Awesome
This Library provides several coq tactics and tacticals to deal with hypothesis during a proof.
Main page and documentation: https://github.com/Matafou/LibHyps
Demo file demo.v acts as a documentation.
Short description:
LibHyps provides utilities for hypothesis manipulations. In particular
a new tactic especialize H
and a set of tacticals to appy or iterate
tactics either on all hypothesis of a goal or on "new' hypothesis after
a tactic. It also provide syntax for a few predefined such iterators.
QUICK REF: especialize (BROKEN IN COQ-8.18)
This tactic is currently broken in coq v8.18. I am working on it. This may need some work on coq side.
-
especialize H at n [as h].
Creates a subgoal to prove the nth dependent premise ofH
, creating necessary evars for non unifiable variables. Once proved the subgoal is used to remove the nth premise ofH
(or of a new created hypothesis if theas
option is given). -
especialize H at * [as h].
Creates one subgoal for each dependent premise ofH
, creating necessary evars for non unifiable variables. Once proved the subgoal is used to remove the premises ofH
(or of a new createdd hypothesis if theas
option is given). -
especialize H until n [as h].
Creates one subgoal for each n first dependent premises ofH
, creating necessary evars for non unifiable variables. Once proved the subgoal is used to remove the premises ofH
(or of a new created hypothesis if theas
option is given).
QUICK REF: Pre-defined tacticals /s /n...
The most useful user-dedicated tacticals are the following
tac /s
try to applysubst
on each new hyp.tac /r
revert each new hyp.tac /n
auto-rename each new hyp.tac /g
group all non-Prop new hyp at the top of the goal.- combine the above, as in
tac /s/n/g
. - usual combinations have shortcuts:
\sng
,\sn
,\ng
,\sg
...
Install
Quick install using opam
If you have not done it already add the coq platform repository to opam!
opam repo add coq-released https://coq.inria.fr/opam/released
and then:
opam install coq-libhyps
Quick install using github:
Clone the github repository:
git clone https://github.com/Matafou/LibHyps
then compile:
configure.sh
make
make install
Quick test:
Require Import LibHyps.LibHyps.
Demo files demo.v.
More information
Deprecation from 1.0.x to 2.0.x
- "!tac", "!!tac" etc are now only loaded if you do:
Import LibHyps.LegacyNotations.
, the composable tacticals described above are preferred. - "tac1 ;; tac2" remains, but you can also use "tac1; { tac2 }".
- "tac1 ;!; tac2" remains, but you can also use "tac1; {< tac2 }".
KNOWN BUGS
Due to Ltac limitation, it is difficult to define a tactic notation
tac1 ; { tac2 }
which delays tac1
and tac2
in all cases.
Sometimes (rarely) you will have to write (idtac; tac1); {idtac; tac2}
. You may then use tactic notation like: Tactic Notation tac1' := idtac; tac1.
.
Examples
Require Import LibHyps.LibHyps.
Lemma foo: forall x y z:nat,
x = y -> forall a b t : nat, a+1 = t+2 -> b + 5 = t - 7 -> (forall u v, v+1 = 1 -> u+1 = 1 -> a+1 = z+2) -> z = b + x-> True.
Proof.
intros.
(* ugly names *)
Undo.
(* Example of using the iterator on new hyps: this prints each new hyp name. *)
intros; {fun h => idtac h}.
Undo.
(* This gives sensible names to each new hyp. *)
intros ; { autorename }.
Undo.
(* short syntax: *)
intros /n.
Undo.
(* same thing but use subst if possible, and group non prop hyps to the top. *)
intros ; { substHyp }; { autorename}; {move_up_types}.
Undo.
(* short syntax: *)
intros /s/n/g.
Undo.
(* Even shorter: *)
intros /s/n/g.
(* Let us instantiate the 2nd premis of h_all_eq_add_add without copying its type: *)
(* BROKEN IN COQ 8.18*)
(* especialize h_all_eq_add_add_ at 2.
{ apply Nat.add_0_l. }
(* now h_all_eq_add_add is specialized *)
Undo 6. *)
Undo 2.
intros until 1.
(** The taticals apply after any tactic. Notice how H:x=y is not new
and hence not substituted, whereas z = b + x is. *)
destruct x eqn:heq;intros /sng.
- apply I.
- apply I.
Qed.
Short Documentation
The following explains how it works under the hood, for people willing to apply more generic iterators to their own tactics. See also the code.
Iterator on all hypothesis
onAllHyps tac
doestac H
for each hypothesisH
of the current goal.onAllHypsRev tac
same asonAllHyps tac
but in reverse order (good for reverting for instance).
Iterators on ALL NEW hypothesis (since LibHyps-1.2.0)
tac1 ;{! tac2 }
appliestac1
to current goal and thentac2
to the list of all new hypothesis in each subgoal (iteration: oldest first). The list is a term of typeLibHyps.TacNewHyps.DList
. See the code.tac1 ;{!< tac2 }
is similar but the list of new hyps is reveresed.
Iterators on EACH NEW hypothesis
-
tac1 ;{ tac2 }
appliestac1
to current goal and thentac2
to each new hypothesis in each subgoal (iteration: older first). -
tac1 ;{< tac2 }
is similar but applies tac2 on newer hyps first. -
tac1 ;; tac2
is a synonym oftac1; { tac2 }
. -
tac1 ;!; tac2
is a synonym oftac1; {< tac2 }
.
Customizable hypothesis auto naming system
Using previous taticals (in particular the ;!;
tactical), some
tactic allow to rename hypothesis automatically.
-
autorename H
renameH
according to the current naming scheme (which is customizable, see below). -
rename_all_hyps
appliesautorename
to all hypothesis. -
!tac
applies tactictac
and then applies autorename to each new hypothesis. Shortcut for:(Tac ;!; revert_if_norename ;; autorename).
.` -
!!tac
same as!tac
with lesser priority (less than;
) to apply renaming after a group of chained tactics.
How to cstomize the naming scheme
The naming engine analyzes the type of hypothesis and generates a name
mimicking the first levels of term structure. At each level the
customizable tactic rename_hyp
is called. One can redefine it at
will. It must be of the following form:
(** Redefining rename_hyp*)
(* First define a naming ltac. It takes the current level n and
the sub-term th being looked at. It returns a "name". *)
Ltac rename_hyp_default n th :=
match th with
| (ind1 _ _) => name (`ind1`)
| (ind1 _ _ ?x ?y) => name (`ind1` ++ x#(S n)x ++ y$n)
| f1 _ ?x = ?y => name (`f1` ++ x#n ++ y#n)
| _ => previously_defined_renaming_tac1 n th (* cumulative with previously defined renaming tactics *)
| _ => previously_defined_renaming_tac2 n th
end.
(* Then overwrite the definition of rename_hyp using the ::= operator. :*)
Ltac rename_hyp ::= my_rename_hyp.
Where:
`id`
to use the name id itselft$n
to recursively call the naming engine on term t, n being the maximum depth allowedname ++ name
to concatenate name parts.
How to define variants of these tacticals?
Some more example of tacticals performing cleaning and renaming on new hypothesis.
(* subst or revert *)
Tactic Notation (at level 4) "??" tactic4(tac1) :=
(tac1 ;; substHyp ;!; revertHyp).
(* subst or rename or revert *)
Tactic Notation "!!!" tactic3(Tac) := (Tac ;; substHyp ;!; revert_if_norename ;; autorename).
(* subst or rename or revert + move up if in (Set or Type). *)
Tactic Notation (at level 4) "!!!!" tactic4(Tac) :=
(Tac ;; substHyp ;!; revert_if_norename ;; autorename ;; move_up_types).