statement stringlengths 1 4.26k | proof stringlengths 0 13k | type stringclasses 21
values | symbolic_name stringlengths 1 154 | library stringclasses 28
values | filename stringclasses 144
values | imports listlengths 0 33 | deps listlengths 0 11 | docstring stringclasses 133
values | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
ringType : Type. | Parameter | ringType | apps.coercion.tests | apps/coercion/tests/test.v | [
"elpi.apps",
"coercion"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | ||
ringType_sort : ringType -> Type. | Parameter | ringType_sort | apps.coercion.tests | apps/coercion/tests/test.v | [
"elpi.apps",
"coercion"
] | [
"ringType"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | ||
natmul : forall (R : ringType) (n : nat), (ringType_sort R). | Parameter | natmul | apps.coercion.tests | apps/coercion/tests/test.v | [
"elpi.apps",
"coercion"
] | [
"ringType",
"ringType_sort"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | ||
ord : nat -> Type. | Axiom | ord | apps.coercion.tests | apps/coercion/tests/test.v | [
"elpi.apps",
"coercion"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | ||
bump : forall n, ord n -> ord (S n). | Axiom | bump | apps.coercion.tests | apps/coercion/tests/test.v | [
"elpi.apps",
"coercion"
] | [
"ord"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | ||
my_solver | := try ((repeat apply: le_n_S); apply: le_0_n). | Ltac | my_solver | apps.coercion.tests | apps/coercion/tests/test_open.v | [
"elpi.apps",
"coercion",
"Corelib",
"ssreflect"
] | [
"apply"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
add1 n : {x : nat | x > 0} | :=
match n with
| O => 1
| S x as y => y
end. | Definition | add1 | apps.coercion.tests | apps/coercion/tests/test_open.v | [
"elpi.apps",
"coercion",
"Corelib",
"ssreflect"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
S (T : Type) : Type | :=
{ sort :> T -> T }. | Structure | S | apps.cs.tests.cs.t.disabled_broken_8.19 | apps/cs/tests/cs.t.disabled_broken_8.19/test.v | [
"elpi.apps",
"cs",
"Coq",
"Bool"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
id1 | := id. | Definition | id1 | apps.cs.tests.cs.t.disabled_broken_8.19 | apps/cs/tests/cs.t.disabled_broken_8.19/test.v | [
"elpi.apps",
"cs",
"Coq",
"Bool"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
sort1 | := sort. | Definition | sort1 | apps.cs.tests.cs.t.disabled_broken_8.19 | apps/cs/tests/cs.t.disabled_broken_8.19/test.v | [
"elpi.apps",
"cs",
"Coq",
"Bool"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
a | := A. | Inductive | a | apps.derive.examples | apps/derive/examples/usage.v | [
"elpi.apps",
"derive.std",
"lens"
] | [] | Once can also run derive recursively, but this has the same bad effect,
all generated concepts will be out of place | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
b | := B : a -> b. | Inductive | b | apps.derive.examples | apps/derive/examples/usage.v | [
"elpi.apps",
"derive.std",
"lens"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
empty | := . | Inductive | empty | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
unit | := tt. | Inductive | unit | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
peano | := Zero | Succ (n : peano). | Inductive | peano | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
option A | := None | Some (_ : A). | Inductive | option | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
pair A B | := Comma (a : A) (b : B). | Inductive | pair | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
seq A | := Nil | Cons (x : A) (xs : seq A). | Inductive | seq | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
box_peano | := Box (n:peano). | Inductive | box_peano | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
rose (A : Type) | := Leaf (a : A) | Node (sib : seq (rose A)). | Inductive | rose | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"seq"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
rose_p (A B : Type) | := Leafp (p : pair A B) | Nodep (sib : pair (rose_p A B) (rose_p A B)). | Inductive | rose_p | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"pair"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
rose_o (A : Type) | := Leafo (a : A) | Nodeo (x: pair (rose A) (rose A)) (sib : option (seq (rose A))). | Inductive | rose_o | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"option",
"pair",
"rose",
"seq"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
nest A | := NilN | ConsN (x : A) (xs : nest (pair A A)). | Inductive | nest | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"pair"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
w A | := via (f : A -> w A). | Inductive | w | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
vect A : peano -> Type | := VNil : vect A Zero | VCons (x : A) n (xs : vect A n) : vect A (Succ n). | Inductive | vect | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
dyn | := box (T : Type) (t : T). | Inductive | dyn | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
zeta Sender (Receiver := Sender) | := Envelope (a : Sender) (ReplyTo := a) (c : Receiver). | Inductive | zeta | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
beta (A : (fun x : Type => x) Type) | := Redex (a : (fun x : Type => x) A). | Inductive | beta | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
iota | := Why n (a : match n in peano return Type with Zero => peano | Succ _ => unit end). | Inductive | iota | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano",
"unit"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
large | :=
| K1 (_ : unit)
| K2 (_ : unit) (_ : unit)
| K3 (_ : unit) (_ : unit) (_ : unit)
| K4 (_ : unit) (_ : unit) (_ : unit) (_ : unit)
| K5 (_ : unit) (_ : unit) (_ : unit) (_ : unit) (_ : unit)
| K6 (_ : unit) (_ : unit) (_ : unit) (_ : unit) (_ : unit) (_ : unit)
| K7 (_ : unit) (_ : unit) (_ : unit) (_ : unit) (... | Inductive | large | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"unit"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
prim_int | := PI (i : PrimInt63.int). | Inductive | prim_int | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
prim_float | := PF (f : PrimFloat.float). | Inductive | prim_float | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
prim_string | := PS (s : lib:elpi.pstring). | Inductive | prim_string | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fo_record | := { f1 : peano; f2 : unit; }. | Record | fo_record | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"f1",
"f2",
"peano",
"unit"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
pa_record A | := { f3 : peano; f4 : A; }. | Record | pa_record | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"f3",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
pr_record A | := { pf3 : peano; pf4 : A; }. | Record | pr_record | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
dep_record | := { f5 : peano; f6 : vect unit f5; }. | Record | dep_record | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano",
"unit",
"vect"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
enum | := E1 | E2 | E3. | Variant | enum | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
is_zero (n:peano) : bool | :=
match n with
| Zero => true
| _ => false
end. | Definition | is_zero | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
sigma_bool | := { depn : peano; depeq : is_zero depn = true }. | Record | sigma_bool | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"is_zero",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
sigma_bool2 | := { depn2 : peano; depeq2 : lib:elpi.is_true (is_zero depn2) }. | Record | sigma_bool2 | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"is_zero",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
is_leq (n m:peano) : bool | :=
match n, m with
| Zero, _ => true
| Succ n, Succ m => is_leq n m
| _, _ => false
end. | Fixpoint | is_leq | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
ord (p : peano) | := mkOrd (n : peano) (l : is_leq n p = true). | Inductive | ord | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"is_leq",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
ord2 (p : peano) | := mkOrd2 (o1 o2 : ord p). | Inductive | ord2 | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"ord",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
val | := V (p : peano) (o : ord p). | Inductive | val | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"ord",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
alias | := seq peano. | Definition | alias | apps.derive.tests | apps/derive/tests/test_derive_corelib.v | [
"elpi",
"Corelib",
"PrimInt63",
"PrimFloat",
"elpi.apps.derive",
"PrimStringEqb"
] | [
"peano",
"seq"
] | to make the coverage cound correct
Inductive eq := ...
Inductive bool := ...
we don't have a copy here because some DBs have special rules | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
eq_test T | := (T -> T -> bool). | Notation | eq_test | apps.derive.tests | apps/derive/tests/test_eq.v | [
"elpi.apps",
"test_derive_corelib",
"derive.eq",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
eq_test2 T1 T2 | := (T1 -> T2 -> bool). | Notation | eq_test2 | apps.derive.tests | apps/derive/tests/test_eqb.v | [
"elpi.apps",
"derive.eqb",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_eqType_ast",
"test_tag",
"test_fields",
"test_derive_corelib.Coverage",
"test_eqType_ast.Coverage",
"test_tag.Coverage",
"test_fields.Coverage",
"Coverage",
"Corelib",
"PosDef"
] | [
"T1",
"T2"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
correct X isX F | := (forall x, isX x -> eq_axiom_at X F x). | Notation | correct | apps.derive.tests | apps/derive/tests/test_eqcorrect.v | [
"elpi.apps",
"derive.eqcorrect",
"test_derive_corelib",
"derive.tests.test_eq",
"test_param1",
"test_param1_functor",
"test_induction",
"test_eqK",
"test_derive_corelib.Coverage",
"tests.test_eq.Coverage",
"test_param1.Coverage",
"test_param1_functor.Coverage",
"test_induction.Coverage",
"... | [
"eq_axiom_at"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
ok T F | := (forall x, eq_axiom_at T F x). | Notation | ok | apps.derive.tests | apps/derive/tests/test_eqOK.v | [
"elpi.apps",
"derive.param1",
"derive.eqOK",
"test_derive_corelib",
"test_eqcorrect",
"test_param1",
"test_param1_trivial",
"test_derive_corelib.Coverage",
"tests.test_eq.Coverage",
"test_eqcorrect.Coverage",
"test_param1.Coverage",
"test_param1_trivial.Coverage",
"Coverage",
"eqK",
"tes... | [
"eq_axiom_at"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
dlist A | := dnil | dcons (a : pair A peano) (l : dlist). | Inductive | dlist | apps.derive.tests | apps/derive/tests/test_eqOK.v | [
"elpi.apps",
"derive.param1",
"derive.eqOK",
"test_derive_corelib",
"test_eqcorrect",
"test_param1",
"test_param1_trivial",
"test_derive_corelib.Coverage",
"tests.test_eq.Coverage",
"test_eqcorrect.Coverage",
"test_param1.Coverage",
"test_param1_trivial.Coverage",
"Coverage",
"eqK",
"tes... | [
"pair",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
F1 | := | K1 : (peano -> peano) -> F1. | Inductive | F1 | apps.derive.tests | apps/derive/tests/test_eqType_ast.v | [
"elpi.apps",
"derive.eqType_ast",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
F2 | := | K2 : F1 -> F2. | Inductive | F2 | apps.derive.tests | apps/derive/tests/test_eqType_ast.v | [
"elpi.apps",
"derive.eqType_ast",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"F1"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
S1 (x : F1) | := | D1. | Inductive | S1 | apps.derive.tests | apps/derive/tests/test_eqType_ast.v | [
"elpi.apps",
"derive.eqType_ast",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"F1"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
S2 (x : F1) | := | D2 : S1 x -> S2. | Inductive | S2 | apps.derive.tests | apps/derive/tests/test_eqType_ast.v | [
"elpi.apps",
"derive.eqType_ast",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"F1",
"S1"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
S3 (f : peano -> peano) | := | D3 x : f x = x -> S3. | Inductive | S3 | apps.derive.tests | apps/derive/tests/test_eqType_ast.v | [
"elpi.apps",
"derive.eqType_ast",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"D3",
"peano"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
test A : bool -> Type | :=
K1 : test true
| K2 : forall x, A -> test (negb x) -> test (negb (negb x)). | Inductive | test | apps.derive.tests | apps/derive/tests/test_invert.v | [
"elpi.apps",
"derive.invert"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
listR A PA : list A -> Type | :=
| nilR : listR (@nil A)
| consR : forall a : A, PA a -> forall xs : list A, listR xs -> listR (cons a xs). | Inductive | listR | apps.derive.tests | apps/derive/tests/test_invert.v | [
"elpi.apps",
"derive.invert"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
I | := TT. | Inductive | I | apps.derive.tests | apps/derive/tests/test_isK.v | [
"elpi.apps",
"test_derive_corelib",
"derive.isK",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
Wrap | := K : I -> Wrap. | Inductive | Wrap | apps.derive.tests | apps/derive/tests/test_isK.v | [
"elpi.apps",
"test_derive_corelib",
"derive.isK",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
Prod (A B : Type) | := PR : A -> B -> Prod A B. | Inductive | Prod | apps.derive.tests | apps/derive/tests/test_isK.v | [
"elpi.apps",
"test_derive_corelib",
"derive.isK",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
Sum (A B : Type) | := InL : A -> Sum A B | InR : B -> Sum A B. | Inductive | Sum | apps.derive.tests | apps/derive/tests/test_isK.v | [
"elpi.apps",
"test_derive_corelib",
"derive.isK",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
List (A : Type) | := Nil | Cons : A -> List A -> List A. | Inductive | List | apps.derive.tests | apps/derive/tests/test_isK.v | [
"elpi.apps",
"test_derive_corelib",
"derive.isK",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
R | := MkR {
proj : nat;
}. | Record | R | apps.derive.tests | apps/derive/tests/test_lens.v | [
"elpi.apps",
"test_derive_corelib",
"derive.lens",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
failing r :
r.(proj) = 0 ->
view R__proj r = r.(proj). | Proof.
simpl.
intros Hpr.
rewrite Hpr.
reflexivity.
Abort. | Lemma | failing | apps.derive.tests | apps/derive/tests/test_lens.v | [
"elpi.apps",
"test_derive_corelib",
"derive.lens",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
working r :
match r with MkR r_proj => r_proj end = 0 ->
view R__proj r = match r with MkR r_proj => r_proj end. | Proof.
simpl.
intros Hpr.
rewrite Hpr.
Fail reflexivity.
unfold proj.
rewrite Hpr.
reflexivity.
Qed. | Lemma | working | apps.derive.tests | apps/derive/tests/test_lens.v | [
"elpi.apps",
"test_derive_corelib",
"derive.lens",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
map T | := (T -> T). | Notation | map | apps.derive.tests | apps/derive/tests/test_map.v | [
"elpi.apps",
"derive.map",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
map1 T | := (forall X Y, (X -> Y) -> T X%type -> T Y%type). | Notation | map1 | apps.derive.tests | apps/derive/tests/test_map.v | [
"elpi.apps",
"derive.map",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"type"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
pred X | := (X -> Type). | Notation | pred | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fin : nat -> Type | :=
FO : fin 0 | FS : forall n : nat, fin n -> fin (S n). | Inductive | fin | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fin_length n (v : fin n) | :=
match v with FO => 0 | FS _ w => S (fin_length _ w) end. | Fixpoint | fin_length | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"fin"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
vec (A : Type) : nat -> Type | :=
vnil : vec 0 | vcons : A -> forall n : nat, vec n -> vec (S n). | Inductive | vec | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
vec_length (A : Type) n (v : vec A n) | :=
match v with vnil _ => 0 | vcons _ _ _ w => S (vec_length _ _ w) end. | Fixpoint | vec_length | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"vec"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
plus' m n | := match n with 0 => m | S n => S (plus' m n) end. | Fixpoint | plus' | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
test m n p q r | := m + n + p + q + r. | Definition | test | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
vec_length_type | := forall (A : Type) (n : nat), vec A n -> nat. | Definition | vec_length_type | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"vec"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
vec_length_rec (vec_length : vec_length_type)
(A : Type) n (v : vec A n) | :=
match v with vnil _ => 0 | vcons _ _ _ w => S (vec_length _ _ w) end. | Definition | vec_length_rec | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"vec",
"vec_length",
"vec_length_type"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
nat2nat | := nat -> nat. | Definition | nat2nat | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
nat2nat2nat | := nat -> nat -> nat. | Definition | nat2nat2nat | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
predn n | := match n with 0 => 0 | S n => S (predn n) end. | Fixpoint | predn | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
quasidn n m | := S (match n with 0 => m | S n => S (quasidn n m) end). | Fixpoint | quasidn | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
weirdn n | := match n with S (S n) => S (weirdn n) | _ => 0 end. | Fixpoint | weirdn | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
bla : nat -> Type | := Bla : nat -> bla 0 | Blu n : bla n -> bla 1. | Inductive | bla | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
silly (n : nat) | := n. | Fixpoint | silly | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
foo (a : unit) : unit | :=
let b := a in
a. | Definition | foo | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"unit"
] | issue #262 | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
upair : Set | := unit * unit. | Definition | upair | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"unit"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
uplist | := list upair. | Definition | uplist | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"upair"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
bar (pl : uplist) (id : unit) : option unit | := None unit. | Fixpoint | bar | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [
"option",
"unit",
"uplist"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
nat_eq (n m : nat) {struct n} : bool | :=
match n, m with
| O, O => true
| S a, S b => nat_eq a b
| _, _ => false
end. | Fixpoint | nat_eq | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
Acc {A : Type} (R : A -> A -> Prop) | (x : A) : Prop | :=
Acc_intro : (forall y : A, R y x -> Acc y) -> Acc x. | Inductive | Acc | apps.derive.tests | apps/derive/tests/test_param1.v | [
"elpi.apps",
"derive.param1",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_derive_corelib.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
func isT | := (forall x, isT x -> isT x). | Notation | func | apps.derive.tests | apps/derive/tests/test_param1_functor.v | [
"elpi.apps",
"derive.param1",
"derive.param1_functor",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_param1",
"test_derive_corelib.Coverage",
"test_param1.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
func1 isT | := (forall A P Q, (forall y : A, P y -> Q y) -> forall x, isT A P x -> isT A Q x). | Notation | func1 | apps.derive.tests | apps/derive/tests/test_param1_functor.v | [
"elpi.apps",
"derive.param1",
"derive.param1_functor",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_param1",
"test_derive_corelib.Coverage",
"test_param1.Coverage",
"Coverage"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
func2 isT | := (forall A P Q, (forall y : A, P y -> Q y) -> forall A1 P1 Q1, (forall y : A1, P1 y -> Q1 y) -> forall x, isT A P A1 P1 x -> isT A Q A1 Q1 x). | Notation | func2 | apps.derive.tests | apps/derive/tests/test_param1_functor.v | [
"elpi.apps",
"derive.param1",
"derive.param1_functor",
"elpi.apps.derive.tests",
"test_derive_corelib",
"test_param1",
"test_derive_corelib.Coverage",
"test_param1.Coverage",
"Coverage"
] | [
"A1",
"P1"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
nth T (x0 : T) | :=
fix rec (n : nat) (l : list T) {struct n} : T :=
match l, n with
| nil, _ => x0
| cons x _, 0 => x
| cons _ xs, S m => rec m xs
end. | Definition | nth | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [] | The Parametricty plugin of K & L asks for an interactive proof here
(the proof to be produced is the match over n in the nil branch) | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
size_of (A : Type) | := A -> nat. | Definition | size_of | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
size_seq (A : Type) : size_of (list A) | := fun _ => 0. | Definition | size_seq | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [
"size_of"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fa | := 0. | Definition | fa | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [] | Fixed by https://github.com/LPCIC/coq-elpi/pull/754 | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
fb | := fa. | Definition | fb | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [
"fa"
] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fa_R | := O_R. | Definition | fa_R | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 | |
fi T | := fix g (s : list T) := tt. | Definition | fi | apps.derive.tests | apps/derive/tests/test_param2.v | [
"elpi.apps",
"derive.param2"
] | [] | https://github.com/LPCIC/coq-elpi | b79963f31d89dc84e7092e9340e96d4b8ed3ac61 |
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