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ProofsCommonTactics: log failing inital goals #104

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Sep 4, 2023
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ProofsCommonTactics: log failing inital goals #104

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125 changes: 66 additions & 59 deletions src/Rewriter/Rewriter/ProofsCommonTactics.v
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Original file line number Diff line number Diff line change
Expand Up @@ -498,70 +498,77 @@ Module Compilers.
fail 1 "Could not find Proper instance" G ] ]
end.

Ltac handle_reified_rewrite_rules_interp exprInfo exprExtraInfo base_interp_head ident_interp_head ident_interp_Proper :=
Ltac handle_reified_rewrite_rules_interp_step exprInfo exprExtraInfo base_interp_head ident_interp_head ident_interp_Proper :=
let not_arrow t := lazymatch t with _ -> _ => fail | _ => idtac end in
repeat first [ assumption
| match goal with
| [ |- UnderLets.interp_related _ _ (Reify.expr_value_to_rewrite_rule_replacement _ ?sda _) _ ]
=> refine (@Reify.expr_value_to_rewrite_rule_replacement_interp_related exprInfo exprExtraInfo sda _ _ _ _);
cbv [Classes.base Classes.ident Classes.ident_interp Classes.base_interp Classes.ident_interp]
first [ assumption
| match goal with
| [ |- UnderLets.interp_related _ _ (Reify.expr_value_to_rewrite_rule_replacement _ ?sda _) _ ]
=> refine (@Reify.expr_value_to_rewrite_rule_replacement_interp_related exprInfo exprExtraInfo sda _ _ _ _);
cbv [Classes.base Classes.ident Classes.ident_interp Classes.base_interp Classes.ident_interp]

| [ |- UnderLets.interp_related_gen ?ii ?R (UnderLets.Base (#_(*ident.ident_list_rect*) @ _ @ _ @ _)%expr) (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_list_rect*) @ _ @ _ @ _)%expr (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_eager_list_rect*) @ _ @ _ @ _)%expr (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_list_case*) @ _ @ _ @ _)%expr (@list_case ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_case A (fun _ => P) N C ls) with (@Thunked.list_case A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_nat_rect*) @ _ @ _ @ _)%expr (@nat_rect (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@nat_rect (fun _ => P) N C ls) with (@Thunked.nat_rect P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_eager_nat_rect*) @ _ @ _ @ _)%expr (@nat_rect (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@nat_rect (fun _ => P) N C ls) with (@Thunked.nat_rect P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_bool_rect*) @ _ @ _ @ _)%expr (@bool_rect (fun _ => ?P) ?T ?F ?b) ]
=> not_arrow P; progress change (@bool_rect (fun _ => P) T F b) with (@Thunked.bool_rect P (fun _ => T) (fun _ => F) b)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_option_rect*) @ _ @ _ @ _)%expr (@option_rect ?A (fun _ => ?P) ?S ?N ?o) ]
=> not_arrow P; progress change (@option_rect A (fun _ => P) S N o) with (@Thunked.option_rect A P S (fun _ => N) o)
| [ |- UnderLets.interp_related_gen ?ii ?R (UnderLets.Base (#_(*ident.ident_list_rect*) @ _ @ _ @ _)%expr) (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_list_rect*) @ _ @ _ @ _)%expr (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_eager_list_rect*) @ _ @ _ @ _)%expr (@list_rect ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_rect A (fun _ => P) N C ls) with (@Thunked.list_rect A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_list_case*) @ _ @ _ @ _)%expr (@list_case ?A (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@list_case A (fun _ => P) N C ls) with (@Thunked.list_case A P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_nat_rect*) @ _ @ _ @ _)%expr (@nat_rect (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@nat_rect (fun _ => P) N C ls) with (@Thunked.nat_rect P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_eager_nat_rect*) @ _ @ _ @ _)%expr (@nat_rect (fun _ => ?P) ?N ?C ?ls) ]
=> not_arrow P; progress change (@nat_rect (fun _ => P) N C ls) with (@Thunked.nat_rect P (fun _ => N) C ls)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_bool_rect*) @ _ @ _ @ _)%expr (@bool_rect (fun _ => ?P) ?T ?F ?b) ]
=> not_arrow P; progress change (@bool_rect (fun _ => P) T F b) with (@Thunked.bool_rect P (fun _ => T) (fun _ => F) b)
| [ |- expr.interp_related_gen ?ii ?R (#_(*ident.ident_option_rect*) @ _ @ _ @ _)%expr (@option_rect ?A (fun _ => ?P) ?S ?N ?o) ]
=> not_arrow P; progress change (@option_rect A (fun _ => P) S N o) with (@Thunked.option_rect A P S (fun _ => N) o)

| [ |- match ?x with pair _ _ => _ end = prod_rect _ _ _ ]
=> cbv [prod_rect]; eta_expand
| [ |- match ?x with pair _ _ => _ end = prod_rect _ _ _ ]
=> cbv [prod_rect]; eta_expand

| [ |- expr.interp_related_gen _ _ (expr.Var _) _ ]
=> cbn [expr.interp_related_gen]
| [ |- expr.interp_related_gen _ _ (expr.Ident ?idc) ?rhs ]
=> let rhs' := open_constr:(_) in
replace rhs with rhs';
[ cbn [expr.interp_related_gen]; now refine (ident_interp_Proper _ idc idc eq_refl)
| try reflexivity ]
| [ |- expr.interp_related_gen _ _ (expr.Abs ?f) _ ]
=> let fh := fresh in set (fh := f); cbn [expr.interp_related_gen]; subst fh; cbv beta; intros
| [ |- expr.interp_related_gen _ _ (expr.LetIn ?v ?f) (LetIn.Let_In ?V ?F) ]
=> rewrite (LetIn.unfold_Let_In V F);
let vh := fresh in
set (vh := v);
let fh := fresh in
set (fh := f);
cbn [expr.interp_related_gen]; subst fh vh; cbv beta;
exists F, V; repeat apply conj; intros
| [ |- expr.interp_related_gen _ _ (?f @ ?x)%expr (?F ?X) ]
=> let fh := fresh in
set (fh := f);
let xh := fresh in
set (xh := x);
cbn [expr.interp_related_gen]; subst fh xh;
exists F, X; repeat apply conj; [ | | try reflexivity ]
| [ |- expr.interp_related_gen _ _ (expr.Var _) _ ]
=> cbn [expr.interp_related_gen]
| [ |- expr.interp_related_gen _ _ (expr.Ident ?idc) ?rhs ]
=> let rhs' := open_constr:(_) in
replace rhs with rhs';
[ cbn [expr.interp_related_gen]; now refine (ident_interp_Proper _ idc idc eq_refl)
| try reflexivity ]
| [ |- expr.interp_related_gen _ _ (expr.Abs ?f) _ ]
=> let fh := fresh in set (fh := f); cbn [expr.interp_related_gen]; subst fh; cbv beta; intros
| [ |- expr.interp_related_gen _ _ (expr.LetIn ?v ?f) (LetIn.Let_In ?V ?F) ]
=> rewrite (LetIn.unfold_Let_In V F);
let vh := fresh in
set (vh := v);
let fh := fresh in
set (fh := f);
cbn [expr.interp_related_gen]; subst fh vh; cbv beta;
exists F, V; repeat apply conj; intros
| [ |- expr.interp_related_gen _ _ (?f @ ?x)%expr (?F ?X) ]
=> let fh := fresh in
set (fh := f);
let xh := fresh in
set (xh := x);
cbn [expr.interp_related_gen]; subst fh xh;
exists F, X; repeat apply conj; [ | | try reflexivity ]

| [ |- _ = _ ] => solve [ fin_tac ]
| [ |- type.eqv _ _ ] => cbn [ident_interp_head type.related]; cbv [respectful]; intros; subst
end
| progress repeat (do 2 eexists; repeat apply conj; [ | | reflexivity ])
| prove_eq_by_Proper ];
[ >
idtac "============================";
idtac "WARNING: UNSOLVED GOAL:";
print_context_and_goal ();
idtac "============================"
.. ].
| [ |- _ = _ ] => solve [ fin_tac ]
| [ |- type.eqv _ _ ] => cbn [ident_interp_head type.related]; cbv [respectful]; intros; subst
end
| progress repeat (do 2 eexists; repeat apply conj; [ | | reflexivity ])
| prove_eq_by_Proper ].

Ltac handle_reified_rewrite_rules_interp exprInfo exprExtraInfo base_interp_head ident_interp_head ident_interp_Proper :=
first [ solve [ repeat handle_reified_rewrite_rules_interp_step exprInfo exprExtraInfo base_interp_head ident_interp_head ident_interp_Proper;
[ >
idtac "============================";
idtac "WARNING: UNSOLVED END GOAL:";
print_context_and_goal ();
idtac "============================"
.. ] ]
| idtac "============================";
idtac "WARNING: UNSOLVED INITIAL GOAL:";
print_context_and_goal ();
idtac "============================" ].

Module Export Tactic.
Ltac prove_interp_good _ :=
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