From c2c3ceae8a2eabed33028bfff306c5664d0b42f2 Mon Sep 17 00:00:00 2001 From: Georges Gonthier Date: Wed, 27 Feb 2019 19:07:29 +0100 Subject: Making {fun ...} structural and extending it to dependent functions Construct `finfun_of` directly from a bespoke indexed inductive type, which both makes it structurally positive (and therefore usable as a container in an `Inductive` definition), and accommodates naturally dependent functions. This is still WIP, because this PR exposed a serious shortcoming of the Coq unification algorithm’s implantation of Miller patterns. This bug defeats the inference of `Canonical` structures for `{ffun S -> T}` when the instances are defined in the dependent case! This causes unmanageable regressions starting in `matrix.v`, so I have not been able to check for any impact past that. I’m pushing this commit so that the Coq issue may be addressed. Made `fun_of_fin` structurally decreasing: Changed the primitive accessor of `finfun_of` from `tfgraph` to the `Funclass` coercion `fun_of_fin`. This will make it possible to define recursive functions on inductive types built using finite functions. While`tfgraph` is still useful to transport the tuple canonical structures to `finfun_of`, it is no longer central to the theory so its role has been reduced. --- mathcomp/solvable/burnside_app.v | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'mathcomp/solvable') diff --git a/mathcomp/solvable/burnside_app.v b/mathcomp/solvable/burnside_app.v index 10cbbaa..34c1c7c 100644 --- a/mathcomp/solvable/burnside_app.v +++ b/mathcomp/solvable/burnside_app.v @@ -686,10 +686,10 @@ move=> p; rewrite inE. by do ?case/orP; move/eqP=> <- a; rewrite !(permM, permE); case: a; do 6?case. Qed. -Definition sop (p : {perm cube}) : seq cube := val (val (val p)). +Definition sop (p : {perm cube}) : seq cube := fgraph (val p). Lemma sop_inj : injective sop. -Proof. by do 2!apply: (inj_comp val_inj); apply: val_inj. Qed. +Proof. by move=> p1 p2 /val_inj/(can_inj fgraphK)/val_inj. Qed. Definition prod_tuple (t1 t2 : seq cube) := map (fun n : 'I_6 => nth F0 t2 n) t1. @@ -700,7 +700,7 @@ Proof. by move=> x n0; rewrite -pvalE unlock enum_rank_ord (tnth_nth F0). Qed. Lemma prod_t_correct : forall (x y : {perm cube}) (i : cube), (x * y) i = nth F0 (prod_tuple (sop x) (sop y)) i. Proof. -move=> x y i; rewrite permM -!sop_spec (nth_map F0) // size_tuple /=. +move=> x y i; rewrite permM -!sop_spec [RHS](nth_map F0) // size_tuple /=. by rewrite card_ord ltn_ord. Qed. -- cgit v1.2.3