Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 84 items • Updated
• 3
Datasets:
fact stringlengths 7 3.87k | type stringclasses 24 values | library stringclasses 13 values | imports listlengths 0 72 | filename stringclasses 416 values | symbolic_name stringlengths 1 67 | docstring stringclasses 596 values |
|---|---|---|---|---|---|---|
TslIdent := { tsl_ident : ident -> ident }. | Class | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | TslIdent | ** Auxiliary functions |
prime_tsl_ident : TslIdent
:= {| tsl_ident := fun id => id ^ "'" |}. | Instance | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | prime_tsl_ident | null |
try_remove_n_lambdas (n : nat) (t : term) {struct n} : term :=
match n, t with
| 0, _ => t
| S n, tLambda _ _ t => try_remove_n_lambdas n t
| S _, _ => t
end. | Fixpoint | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | try_remove_n_lambdas | null |
tsl_constructor_body (c : constructor_body) : constructor_body :=
{| cstr_name := tsl_ident c.(cstr_name);
cstr_args := cstr_args c;
cstr_indices := cstr_indices c;
cstr_type := cstr_type c;
cstr_arity := cstr_arity c |}. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | tsl_constructor_body | * Plugin |
remove_last_n {A} (l : list A) (n : nat) : list A :=
firstn (#|l| - n) l. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | remove_last_n | null |
new_cstr mdecl (idc : ident) (ctor : term) : constructor_body :=
let '(args, concl) := decompose_prod_assum [] ctor in
let (hd, indices) := decompose_app concl in
{| cstr_name := idc;
cstr_args := remove_last_n args #|mdecl.(ind_params)|;
cstr_indices := skipn mdecl.(ind_npars) indices;
cstr_type := ctor;
cstr_arity := context_assumptions args |}. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | new_cstr | null |
test := bool'. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | test | Here we add a silly constructor to bool. |
test' : nat -> bool' -> bool -> bool' := foo. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | test | null |
tm :=
| var : nat -> tm
| lam : tm -> tm
| app : tm -> tm -> tm. | Inductive | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | tm | Here is a useful usecase: add a case to a syntax. |
test2 := letin. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | test2 | null |
test3 := foo'. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | test3 | null |
test4 := foo''. | Definition | examples | [
"MetaRocq.Utils",
"All",
"utils",
"MetaRocq.Template"
] | examples/add_constructor.v | test4 | null |
constructor (goal : Ast.term): TemplateMonad typed_term :=
let '(hd, iargs) := decompose_app goal in
match hd with
| Ast.tInd ind u =>
qi <- tmQuoteInductive (inductive_mind ind) ;;
match nth_error qi.(Ast.Env.ind_bodies) (inductive_ind ind) with
| Some oib =>
let cstrs := Ast.Env.ind_ctors oib in
match cstrs with
| [] => tmFail "no constructor in this inductive type"
| hd :: _ =>
let args := cstr_args hd in
let params := firstn qi.(ind_npars) iargs in
let args := (params ++ map (fun _ => Ast.hole) args)%list in
let term := Ast.tApp (Ast.tConstruct ind 0 u) args in
term' <- tmEval all term ;;
tmUnquote term'
end
| None => tmFail "anomaly"
end
| _ => tmFail "goal is not an inductive type"
end. | Definition | examples | [
"Stdlib",
"List",
"Loader",
"MetaRocq.Template",
"All"
] | examples/constructor_tac.v | constructor | null |
constructor_tac :=
match goal with
|- ?T =>
let k tm := refine tm.(my_projT2) in
unshelve quote_term T ltac:(fun gl => run_template_program (constructor gl) k)
end. | Ltac | examples | [
"Stdlib",
"List",
"Loader",
"MetaRocq.Template",
"All"
] | examples/constructor_tac.v | constructor_tac | null |
d : Ast.term. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | d | Build a definition * |
id_nat : nat -> nat := fun x => x. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | id_nat | To quote existing definitions * |
add (a b : nat) : nat :=
match a with
| 0 => b
| S a => S (add a b)
end. | Fixpoint | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | add | Fixpoints * |
add' (a b : nat) : nat :=
match b with
| 0 => a
| S b => S (add' a b)
end. | Fixpoint | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | add | null |
even (a : nat) : bool :=
match a with
| 0 => true
| S a => odd a
end
with odd (a : nat) : bool :=
match a with
| 0 => false
| S a => even a
end. | Fixpoint | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | even | null |
Nat_module := (MPfile ["Datatypes"; "Init"; "Corelib"], "nat"). | Notation | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | Nat_module | null |
prod' A B : Type :=
pair' { fst' : A ; snd' : B }. | Record | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | prod | null |
one_i : one_inductive_entry :=
{|
mind_entry_typename := "demoBool";
mind_entry_arity := tSort Sort.type0;
mind_entry_consnames := ["demoTrue"; "demoFalse"];
mind_entry_lc := [tRel 1; tRel 1];
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | one_i | Reflecting Inductives |
one_i2 : one_inductive_entry :=
{|
mind_entry_typename := "demoBool2";
mind_entry_arity := tSort Sort.type0;
mind_entry_consnames := ["demoTrue2"; "demoFalse2"];
mind_entry_lc := [tRel 0; tRel 0];
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | one_i2 | null |
mut_i : mutual_inductive_entry :=
{|
mind_entry_record := None;
mind_entry_finite := Finite;
mind_entry_params := [];
mind_entry_inds := [one_i; one_i2];
mind_entry_universes := Monomorphic_entry (LevelSet.empty, ConstraintSet.empty);
mind_entry_template := false;
mind_entry_variance := None;
mind_entry_private := None;
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | mut_i | null |
anonb := {| binder_name := nAnon; binder_relevance := Relevant |}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | anonb | null |
bnamed n := {| binder_name := nNamed n; binder_relevance := Relevant |}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | bnamed | null |
mkImpl (A B : term) : term :=
tProd anonb A B. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | mkImpl | null |
one_list_i : one_inductive_entry :=
{|
mind_entry_typename := "demoList";
mind_entry_arity := tSort Sort.type0;
mind_entry_consnames := ["demoNil"; "demoCons"];
mind_entry_lc := [tApp (tRel 1) [tRel 0];
mkImpl (tRel 0) (mkImpl (tApp (tRel 2) [tRel 1]) (tApp (tRel 3) [tRel 2]))];
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | one_list_i | null |
mut_list_i : mutual_inductive_entry :=
{|
mind_entry_record := None;
mind_entry_finite := Finite;
mind_entry_params := [{| decl_name := bnamed "A"; decl_body := None;
decl_type := (tSort Sort.type0) |}];
mind_entry_inds := [one_list_i];
mind_entry_universes := Monomorphic_entry (LevelSet.empty, ConstraintSet.empty);
mind_entry_template := false;
mind_entry_variance := None;
mind_entry_private := None;
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | mut_list_i | null |
one_pt_i : one_inductive_entry :=
{|
mind_entry_typename := "Point";
mind_entry_arity := tSort Sort.type0;
mind_entry_consnames := ["mkPoint"];
mind_entry_lc := [
mkImpl (tRel 0) (mkImpl (tRel 1) (tApp (tRel 3) [tRel 2]))];
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | one_pt_i | Records |
mut_pt_i : mutual_inductive_entry :=
{|
mind_entry_record := Some (Some "pp");
mind_entry_finite := BiFinite;
mind_entry_params := [{| decl_name := bnamed "A"; decl_body := None;
decl_type := (tSort Sort.type0) |}];
mind_entry_inds := [one_pt_i];
mind_entry_universes := Monomorphic_entry ContextSet.empty;
mind_entry_template := false;
mind_entry_variance := None;
mind_entry_private := None;
|}. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | mut_pt_i | null |
demoList (A : Set) : Set :=
demoNil : demoList A | demoCons : A -> demoList A -> demoList A
*)
Notation inat :=
{| inductive_mind := Nat_module; inductive_ind := 0 |}. | Inductive | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | demoList | null |
inat :=
{| inductive_mind := Nat_module; inductive_ind := 0 |}. | Notation | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | inat | Putting the above commands in monadic program |
printInductive (q : qualid): TemplateMonad unit :=
kn <- tmLocate1 q ;;
match kn with
| IndRef ind => (tmQuoteInductive ind.(inductive_mind)) >>= tmPrint
| _ => tmFail ("[" ^ q ^ "] is not an inductive")
end. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | printInductive | null |
cnat : Set := O :cnat | S : cnat -> cnat. | CoInductive | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | cnat | null |
printConstant (q : qualid) b : TemplateMonad unit :=
kn <- tmLocate1 q ;;
match kn with
| ConstRef kn => (tmQuoteConstant kn b) >>= tmPrint
| _ => tmFail ("[" ^ q ^ "] is not a constant")
end. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | printConstant | null |
six : nat. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | six | null |
printConstant' (name : qualid): TemplateMonad unit :=
gr <- tmLocate1 name ;;
match gr with
| ConstRef kn => X <- tmUnquote (tConst kn []) ;;
X' <- tmEval all (my_projT2 X) ;;
tmPrint X'
| _ => tmFail ("[" ^ name ^ "] is not a constant")
end. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | printConstant | null |
NonRec (A:Set) (C: A -> Set): Set :=
| SS : forall (f:A), C f -> NonRec A C. | Inductive | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | NonRec | null |
T : Type :=
| toto : Type -> T. | Inductive | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | T | null |
streamn : Set :=
scons : nat -> streamn -> streamn. | CoInductive | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | streamn | Cofixpoints |
ones : streamn := scons 1 ones. | CoFixpoint | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | ones | null |
kername_of_qualid (q : qualid) : TemplateMonad kername :=
gr <- tmLocate1 q ;;
match gr with
| ConstRef kn => ret kn
| IndRef ind => ret ind.(inductive_mind)
| ConstructRef ind _ => ret ind.(inductive_mind)
| VarRef _ => tmFail ("tmLocate: " ^ q ^ " is a Var")
end. | Definition | examples | [
"Stdlib",
"MetaRocq.Utils",
"MetaRocq.Template",
"All",
"utils"
] | examples/demo.v | kername_of_qualid | Cofixpoints |
foo := (fun x : nat => fun x : nat => x). | Definition | examples | [
"PCUICCumulativity",
"MetaRocq.Template",
"PCUICSafeChecker",
"All",
"utils",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"Erasure",
"PCUICSafeRetyping",
"metarocq_tour_prelude",
"PCUICTypeChecker",
"PCUICAst",
"TemplateMonad",
"config",
"PCUICErrors",
"MetaRocq.SafeCheckerPlugin",
"PCUICReduction",
"PCUICSafeLemmata",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.ErasurePlugin",
"MetaRocq.Utils",
"PCUICWfEnv",
"MetaRocq.Examples",
"PCUICWfEnvImpl"
] | examples/metarocq_tour.v | foo | null |
test (p : Ast.Env.program) : string :=
erase_and_print_template_program default_erasure_config [] p. | Definition | examples | [
"PCUICCumulativity",
"MetaRocq.Template",
"PCUICSafeChecker",
"All",
"utils",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"Erasure",
"PCUICSafeRetyping",
"metarocq_tour_prelude",
"PCUICTypeChecker",
"PCUICAst",
"TemplateMonad",
"config",
"PCUICErrors",
"MetaRocq.SafeCheckerPlugin",
"PCUICReduction",
"PCUICSafeLemmata",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.ErasurePlugin",
"MetaRocq.Utils",
"PCUICWfEnv",
"MetaRocq.Examples",
"PCUICWfEnvImpl"
] | examples/metarocq_tour.v | test | Running erasure live in Rocq |
zerocst := Eval lazy in test zero. | Definition | examples | [
"PCUICCumulativity",
"MetaRocq.Template",
"PCUICSafeChecker",
"All",
"utils",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"Erasure",
"PCUICSafeRetyping",
"metarocq_tour_prelude",
"PCUICTypeChecker",
"PCUICAst",
"TemplateMonad",
"config",
"PCUICErrors",
"MetaRocq.SafeCheckerPlugin",
"PCUICReduction",
"PCUICSafeLemmata",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.ErasurePlugin",
"MetaRocq.Utils",
"PCUICWfEnv",
"MetaRocq.Examples",
"PCUICWfEnvImpl"
] | examples/metarocq_tour.v | zerocst | null |
singleton_elim :=
((fun (X : Set) (x : X) (e : x = x) =>
match e in eq _ x' return bool with
| eq_refl => true
end)). | Definition | examples | [
"PCUICCumulativity",
"MetaRocq.Template",
"PCUICSafeChecker",
"All",
"utils",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"Erasure",
"PCUICSafeRetyping",
"metarocq_tour_prelude",
"PCUICTypeChecker",
"PCUICAst",
"TemplateMonad",
"config",
"PCUICErrors",
"MetaRocq.SafeCheckerPlugin",
"PCUICReduction",
"PCUICSafeLemmata",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.ErasurePlugin",
"MetaRocq.Utils",
"PCUICWfEnv",
"MetaRocq.Examples",
"PCUICWfEnvImpl"
] | examples/metarocq_tour.v | singleton_elim | null |
Instance default_checker_flags. | Existing | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | Instance | null |
Instance default_normalizing. | Existing | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | Instance | null |
bAnon := {| binder_name := nAnon; binder_relevance := Relevant |}. | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | bAnon | null |
bNamed s := {| binder_name := nNamed s; binder_relevance := Relevant |}. | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | bNamed | null |
tImpl X Y := tProd bAnon X (lift0 1 Y). | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | tImpl | null |
univ := Level.level "s". | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | univ | null |
gctx : global_env_ext :=
({| universes := (LS.union (LevelSet.singleton Level.lzero) (LevelSet.singleton univ), ConstraintSet.empty);
declarations := []; retroknowledge := Retroknowledge.empty |}, Monomorphic_ctx). | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | gctx | null |
kername_of_string (s : string) : kername :=
(MPfile [], s). | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | kername_of_string | We use the environment checker to produce the proof that gctx, which is a singleton with only
universe "s" declared is well-formed. |
Instance normalization. | Existing | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | Instance | null |
assume_normalization : Normalization. | Instance | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | assume_normalization | We use the environment checker to produce the proof that gctx, which is a singleton with only
universe "s" declared is well-formed. |
make_wf_env_ext (Σ : global_env_ext) : EnvCheck wf_env_ext wf_env_ext :=
'(exist Σ' pf) <- check_wf_ext optimized_abstract_env_impl Σ ;;
ret Σ'. | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | make_wf_env_ext | null |
gctx_wf_env : wf_env_ext. | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | gctx_wf_env | null |
inh (Σ : wf_env_ext) Γ T := (∑ t, forall Σ0 : global_env_ext, abstract_env_ext_rel Σ Σ0 -> ∥ typing Σ0 Γ t T ∥). | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | inh | There is always a proof of `forall x : Sort s, x -> x` |
check_inh (Σ : wf_env_ext) Γ
(wfΓ : forall Σ0 : global_env_ext, abstract_env_ext_rel Σ Σ0 -> ∥ wf_local Σ0 Γ ∥) t {T} : typing_result (inh Σ Γ T) :=
prf <- check_type_wf_env_fast optimized_abstract_env_impl Σ Γ wfΓ t (T := T) ;;
ret (t; prf). | Definition | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | check_inh | null |
fill_inh t :=
lazymatch goal with
[ wfΓ : forall _ _ , ∥ wf_local _ ?Γ ∥ |- inh ?Σ ?Γ ?T ] =>
let t := uconstr:(check_inh Σ Γ wfΓ t (T:=T)) in
let proof := eval cbn in t in
match proof with
| Checked ?d => exact_no_check d
| TypeError ?e =>
let str := eval cbn in (string_of_type_error Σ e) in
fail "Failed to inhabit " T " : " str
| _ => fail "Anomaly: unexpected return value: " proof
end
| [ |- inh _ ?Γ _ ] => fail "Missing local wellformedness assumption for" Γ
end. | Ltac | examples | [
"PCUICLiftSubst",
"Equations",
"MetaRocq.Template",
"PCUICSafeChecker",
"utils",
"PCUICSN",
"PCUICTyping",
"MetaRocq.SafeChecker",
"Loader",
"PCUICTypeChecker",
"Universes",
"PCUICAst",
"PCUICAstUtils",
"config",
"PCUICErrors",
"MetaRocq.PCUIC",
"MetaRocq.Common",
"MetaRocq.Utils",
"PCUICWfEnv",
"PCUICWfEnvImpl"
] | examples/metarocq_tour_prelude.v | fill_inh | null |
banon := {| binder_name := nAnon; binder_relevance := Relevant |}. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | banon | null |
bnamed n := {| binder_name := nNamed n; binder_relevance := Relevant |}. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | bnamed | null |
Instance config.default_checker_flags. | Existing | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | Instance | null |
var := nat. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | var | null |
eq_var (x y:var) : {x=y}+{x<>y}. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | eq_var | null |
form :=
| Var (x:var) | Fa | Tr | Imp (f1 f2:form) | And (f1 f2:form) | Or (f1 f2:form). | Inductive | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | form | null |
eq_form (f1 f2:form) : {f1=f2}+{f1<>f2}. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | eq_form | null |
not f := Imp f Fa. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | not | null |
seq := mkS { hyps : list form; concl : form }. | Record | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | seq | null |
size f :=
match f with
| Fa | Tr => 1
| Var _ => 1
| Imp f1 f2 => S (size f1 + size f2)
| And f1 f2 => S (size f1 + size f2)
| Or f1 f2 => S (size f1 + size f2)
end. | Fixpoint | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | size | null |
hyps_size h :=
List.fold_right (fun h n => n + size h) 0 h. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | hyps_size | null |
seq_size s :=
hyps_size (hyps s) + size (concl s). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | seq_size | null |
is_leaf s :=
let cl := concl s in
List.fold_right (fun h b => orb b (if eq_form Fa h then true else
if eq_form h cl then true else false))
false (hyps s). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | is_leaf | null |
Propositional_Logic prop :=
{ Pfalse : prop;
Ptrue : prop;
Pand : prop -> prop -> prop ;
Por : prop -> prop -> prop ;
Pimpl : prop -> prop -> prop}. | Class | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | Propositional_Logic | null |
semGen A `{Propositional_Logic A} f (l:var->A) :=
match f with
| Fa => Pfalse
| Tr => Ptrue
| Var x => l x
| Imp a b => Pimpl (semGen A a l) (semGen A b l)
| And a b => Pand (semGen A a l) (semGen A b l)
| Or a b => Por (semGen A a l) (semGen A b l)
end. | Fixpoint | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | semGen | null |
Propositional_Logic_Prop : Propositional_Logic Prop :=
{| Pfalse := False; Ptrue := True; Pand := and; Por := or; Pimpl := fun A B => A -> B |}. | Instance | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | Propositional_Logic_Prop | null |
sem := semGen Prop. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | sem | null |
valid s :=
forall l, (forall h, In h (hyps s) -> sem h l) -> sem (concl s) l. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | valid | null |
is_leaf_sound s :
is_leaf s = true -> valid s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | is_leaf_sound | null |
subgoal := list (list seq). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | subgoal | null |
valid_subgoal (sg:subgoal) :=
exists2 sl, In sl sg & forall s, In s sl -> valid s. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | valid_subgoal | null |
pick_hyp {A} (h:list A) :=
match h with
| nil => nil
| a::l =>
(a,l)::List.map (fun p => (fst p,a::snd p)) (pick_hyp l)
end. | Fixpoint | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | pick_hyp | null |
on_hyp h rh cl :=
match h with
| Imp a b => (mkS (b::rh) cl:: mkS rh a ::nil) :: nil
| And a b => (mkS(a::b::rh)cl::nil)::nil
| Or a b => (mkS(a::rh)cl::mkS(b::rh)cl::nil)::nil
| (Var _|Tr|Fa) => nil
end. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyp | null |
on_hyps s : subgoal :=
List.flat_map (fun p:form*list form => let (h,rh) := p in
on_hyp h rh (concl s))
(pick_hyp (hyps s)). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyps | null |
decomp_step s : subgoal :=
match concl s with
| Imp a b => (mkS (a::hyps s) b::nil)::nil
| And a b => (mkS (hyps s) a::mkS (hyps s) b::nil)::nil
| Or a b => (mkS(hyps s)a::nil)::(mkS(hyps s) b::nil)::on_hyps s
| _ => on_hyps s
end. | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | decomp_step | null |
result := Valid | CounterModel | Abort. | Inductive | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | result | null |
tauto_proc n s {struct n} :=
if is_leaf s then Valid else
match n with
| 0 => Abort
| S n =>
let fix tauto_and ls :=
match ls with
| nil => Valid
| s1::ls => match tauto_proc n s1 with
| Valid => tauto_and ls
| s => s
end
end in
let fix tauto_or lls :=
match lls with
| ls::lls =>
match tauto_and ls with
| Valid => Valid
| CounterModel => tauto_or lls
| Abort => Abort
end
| nil => CounterModel
end in
tauto_or (decomp_step s)
end. | Fixpoint | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | tauto_proc | null |
tauto_s f := tauto_proc (size f) (mkS nil f). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | tauto_s | null |
pick_hyp_def {A} (f:A) rh h :
In (f,rh) (pick_hyp h) <-> exists rh1 rh2, rh=rh1++rh2 /\ h = rh1++f::rh2. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | pick_hyp_def | null |
hyps_size_app h1 h2 :
hyps_size (h1++h2) = hyps_size h1 + hyps_size h2. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | hyps_size_app | null |
on_hyp_size h1 rh cl ls sg :
In ls (on_hyp h1 rh cl) -> In sg ls -> seq_size sg < size h1 + hyps_size rh + size cl. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyp_size | null |
on_hyps_size s ls sg :
In ls (on_hyps s) -> In sg ls -> seq_size sg < seq_size s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyps_size | null |
decomp_step_size s ls sg :
In ls (decomp_step s) -> In sg ls -> seq_size sg < seq_size s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | decomp_step_size | null |
on_hyp_sound f rh cl :
valid_subgoal (on_hyp f rh cl) -> valid (mkS (f::rh) cl). | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyp_sound | null |
on_hyps_sound s :
valid_subgoal (on_hyps s) ->
valid s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | on_hyps_sound | null |
step_sound s :
valid_subgoal (decomp_step s) -> valid s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | step_sound | null |
tauto_sound n s :
tauto_proc n s = Valid -> valid s. | Lemma | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | tauto_sound | null |
tImpl (A B : term) :=
tProd banon A (lift0 1 B). | Definition | examples | [
"MetaRocq.Utils",
"Equations",
"MetaRocq.Template",
"All",
"utils"
] | examples/tauto.v | tImpl | null |
End of preview. Expand
in Data Studio
Coq-MetaCoq
Structured dataset of formalizations from MetaCoq (Coq meta-theory formalized in Coq).
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Full declaration (name, signature, body) |
| type | string | Definition, Lemma, Instance, Class, Inductive, etc. |
| library | string | Sub-library (common, pcuic, erasure, safechecker, etc.) |
| imports | list | Require Import statements |
| filename | string | Source file path |
| symbolic_name | string | Declaration identifier |
| docstring | string | Documentation comment (5% coverage) |
Statistics
By Type
| Type | Count |
|---|---|
| Lemma | 8,418 |
| Definition | 5,208 |
| Instance | 1,644 |
| Ltac | 567 |
| Fixpoint | 414 |
| Notation | 384 |
| Inductive | 316 |
| Existing | 139 |
| Equations | 122 |
| Record | 121 |
| Class | 103 |
| Theorem | 99 |
| Other | 346 |
Docstring Coverage
- 1,000 entries (5%) have documentation
Example Entry
Use Cases
- Meta-theoretical research in formal verification
- Machine learning for proof automation
- Meta-programming studies
- Certified programming analysis
Citation
Changelog
- v2.0 (Jan 2025): Re-extraction with improved schema
- 10,490 -> 17,881 entries (+70%)
- Added docstring column (5% coverage)
- Changed imports from string to list
- Removed index_level column
- fact now includes full signature
- v1.0 (Dec 2024): Initial release
- Downloads last month
- 9
Source:
MetaCoq/metacoq
Entries:
17,881
Files processed:
595
License:
MIT
Size of downloaded dataset files:
1.4 MB
Size of the auto-converted Parquet files:
1.4 MB
Number of rows:
17,881