z) + = monoidhomcomp (x.1, x.2.1) (z.1, z.2.1) ((f z).1, (f z).2.1.1) a0 (grothendieckhom z) + a2 : cgrouphom (f x) (f z) + = grothendiecklem4 x (f z) a1 + b0 : cmoncgrouphom x (f y) + = monoidhomcomp (x.1, x.2.1) (y.1, y.2.1) ((f y).1, (f y).2.1.1) g (grothendieckhom y) + b1 : cgrouphom (f x) (f y) + = grothendiecklem4 x (f y) b0 + c0 : cmoncgrouphom y (f z) + = monoidhomcomp (y.1, y.2.1) (z.1, z.2.1) ((f z).1, (f z).2.1.1) h (grothendieckhom z) + c1 : cgrouphom (f y) (f z) + = grothendiecklem4 y (f z) c0 + d : cgrouphom (f x) (f z) + = monoidhomcomp ((f x).1, (f x).2.1.1) ((f y).1, (f y).2.1.1) ((f z).1, (f z).2.1.1) + (Fmor x y g) (Fmor y z h) + P (k : (f x).1.1) : hProp + = ( Path (f z).1.1 (a2.1 k) (d.1 k) + , (f z).1.2 (a2.1 k) (d.1 k) ) + ps (k : pair x) : (P (qpr x k)).1 + = let + q0 : Path (f z).1.1 (a2.1 (qpr x k)) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) + = comp (<_> (f z).1.1) (qop z (qpr z (h.1 (g.1 k.1), id z)) (qinveq z (h.1 (g.1 k.2), id z) @ i)) + [ (i = 0) -> grothendiecklem3 x (f z) a1 k @ -j + , (i = 1) -> comp (<_> (f z).1.1) (qopeq z (h.1 (g.1 k.1), id z) (id z, h.1 (g.1 k.2)) @ j) + [ (j = 0) -> <_> qop z (qpr z (h.1 (g.1 k.1), id z)) (qpr z (id z, h.1 (g.1 k.2))) + , (j = 1) -> qpr z ((hid z).2 (h.1 (g.1 k.1)) @ l, (hid z).1 (h.1 (g.1 k.2)) @ l) ]] + q1 : Path (f y).1.1 (b1.1 (qpr x k)) (qpr y (g.1 k.1, g.1 k.2)) + = comp (<_> (f y).1.1) (qop y (qpr y (g.1 k.1, id y)) (qinveq y (g.1 k.2, id y) @ i)) + [ (i = 0) -> grothendiecklem3 x (f y) b0 k @ -j + , (i = 1) -> comp (<_> (f y).1.1) (qopeq y (g.1 k.1, id y) (id y, g.1 k.2) @ j) + [ (j = 0) -> <_> qop y (qpr y (g.1 k.1, id y)) (qpr y (id y, g.1 k.2)) + , (j = 1) -> qpr y ((hid y).2 (g.1 k.1) @ l, (hid y).1 (g.1 k.2) @ l) ]] + q2 (k : pair y) : Path (f z).1.1 (c1.1 (qpr y k)) (qpr z (h.1 k.1, h.1 k.2)) + = comp (<_> (f z).1.1) (qop z (qpr z (h.1 k.1, id z)) (qinveq z (h.1 k.2, id z) @ i)) + [ (i = 0) -> grothendiecklem3 y (f z) c0 k @ -j + , (i = 1) -> comp (<_> (f z).1.1) (qopeq z (h.1 k.1, id z) (id z, h.1 k.2) @ j) + [ (j = 0) -> <_> qop z (qpr z (h.1 k.1, id z)) (qpr z (id z, h.1 k.2)) + , (j = 1) -> qpr z ((hid z).2 (h.1 k.1) @ l, (hid z).1 (h.1 k.2) @ l) ]] + q3 : Path (f z).1.1 (c1.1 (b1.1 (qpr x k))) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) + = comp (<_> (f z).1.1) (c1.1 (q1 @ i)) + [ (i = 0) -> <_> c1.1 (b1.1 (qpr x k)) + , (i = 1) -> q2 (g.1 k.1, g.1 k.2) ] + q4 : Path (f z).1.1 (c1.1 (b1.1 (qpr x k))) (qpr z (h.1 (g.1 k.1), h.1 (g.1 k.2))) + = comp (<_> (f z).1.1) (c1.1 (q1 @ i)) + [ (i = 0) -> <_> c1.1 (b1.1 (qpr x k)) + , (i = 1) -> q2 (g.1 k.1, g.1 k.2) ] + in comp (<_> (f z).1.1) (q0 @ i) + [ (i = 0) -> <_> a2.1 (qpr x k) + , (i = 1) -> q3 @ -j ] + p : Path ((f x).1.1 -> (f z).1.1) a2.1 d.1 + = \ (k : (f x).1.1) -> (setquotunivprop (pair x) (peqrel x) P ps k @ i) + in lemSig ((f x).1.1 -> (f z).1.1) + (ismonoidhom ((f x).1, (f x).2.1.1) ((f z).1, (f z).2.1.1)) + (propismonoidhom ((f x).1, (f x).2.1.1) ((f z).1, (f z).2.1.1)) + a2 d p in (f, Fmor, Fid, p) grothendieck_univarr (x : cA CMon) : univarr CMon Ab x Fforgetful -- 2.34.1