dan/HITs-Examples
1
0
Fork 0
mirror of https://github.com/nmvdw/HITs-Examples synced 2025-11-03 07:03:51 +01:00
Code Issues Releases Wiki Activity

Port the FiniteSets library to HitTactics

Browse Source
This commit is contained in:
Dan Frumin
2017-05-24 13:54:00 +02:00
parent 25d1e1c969
commit 826b6ba233
5 changed files with 160 additions and 251 deletions
Download Patch File Download Diff File Expand all files Collapse all files

85
prelude/HitTactics.v Normal file
View File

@@ -0,0 +1,85 @@
Class HitRecursion (H : Type) := {
indTy : Type;
recTy : Type;
H_inductor : indTy;
H_recursor : recTy
}.
Definition hrecursion (H : Type) {HR : HitRecursion H} : @recTy H HR :=
@H_recursor H HR.
Definition hinduction (H : Type) {HR : HitRecursion H} : @indTy H HR :=
@H_inductor H HR.
Ltac hrecursion_ :=
lazymatch goal with
| [ |- ?T -> ?P ] =>
let hrec1 := eval cbv[hrecursion H_recursor] in (hrecursion T) in
let hrec := eval simpl in hrec1 in
match type of hrec with
| ?Q =>
match (eval simpl in Q) with
| forall Y, T -> Y =>
simple refine (hrec P)
| forall Y _, T -> Y =>
simple refine (hrec P _)
| forall Y _ _, T -> Y =>
simple refine (hrec P _ _)
| forall Y _ _ _, T -> Y =>
simple refine (hrec P _ _ _)
| forall Y _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _)
| forall Y _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _)
| forall Y _ _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _ _ _ _, T -> Y =>
simple refine (hrec P _ _ _ _ _ _ _ _ _ _)
| _ => fail "Cannot handle the recursion principle (too many parameters?) :("
end
end
| [ |- forall (target:?T), ?P] =>
let hind1 := eval cbv[hinduction H_inductor] in (hinduction T) in
let hind := eval simpl in hind1 in
match type of hind with
| ?Q =>
match (eval simpl in Q) with
| forall Y , (forall x, Y x) =>
simple refine (hind (fun target => P) _)
| forall Y _, (forall x, Y x) =>
simple refine (hind (fun target => P) _)
| forall Y _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _)
| forall Y _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _)
| forall Y _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _)
| forall Y _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _)
| forall Y _ _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _ _ _ _)
| forall Y _ _ _ _ _ _ _ _ _, (forall x, Y x) =>
simple refine (hind (fun target => P) _ _ _ _ _ _ _ _ _)
| _ => fail "Cannot handle the induction principle (too many parameters?) :("
end
end
(*| _ => fail "I am sorry, but something went wrong!"*)
end.
Tactic Notation "hrecursion" := hrecursion_; simpl.
Tactic Notation "hrecursion" ident(x) := revert x; hrecursion.
Tactic Notation "hinduction" := hrecursion_; simpl.
Tactic Notation "hinduction" ident(x) := revert x; hrecursion.