Proof Assistant Projects
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Digesting proof assistant libraries for AI ingestion. • 84 items • Updated • 3
fact stringlengths 6 103k | type stringclasses 14
values | library stringclasses 13
values | imports listlengths 1 10 | filename stringclasses 157
values | symbolic_name stringlengths 1 54 | docstring stringclasses 185
values |
|---|---|---|---|---|---|---|
rev_tac_condFs_ok :=
match goal with
| |- is_unary _ => is_unary Fs_ok
| |- rules_preserve_vars _ => rules_preserve_vars
| |- WF _ => idtac
end. | Ltac | Conversion | [
"From CoLoR Require Import Srs ATrs SReverse ATerm_of_String String_of_ATerm",
"From CoLoR Require Import AVariables"
] | Conversion/AReverse.v | rev_tac_cond | null |
rev_tacFs_ok :=
(rewrite <- WF_red_rev_eq || rewrite <- WF_red_mod_rev_eq);
rev_tac_cond Fs_ok. | Ltac | Conversion | [
"From CoLoR Require Import Srs ATrs SReverse ATerm_of_String String_of_ATerm",
"From CoLoR Require Import AVariables"
] | Conversion/AReverse.v | rev_tac | null |
ar(_ : letter) := 1.
Import ATrs. | Definition | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | ar | corresponding algebraic signature |
ASig_of_SSig:= mkSignature ar (@VSignature.beq_symb_ok SSig).
Notation ASig := ASig_of_SSig.
Notation term := (term ASig). Notation terms := (vector term).
Notation context := (context ASig).
Import AUnary. | Definition | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | ASig_of_SSig | null |
is_unary_sig: is_unary ASig.
Proof. intro. refl. Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | is_unary_sig | null |
arity:= arity1 is_unary_sig. | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | arity | null |
is_unary:= try (exact is_unary_sig).
Notation Fun1 := (Fun1 is_unary_sig). Notation Cont1 := (Cont1 is_unary_sig).
Notation cont := (cont is_unary_sig).
Notation term_ind_forall := (term_ind_forall is_unary_sig). | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | is_unary | null |
term_of_string(s : string) : term :=
match s with
| List.nil => Var 0
| a :: w => @Fun ASig a (Vcons (term_of_string w) Vnil)
end. | Fixpoint | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | term_of_string | conversion string <-> term |
var_term_of_string: forall s, var (term_of_string s) = 0.
Proof.
induction s; auto.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | var_term_of_string | null |
reset_term_of_string:
forall s, reset (term_of_string s) = term_of_string s.
Proof.
induction s. refl. unfold reset. simpl. apply args_eq.
fold (reset (term_of_string s)). rewrite IHs. refl.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | reset_term_of_string | null |
string_of_term(t : term) : string :=
match t with
| Var _ => List.nil
| Fun f ts => f :: Vmap_first List.nil string_of_term ts
end. | Fixpoint | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_term | null |
string_of_term_epi: forall s, string_of_term (term_of_string s) = s.
Proof. induction s; simpl; intros. refl. rewrite IHs. refl. Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_term_epi | null |
term_of_string_epi: forall t, maxvar t = 0 ->
term_of_string (string_of_term t) = t.
Proof.
intro t; pattern t; apply term_ind_forall; clear t.
simpl in *. intros. subst. refl.
intros f t IH. unfold AUnary.Fun1. simpl.
rewrite (Vcast_cons (is_unary_sig f)), Vcast_refl. simpl.
rewrite max_0_r. intro h. rewrite (IH h)... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | term_of_string_epi | null |
string_of_term_sub: forall s l,
string_of_term (sub s l) = string_of_term l ++ string_of_term (s (var l)).
Proof.
intro s. apply term_ind_forall. refl. intros f t IH.
rewrite sub_fun1. simpl.
rewrite !(Vcast_cons (is_unary_sig f)). simpl.
rewrite IH. refl.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_term_sub | null |
string_of_cont(c : context) : string :=
match c with
| Hole => List.nil
| @Cont _ f _ _ _ _ d _ => f :: string_of_cont d
end. | Fixpoint | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_cont | conversion string <-> context |
string_of_cont_cont: forall t,
string_of_cont (cont t) = string_of_term t.
Proof.
apply term_ind_forall. refl. intros f t IH. simpl.
rewrite !(Vcast_cons (is_unary_sig f)). simpl. rewrite IH. refl.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_cont_cont | null |
string_of_term_fill: forall t c,
string_of_term (fill c t) = string_of_cont c ++ string_of_term t.
Proof.
induction c. refl. simpl. rewrite Vmap_first_cast. arity. simpl. rewrite IHc.
refl.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | string_of_term_fill | null |
cont_of_string(s : string) : context :=
match s with
| List.nil => Hole
| a :: w => Cont1 a (cont_of_string w)
end. | Fixpoint | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | cont_of_string | null |
sub_of_strings := single 0 (term_of_string s). | Definition | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | sub_of_string | conversion string <-> substitution |
term_of_string_fill: forall c s,
term_of_string (SContext.fill c s) = fill (cont_of_string (lft c))
(sub (sub_of_string (rgt c)) (term_of_string s)).
Proof.
intros [l r] s. elim l; unfold SContext.fill; simpl.
elim s. refl. intros. simpl. rewrite H. refl.
intros.
rewrite H, (Vcast_cons (cont_aux is_unary_sig a)), ... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | term_of_string_fill | null |
term_of_string_app: forall s1 s2,
term_of_string (s1 ++ s2) = sub (sub_of_string s2) (term_of_string s1).
Proof.
induction s1. refl. intro. simpl. apply args_eq. rewrite IHs1. refl.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | term_of_string_app | null |
rule_of_srule(x : srule) :=
mkRule (term_of_string (Srs.lhs x)) (term_of_string (Srs.rhs x)). | Definition | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | rule_of_srule | rules |
trs_of_srsR := List.map rule_of_srule R. | Definition | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | trs_of_srs | null |
rules_preserve_vars_trs_of_srs:
forall R, rules_preserve_vars (trs_of_srs R).
Proof.
unfold rules_preserve_vars. induction R; simpl; intuition.
unfold rule_of_srule in H0. destruct a. simpl in H0. inversion H0.
rewrite !vars_var; is_unary. rewrite !var_term_of_string.
unfold incl; simpl; intuition.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | rules_preserve_vars_trs_of_srs | null |
preserve_vars:= try (apply rules_preserve_vars_trs_of_srs). | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | preserve_vars | null |
red_of_sred: forall x y,
Srs.red R x y -> red (trs_of_srs R) (term_of_string x) (term_of_string y).
Proof.
intros. do 3 destruct H. decomp H. subst x. subst y.
rewrite !term_of_string_fill.
apply red_rule.
change (List.In (rule_of_srule (Srs.mkRule x0 x1)) (trs_of_srs R)).
unfold trs_of_srs. apply in_map. exact H0.
... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | red_of_sred | null |
rtc_red_of_sred: forall x y,
Srs.red R # x y -> red (trs_of_srs R) # (term_of_string x) (term_of_string y).
Proof.
intros. elim H; intros. apply rt_step. apply red_of_sred. exact H0.
apply rt_refl. eapply rt_trans. apply H1. exact H3.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | rtc_red_of_sred | null |
sred_of_red: forall t u,
red (trs_of_srs R) t u -> Srs.red R (string_of_term t) (string_of_term u).
Proof.
intros. redtac. subst. rewrite !string_of_term_fill, !string_of_term_sub,
(rules_preserve_vars_var is_unary_sig (rules_preserve_vars_trs_of_srs R) lr).
set (c' := mkContext (string_of_cont c) (string_of_term ... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | sred_of_red | null |
rtc_sred_of_red: forall t u, red (trs_of_srs R) # t u ->
Srs.red R # (string_of_term t) (string_of_term u).
Proof.
induction 1. apply rt_step. apply sred_of_red. hyp.
apply rt_refl. apply rt_trans with (string_of_term y); hyp.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | rtc_sred_of_red | null |
red_mod_of_sred_mod: forall x y, Srs.red_mod E R x y ->
red_mod (trs_of_srs E) (trs_of_srs R) (term_of_string x) (term_of_string y).
Proof.
intros. do 2 destruct H. exists (term_of_string x0). split.
apply rtc_red_of_sred. exact H. apply red_of_sred. exact H0.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | red_mod_of_sred_mod | null |
WF_red_mod_of_WF_sred_mod:
WF (red_mod (trs_of_srs E) (trs_of_srs R)) -> WF (Srs.red_mod E R).
Proof.
unfold WF. intro H.
cut (forall t s, t = term_of_string s -> SN (Srs.red_mod E R) s).
intros. apply H0 with (term_of_string x). refl.
intro t. gen (H t). induction 1. intros. apply SN_intro. intros.
apply H1 with (t... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | WF_red_mod_of_WF_sred_mod | null |
sred_mod_of_red_mod: forall t u,
red_mod (trs_of_srs E) (trs_of_srs R) t u ->
Srs.red_mod E R (string_of_term t) (string_of_term u).
Proof.
intros. do 2 destruct H. exists (string_of_term x); split.
apply rtc_sred_of_red. hyp. apply sred_of_red. hyp.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | sred_mod_of_red_mod | preservation of termination |
WF_sred_mod_of_WF_red_mod:
WF (Srs.red_mod E R) -> WF (red_mod (trs_of_srs E) (trs_of_srs R)).
Proof.
intro. rewrite WF_red_mod0; is_unary; preserve_vars.
cut (forall s, SN (Srs.red_mod E R) s -> forall t, maxvar t = 0 ->
t = term_of_string s -> SN (red_mod0 (trs_of_srs E) (trs_of_srs R)) t).
intros. intro t. dest... | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | WF_sred_mod_of_WF_red_mod | null |
WF_red_mod:
WF (Srs.red_mod E R) <-> WF (red_mod (trs_of_srs E) (trs_of_srs R)).
Proof.
split; intro. apply WF_sred_mod_of_WF_red_mod. hyp.
apply WF_red_mod_of_WF_sred_mod. hyp.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | WF_red_mod | null |
WF_red: WF (Srs.red R) <-> WF (red (trs_of_srs R)).
Proof. rewrite <- Srs.red_mod_empty, <- red_mod_empty. apply WF_red_mod. Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | WF_red | null |
as_trs:= rewrite WF_red_mod || rewrite WF_red. | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN VecUtil ListUtil NatUtil"
] | Conversion/ATerm_of_String.v | as_trs | tactics for Rainbow |
beq_statuss1 s2 :=
match s1, s2 with
| Lex, Lex
| Mul, Mul => true
| _, _ => false
end. | Definition | Conversion | [
"From CoLoR Require Import LogicUtil ATerm VecUtil",
"From CoLoR Require Import term_spec EqUtil",
"From CoLoR Require Import NatUtil",
"From Stdlib Require Import List Relations",
"From CoLoR Require Import term SN ASubstitution",
"From CoLoR Require Import rpo rpo_extension",
"From CoLoR Require Impor... | Conversion/Coccinelle.v | beq_status | decide compatibility of statuses wrt precedences |
beq_status_ok: forall s1 s2, beq_status s1 s2 = true <-> s1 = s2.
Proof.
beq_symb_ok.
Qed. | Lemma | Conversion | [
"From CoLoR Require Import LogicUtil ATerm VecUtil",
"From CoLoR Require Import term_spec EqUtil",
"From CoLoR Require Import NatUtil",
"From Stdlib Require Import List Relations",
"From CoLoR Require Import term SN ASubstitution",
"From CoLoR Require Import rpo rpo_extension",
"From CoLoR Require Impor... | Conversion/Coccinelle.v | beq_status_ok | null |
prec_eq_statuss p o := apply (bprec_eq_status_ok s p o); check_eq
|| fail 10 "statuses incompatible with precedences". | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil ATerm VecUtil",
"From CoLoR Require Import term_spec EqUtil",
"From CoLoR Require Import NatUtil",
"From Stdlib Require Import List Relations",
"From CoLoR Require Import term SN ASubstitution",
"From CoLoR Require Import rpo rpo_extension",
"From CoLoR Require Impor... | Conversion/Coccinelle.v | prec_eq_status | null |
as_srs_condFs_ok :=
match goal with
| |- is_unary _ => is_unary Fs_ok
| |- rules_preserve_vars _ => rules_preserve_vars
| |- WF _ => idtac
end. | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN ListUtil Srs ATrs AUnary VecUtil",
"From CoLoR Require Import AVariables"
] | Conversion/String_of_ATerm.v | as_srs_cond | null |
as_srsFs_ok :=
(rewrite WF_red_mod || rewrite WF_red); as_srs_cond Fs_ok. | Ltac | Conversion | [
"From CoLoR Require Import LogicUtil RelUtil SN ListUtil Srs ATrs AUnary VecUtil",
"From CoLoR Require Import AVariables"
] | Conversion/String_of_ATerm.v | as_srs | null |
co_scc:= check_eq || fail 10 "not a co_scc".
From CoLoR Require Import AVariables. | Ltac | DP | [
"From CoLoR Require Import AGraph Union ATrs RelUtil ListUtil LogicUtil SN",
"From CoLoR Require Import AVariables"
] | DP/ADecomp.v | co_scc | tactics |
graph_decompSig f d :=
apply WF_decomp_co_scc with (approx := f) (cs := d);
[idtac
| rules_preserve_vars
| incl_rule Sig || fail 10 "the decomposition does not contain all DPs"
| incl_rule Sig || fail 10 "the decomposition contains a rule that is not a DP"
| check_eq || fail 10 "the decomposition is... | Ltac | DP | [
"From CoLoR Require Import AGraph Union ATrs RelUtil ListUtil LogicUtil SN",
"From CoLoR Require Import AVariables"
] | DP/ADecomp.v | graph_decomp | null |
negb_subterm(t u : term) := negb (bsubterm u t). | Definition | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | negb_subterm | definition of dependancy pairs |
mkdp(S : rules) : rules :=
match S with
| nil => nil
| a :: S' => let (l, r) := a in
map (mkRule l) (filter (negb_subterm l) (calls R r)) ++ mkdp S'
end. | Fixpoint | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | mkdp | null |
dp:= mkdp R. | Definition | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | dp | null |
mkdp_app: forall l1 l2, mkdp (l1 ++ l2) = mkdp l1 ++ mkdp l2.
Proof.
induction l1; simpl; intros. refl. destruct a as [l r].
rewrite app_ass, IHl1. refl.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | mkdp_app | null |
mkdp_elim: forall l t S, In (mkRule l t) (mkdp S) -> exists r,
In (mkRule l r) S /\ In t (calls R r) /\ negb_subterm l t = true.
Proof.
induction S; simpl; intros. contr. destruct a.
rewrite in_app in H. destruct H. destruct (in_map_elim H). destruct H0.
injection H1. intros. subst x. subst lhs. clear H1.
rewrite fi... | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | mkdp_elim | null |
dp_intro: forall l r t, In (mkRule l r) R -> In t (calls R r) ->
negb_subterm l t = true -> In (mkRule l t) dp.
Proof.
intros. ded (in_elim H). do 2 destruct H2. ded (in_elim H0). do 2 destruct H3.
unfold dp. rewrite H2, mkdp_app. simpl. rewrite H3, filter_app, map_app. simpl.
rewrite H1. apply in_appr. apply in_app... | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | dp_intro | basic properties |
dp_elim: forall l t, In (mkRule l t) dp -> exists r,
In (mkRule l r) R /\ In t (calls R r) /\ negb_subterm l t = true.
Proof.
intros. apply mkdp_elim. hyp.
Qed.
Arguments dp_elim [l t] _. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | dp_elim | null |
in_calls_hd_red_dp: forall l r t s, In (mkRule l r) R ->
In t (calls R r) -> negb_subterm l t = true -> hd_red dp (sub s l) (sub s t).
Proof.
intros. exists l. exists t. exists s. intuition.
eapply dp_intro. apply H. hyp. hyp.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | in_calls_hd_red_dp | null |
lhs_dp: incl (map lhs dp) (map lhs R).
Proof.
unfold incl. intros. ded (in_map_elim H). do 2 destruct H0. subst a.
destruct x as [l r]. ded (dp_elim H0). do 2 destruct H1.
change (In (lhs (mkRule l x)) (map lhs R)). apply in_map. exact H1.
Qed.
(*FIXME: to be finished | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | lhs_dp | null |
is_notvar_lhs_dp_aux:
forall S, forallb (@is_notvar_lhs Sig) (mkdp S) = true.
Proof.
induction S; simpl; intros. refl. destruct a. simpl. rewrite forallb_app.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | is_notvar_lhs_dp_aux | null |
is_notvar_lhs_dp: forallb (@is_notvar_lhs Sig) dp = true.
Proof.
unfold dp.
Qed.*) | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | is_notvar_lhs_dp | null |
chain:= int_red R # @ hd_red dp. | Definition | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain | dependency chains |
in_calls_chain: forall l r t s, In (mkRule l r) R ->
In t (calls R r) -> negb_subterm l t = true -> chain (sub s l) (sub s t).
Proof.
intros. unfold chain, compose. exists (sub s l). split. apply rt_refl.
eapply in_calls_hd_red_dp. apply H. hyp. hyp.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | in_calls_chain | null |
gt_chain: forall f ts us v,
Vrel1 (red R) ts us -> chain (Fun f us) v -> chain (Fun f ts) v.
Proof.
unfold chain, compose. intros. do 2 destruct H0. exists x. split.
apply rt_trans with (y := Fun f us). apply rt_step. apply Vgt_prod_fun.
exact H. exact H0. exact H1.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | gt_chain | null |
chain_mins t := chain s t
/\ lforall (SN (red R)) (direct_subterms s)
/\ lforall (SN (red R)) (direct_subterms t). | Definition | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain_min | minimal dependency chain (subterms are terminating) |
chain_min_incl_chain: chain_min << chain.
Proof.
red. intros x y cmin. elim cmin. auto.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain_min_incl_chain | null |
gt_chain_min: forall f ts us v, Vrel1 (red R) ts us ->
Vforall (SN (red R)) ts -> chain_min (Fun f us) v -> chain_min (Fun f ts) v.
Proof.
intros f ts us v gt_ts_us sn_ts chain_min_fus_v.
unfold chain_min in chain_min_fus_v.
destruct chain_min_fus_v as [chain_fus_v sn].
destruct sn as [esn_us esn_ts].
unfold chain_m... | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | gt_chain_min | null |
dp_elim_vars: forall l t, In (mkRule l t) dp -> exists r,
In (mkRule l r) R /\ In t (calls R r) /\ negb_subterm l t = true
/\ incl (vars t) (vars l).
Proof.
intros. destruct (dp_elim H). decomp H0. exists x. intuition.
trans (vars x). unfold incl. intros.
eapply subterm_eq_vars. eapply in_calls_subterm. apply H3. ... | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | dp_elim_vars | dp preserves variables |
dp_preserve_vars: rules_preserve_vars dp.
Proof.
unfold rules_preserve_vars. intros. destruct (dp_elim_vars H). intuition.
Qed.
Notation capa := (capa R).
Notation cap := (cap R).
Notation alien_sub := (alien_sub R).
Notation SNR := (SN (red R)). | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | dp_preserve_vars | null |
chain_min_fun: forall f, defined f R = true
-> forall ts, SN chain_min (Fun f ts) -> Vforall SNR ts -> SNR (Fun f ts).
Proof.
cut (forall t, SN chain_min t -> forall f, defined f R = true
-> forall ts, t = Fun f ts -> Vforall SNR ts -> SNR t).
intros. apply H with (f := f) (ts := ts); (hyp || refl).
intros t H. el... | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain_min_fun | null |
chain_fun: forall f, defined f R = true
-> forall ts, SN chain (Fun f ts) -> Vforall SNR ts -> SNR (Fun f ts).
Proof.
intros f defined_f ts sn_chain_f_ts sn_ts.
apply chain_min_fun; auto.
apply (SN_incl chain). apply chain_min_incl_chain. hyp.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain_fun | null |
WF_chain: WF chain -> WF (red R).
Proof.
intro Hwf. unfold WF. apply term_ind_forall.
apply sn_var. apply hyp1.
intro f. case_eq (defined f R); intros.
apply chain_fun. hyp. apply Hwf. hyp.
apply sn_args_sn_fun; auto.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | WF_chain | null |
chain_hd_red_mod: chain << hd_red_mod R dp.
Proof.
unfold chain, hd_red_mod. comp. apply rtc_incl.
apply int_red_incl_red.
Qed. | Lemma | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain_hd_red_mod | null |
chain:= no_relative_rules; apply WF_chain;
[ check_eq || fail 10 "a LHS is a variable"
| rules_preserve_vars
| idtac]. | Ltac | DP | [
"From CoLoR Require Import LogicUtil ATrs ACalls ACap ASN RelUtil ListUtil",
"From CoLoR Require Import AVariables"
] | DP/ADP.v | chain | null |
hyp': rules_preserve_vars DP.
Proof.
apply dp_preserve_vars. exact hyp.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | hyp' | null |
dp_grapha1 a2 := In a1 DP /\ In a2 DP
/\ exists p, exists s,
int_red R # (sub s (rhs a1)) (sub s (shift p (lhs a2))). | Definition | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | dp_graph | dependancy pairs graph |
restricted_dp_graph: is_restricted dp_graph DP.
Proof.
unfold is_restricted, dp_graph, inclusion. intros. intuition.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | restricted_dp_graph | null |
chain_dpa t u := In a DP /\
exists s, int_red R # t (sub s (lhs a)) /\ u = sub s (rhs a). | Definition | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dp | chain relation for a given dependency pair |
chain_dp_chain: forall a, chain_dp a << Chain.
Proof.
unfold inclusion. intros. destruct H. do 2 destruct H0.
exists (sub x0 (lhs a)). intuition.
subst y. destruct a. simpl. apply hd_red_rule. exact H.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dp_chain | null |
chain_chain_dp: forall t u, Chain t u -> exists a, chain_dp a t u.
Proof.
intros. do 2 destruct H. redtac. subst x. subst u. exists (mkRule l r).
unfold chain_dp. simpl. intuition. exists s. intuition.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_chain_dp | null |
chain_dps(a : rule) (l : rules) : relation term :=
match l with
| nil => chain_dp a
| b :: m => chain_dp a @ chain_dps b m
end. | Fixpoint | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dps | iteration of chain steps given a list of dependency pairs |
chain_dps_app: forall l a b m,
chain_dps a (l ++ b :: m) << chain_dps a l @ chain_dps b m.
Proof. induction l; simpl; intros. refl. assoc. comp. apply IHl. Qed.
Arguments chain_dps_app [l a b m] _ _ _. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dps_app | null |
chain_dps_app': forall a l m b p, a :: l = m ++ b :: p ->
chain_dps a l << chain_dps a (tail m) % @ chain_dps b p.
Proof.
intros. destruct m; simpl in H; injection H; unfold inclusion; intros.
subst p. subst b. exists x. unfold clos_refl. intuition auto with *.
subst r. subst l. simpl. ded (chain_dps_app _ _ H2). do... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dps_app' | null |
chain_dps_iter_chain:
forall l a, chain_dps a l << iter Chain (length l).
Proof.
induction l; simpl; intros. apply chain_dp_chain.
comp. apply chain_dp_chain. apply IHl.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dps_iter_chain | null |
iter_chain_chain_dps: forall n t u, iter Chain n t u ->
exists a, exists l, length l = n /\ chain_dps a l t u.
Proof.
induction n; simpl; intros. ded (chain_chain_dp H). destruct H0.
exists x. exists nil. intuition.
do 2 destruct H. ded (chain_chain_dp H). destruct H1. exists x0.
ded (IHn _ _ H0). do 3 destruct H2. ... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | iter_chain_chain_dps | null |
chain_dp2_dp_graph: forall a1 a2 t u v,
chain_dp a1 t u -> chain_dp a2 u v -> dp_graph a1 a2.
Proof.
intros. destruct a1 as [l0 r0]. destruct a2 as [l1 r1].
destruct H. simpl in H1. do 2 destruct H1. subst u. rename x into s0.
destruct H0. simpl in H2. do 2 destruct H2. subst v. rename x into s1.
unfold dp_graph. in... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dp2_dp_graph | two consecutive chain steps provide a dp_graph step |
chain_dps_path_dp_graph: forall l a b t u,
chain_dps a (l ++ b :: nil) t u -> path dp_graph a b l.
Proof.
induction l; simpl; intros; do 2 destruct H.
eapply chain_dp2_dp_graph. apply H. apply H0.
ded (IHl _ _ _ _ H0). intuition.
destruct l; simpl in H0; do 2 destruct H0.
eapply chain_dp2_dp_graph. apply H. apply H0... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dps_path_dp_graph | null |
chain_dp_hd_red_mod: forall a, chain_dp a << hd_red_mod R (a::nil).
Proof.
unfold inclusion. intros. destruct H. do 2 destruct H0. subst y.
destruct a. simpl. simpl in H0. exists (sub x0 lhs). split.
apply incl_elim with (R := int_red R #). apply rtc_incl.
apply int_red_incl_red. exact H0. apply hd_red_rule. simpl. au... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | chain_dp_hd_red_mod | compatibility properties of chains |
compat_chain_dp: forall a, chain_dp a << succ_eq#.
Proof.
intros. incl_trans (red_mod R DP).
apply incl_trans with Chain; try incl_refl.
apply chain_dp_chain.
incl_trans (hd_red_mod R DP). apply chain_hd_red_mod.
apply hd_red_mod_incl_red_mod. incl_trans (succ_eq!).
apply compat_red_mod_tc; hyp. apply tc_incl_rtc.
Qed... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | compat_chain_dp | null |
compat_chain_dps: forall l a, chain_dps a l << succ_eq#.
Proof.
induction l; simpl; intros. apply compat_chain_dp.
incl_trans (succ_eq# @ succ_eq#).
comp. apply compat_chain_dp. apply IHl. apply comp_rtc_idem.
Qed. | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | compat_chain_dps | null |
compat_chain_dp_strict: forall a,
succ (lhs a) (rhs a) -> chain_dp a << succ.
Proof.
unfold inclusion. intros. destruct H0. do 2 destruct H1. subst y.
apply (absorbs_left_rtc Habsorb). exists (sub x0 (lhs a)). split.
apply incl_elim with (R := int_red R #). 2: exact H1.
apply rtc_incl.
incl_trans (red R). apply int_... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | compat_chain_dp_strict | null |
WF_cycles: WF (chain R).
Proof.
set (n := length DP). apply WF_iter with (S n). intro.
assert (Hwf' : WF (succ @ succ_eq#)). apply absorb_WF_modulo_r; hyp.
gen (Hwf' x). induction 1. apply SN_intro; intros. apply H0.
ded (iter_chain_chain_dps H1). do 3 destruct H2.
assert (length x1 > 0). lia. ded (last_intro H4). do ... | Lemma | DP | [
"From Stdlib Require Import Lia",
"From CoLoR Require Import LogicUtil ATrs ListUtil RelUtil RelSub Path ARelation",
"From CoLoR Require Export ADP"
] | DP/ADPGraph.v | WF_cycles | proof of the criterion based on cycles |
dpg_unif_N_correct:=
(apply dpg_unif_N_mark_correct || apply dpg_unif_N_correct);
(check_eq || fail 10 "a LHS is a variable"). | Ltac | DP | [
"From Stdlib Require Import Lia Compare_dec",
"From CoLoR Require Import ADecomp AUnif ARenCap ATrs ListUtil RelUtil AGraph"
] | DP/ADPUnif.v | dpg_unif_N_correct | tactics |
dp_trans:= chain; eapply WF_incl; [apply hd_red_Mod_of_chain | idtac]. | Ltac | DP | [
"From CoLoR Require Import LogicUtil ATrs RelUtil RelSub SN AShift ADPGraph",
"From CoLoR Require Export ADP",
"From Stdlib Require Import List Lia"
] | DP/AGraph.v | dp_trans | tactics |
hder1 r2 := In r1 D /\ In r2 D /\
match rhs r1 with
| Var _ => True
| Fun f _ =>
match lhs r2 with
| Var _ => True
| Fun g _ => f=g
end
end. | Definition | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde | null |
hde_restricted: is_restricted hde D.
Proof.
unfold is_restricted. intros. unfold hde in H; tauto.
Qed.
Notation eq_rule_dec := (@eq_rule_dec Sig).
Notation eq_symb_dec := (@eq_symb_dec Sig). | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_restricted | null |
hde_dec: forall r1 r2, {hde r1 r2} + {~hde r1 r2}.
Proof.
intros. unfold hde.
destruct (In_dec eq_rule_dec r1 D); try tauto.
destruct (In_dec eq_rule_dec r2 D); try tauto.
destruct (rhs r1). left; auto. destruct (lhs r2); auto.
destruct (eq_symb_dec f f0); try tauto.
Defined. | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_dec | null |
int_red_hd_rules_graph_incl_hde:
hd_rules_graph (int_red R #) D << hde D.
Proof.
unfold inclusion. intros. destruct x. destruct y. destruct H. destruct H0.
do 2 destruct H1. unfold hde. destruct lhs0; destruct rhs; simpl; auto.
intuition; auto.
ded (int_red_rtc_preserve_hd H1). destruct H2. simpl in H2. inversion H2... | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | int_red_hd_rules_graph_incl_hde | null |
dup_hd_rules_graph_incl_hde: hd_rules_graph (red R #) D << hde D.
Proof.
unfold inclusion. intros. apply (@int_red_hd_rules_graph_incl_hde _ R D x y).
destruct H. decomp H0. rewrite forallb_forall in hd_hyp. ded (hd_hyp _ H).
compute in H0. destruct x. destruct rhs. discr. destruct f.
unfold hd_rules_graph. intuition.... | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | dup_hd_rules_graph_incl_hde | null |
hd_eq(u v : term Sig) :=
match u with
| Var _ => true
| Fun f _ =>
match v with
| Var _ => true
| Fun g _ => beq_symb f g
end
end.
Notation mem := (mem (@beq_rule Sig)).
Notation mem_ok := (mem_ok (@beq_rule_ok Sig)). | Definition | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hd_eq | null |
hde_boolr1 r2 :=
mem r1 D && mem r2 D && hd_eq (rhs r1) (lhs r2). | Definition | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_bool | null |
hde_bool_correct_aux: forall x y, hde D x y <-> Graph hde_bool x y.
Proof.
intros x y. unfold hde, hde_bool, hd_eq, Graph; simpl.
pose proof (fun s x y => proj1 (@beq_symb_ok s x y)).
pose proof (fun s x y => proj2 (@beq_symb_ok s x y)).
rewrite <- !mem_ok. destruct (rhs x); bool; intuition auto with core;
repeat matc... | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_bool_correct_aux | null |
hde_bool_correct: hd_rules_graph (int_red R #) D << Graph (hde_bool D).
Proof.
incl_trans (hde D). apply int_red_hd_rules_graph_incl_hde.
intros x y. rewrite hde_bool_correct_aux. auto.
Qed.
Notation Sig' := (dup_sig Sig).
Notation R' := (dup_int_rules R).
Variable hyp : forallb (@is_notvar_lhs Sig') R' = true. | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_bool_correct | null |
hde_bool_mark_correct:
hd_rules_graph (red (dup_int_rules R) #) (dup_hd_rules D)
<< Graph (hde_bool (dup_hd_rules D)).
Proof.
incl_trans (hde (dup_hd_rules D)).
2:{ intros x y. rewrite hde_bool_correct_aux. auto. }
intros x y h. destruct h. decomp H0. unfold hde. intuition.
destruct (in_map_elim H). destruct H0. d... | Lemma | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_bool_mark_correct | null |
hde_bool_correct:=
(apply hde_bool_mark_correct || apply hde_bool_correct);
(check_eq || fail 10 "a LHS is a variable"). | Ltac | DP | [
"From CoLoR Require Import ADecomp ADuplicateSymb ATrs ListUtil RelSub RelUtil"
] | DP/AHDE.v | hde_bool_correct | tactics |
use_SCC_tagh M S R t :=
let x := fresh in
(set (x := SCC_tag_fast h M t); norm_in x (SCC_tag_fast h M t);
match eval compute in x with
| Some ?X1 =>
let Hi := fresh in
(assert (Hi : X1 < length R);
[ norm (length R); lia
| let L := fresh in
... | Ltac | DP | [
"From Stdlib Require Import Permutation Multiset Setoid PermutSetoid",
"From CoLoR Require Import SCCTopoOrdering AGraph ATrs RelUtil RelSub BoundNat"
] | DP/ASCCUnion.v | use_SCC_tag | tactics |
use_SCC_hypM l :=
let b := fresh "b" in
(set (b := Vnth (Vnth M l) l);
norm_in b (Vnth (Vnth M l) l);
match eval compute in b with
| false => apply WF_hd_red_Mod_SCC_fast_trivial with (Hi:=l); eauto
| true => eapply WF_incl;
[eapply hd_red_Mod_SCC'_hd_red_Mod_fast with (Hi:=... | Ltac | DP | [
"From Stdlib Require Import Permutation Multiset Setoid PermutSetoid",
"From CoLoR Require Import SCCTopoOrdering AGraph ATrs RelUtil RelSub BoundNat"
] | DP/ASCCUnion.v | use_SCC_hyp | null |
End of preview. Expand in Data Studio
Coq-CoLoR
A library on rewriting theory, lambda-calculus and termination.
Source
- Repository: https://github.com/fblanqui/color
- License: CeCILL-2.1
Statistics
| Property | Value |
|---|---|
| Total Entries | 3,304 |
| Files Processed | 264 |
Type Distribution
| Type | Count |
|---|---|
| Lemma | 2,015 |
| Definition | 540 |
| Parameter | 223 |
| Fixpoint | 172 |
| Ltac | 157 |
| Inductive | 101 |
| Theorem | 27 |
| Program | 25 |
| Record | 19 |
| Let | 11 |
| Instance | 7 |
| Axiom | 4 |
| Coercion | 2 |
| Remark | 1 |
Schema
| Column | Type | Description |
|---|---|---|
fact |
string | Declaration body (name, signature, proof) |
type |
string | Declaration type |
library |
string | Library component |
imports |
list[string] | Import statements |
filename |
string | Source file path |
symbolic_name |
string | Declaration identifier |
docstring |
string | Documentation comment (if present) |
Creator
Charles Norton (phanerozoic)
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