Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
fact stringlengths 7 1.62k | statement stringlengths 3 176 | proof stringlengths 0 1.55k | type stringclasses 5
values | symbolic_name stringlengths 1 27 | library stringclasses 7
values | filename stringclasses 53
values | imports listlengths 0 0 | deps listlengths 0 13 | docstring stringclasses 0
values | line_start int64 1 189 | line_end int64 1 193 | has_proof bool 2
classes | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7 "~" := ceq. | 7 "~" := ceq. | notation | ceq | example | example/approx.jonprl | [] | [] | null | 1 | 1 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
7 "≼" := approx. | 7 "≼" := approx. | notation | approx | example | example/approx.jonprl | [] | [] | null | 2 | 2 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
ceq-refl-thru-approx : [ {x:base} x ~ x ]
{
intro; aux {auto};
capprox; areflexivity
}. | ceq-refl-thru-approx : [ {x:base} x ~ x ] | {
intro; aux {auto};
capprox; areflexivity
}. | theorem | ceq-refl-thru-approx | example | example/approx.jonprl | [] | [] | null | 4 | 8 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
11 "⇓" := has-value. | 11 "⇓" := has-value. | notation | has-value | example | example/approx.jonprl | [] | [] | null | 10 | 10 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
10 "¬" := not. | 10 "¬" := not. | notation | not | example | example/approx.jonprl | [] | [] | null | 11 | 11 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
bottom-diverges : [ ¬ bot ⇓ ] {
unfold <not implies>;
intro; aux {auto; unfold <has-value>; auto};
bot-div #1
}. | bottom-diverges : [ ¬ bot ⇓ ] | {
unfold <not implies>;
intro; aux {auto; unfold <has-value>; auto};
bot-div #1
}. | theorem | bottom-diverges | example | example/approx.jonprl | [] | [
"has-value",
"implies",
"not"
] | null | 13 | 17 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
trivial-assertion : [unit] {
assert [unit -> unit];
auto
}. | trivial-assertion : [unit] | {
assert [unit -> unit];
auto
}. | theorem | trivial-assertion | example | example/assert.jonprl | [] | [
"assert"
] | null | 1 | 4 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
100 "∈" := member. | 100 "∈" := member. | notation | member | example | example/atoms.jonprl | [] | [] | null | 1 | 1 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
100 "~" := ceq. | 100 "~" := ceq. | notation | ceq | example | example/atoms.jonprl | [] | [] | null | 2 | 2 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
11 "⇓" := has-value. | 11 "⇓" := has-value. | notation | has-value | example | example/atoms.jonprl | [] | [] | null | 3 | 3 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
decode : (0). | decode : (0). | operator | decode | example | example/atoms.jonprl | [] | [] | null | 5 | 5 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[decode(A)] =def= [
match A {
"unit" => unit
| "void" => void
| _ => bot
}
]. | [decode(A)] | =def= [
match A {
"unit" => unit
| "void" => void
| _ => bot
}
]. | definition | decode | example | example/atoms.jonprl | [] | [] | null | 6 | 12 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
code : (). | code : (). | operator | code | example | example/atoms.jonprl | [] | [] | null | 14 | 14 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[code] =def= [{A : atom | decode(A) ⇓}]. | [code] | =def= [{A : atom | decode(A) ⇓}]. | definition | code | example | example/atoms.jonprl | [] | [
"decode"
] | null | 15 | 15 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
code-wf : [code ∈ U{i}] {
unfold <code has-value>; auto;
}. | code-wf : [code ∈ U{i}] | {
unfold <code has-value>; auto;
}. | theorem | code-wf | example | example/atoms.jonprl | [] | [
"code",
"has-value"
] | null | 17 | 19 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
decode-wf : [
{s:code} decode(s) ∈ U{i}
] {
intro @i; aux {lemma <code-wf>};
unfold <code decode unit>; auto;
elim #1;
assert [bot ⇓] <bot-has-value>;
aux { chyp-subst <- #4 [h. h ⇓]; auto };
bot-div <bot-has-value>
}. | decode-wf : [
{s:code} decode(s) ∈ U{i}
] | {
intro @i; aux {lemma <code-wf>};
unfold <code decode unit>; auto;
elim #1;
assert [bot ⇓] <bot-has-value>;
aux { chyp-subst <- #4 [h. h ⇓]; auto };
bot-div <bot-has-value>
}. | theorem | decode-wf | example | example/atoms.jonprl | [] | [
"assert",
"code",
"code-wf",
"decode"
] | null | 21 | 31 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
instantiate-hyps {
@{ [H : A -> B, H' : A |- _] => elim <H> [H']
| [H : A => B, H' : A |- _] => elim <H> [H']
}
}. | instantiate-hyps | {
@{ [H : A -> B, H' : A |- _] => elim <H> [H']
| [H : A => B, H' : A |- _] => elim <H> [H']
}
}. | tactic | instantiate-hyps | example | example/choice.jonprl | [] | [] | null | 1 | 5 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
destruct-hyps {
*{ @{ [H : A * B |- _] => elim <H>; thin <H>} }
}. | destruct-hyps | {
*{ @{ [H : A * B |- _] => elim <H>; thin <H>} }
}. | tactic | destruct-hyps | example | example/choice.jonprl | [] | [] | null | 7 | 9 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
axiom-of-choice : [{A:U{i}} {B:U{i}} {Q : A -> B -> U{i}} (φ : (c:A) -> (b:B) * Q c b) (f : A -> B) * (a : A) Q a (f a)]
{
auto; intro [lam(w. spread(φ w; x.y.x))]; auto;
instantiate-hyps; auto; reduce;
@{ [H : =(y; φ a; _) |- _] => hyp-subst <- <H> [h. _ _ spread(h; x.y.x)] };
auto; destruct-hyps; reduce; auto... | axiom-of-choice : [{A:U{i}} {B:U{i}} {Q : A -> B -> U{i}} (φ : (c:A) -> (b:B) * Q c b) (f : A -> B) * (a : A) Q a (f a)] | {
auto; intro [lam(w. spread(φ w; x.y.x))]; auto;
instantiate-hyps; auto; reduce;
@{ [H : =(y; φ a; _) |- _] => hyp-subst <- <H> [h. _ _ spread(h; x.y.x)] };
auto; destruct-hyps; reduce; auto
}. | theorem | axiom-of-choice | example | example/choice.jonprl | [] | [
"destruct-hyps",
"instantiate-hyps"
] | null | 11 | 17 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
7 "~" := ceq. | 7 "~" := ceq. | notation | ceq | example | example/computational-equality.jonprl | [] | [] | null | 1 | 1 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
test : [lam(x.x) ~ lam(x.x)] {
auto
}. | test : [lam(x.x) ~ lam(x.x)] | {
auto
}. | theorem | test | example | example/computational-equality.jonprl | [] | [] | null | 3 | 5 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
test2 : [spread(lam(x.x); x.y.x) ~ spread(lam(x.x); x.y.y)] {
auto
}. | test2 : [spread(lam(x.x); x.y.x) ~ spread(lam(x.x); x.y.y)] | {
auto
}. | theorem | test2 | example | example/computational-equality.jonprl | [] | [] | null | 7 | 9 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
test3 : [lam(x.x) ~ lam(x.spread(<x,x>; x._.x))] {
auto; csymmetry; step; auto
}. | test3 : [lam(x.x) ~ lam(x.spread(<x,x>; x._.x))] | {
auto; csymmetry; step; auto
}. | theorem | test3 | example | example/computational-equality.jonprl | [] | [] | null | 11 | 13 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
computational-eta : [{A:U{i}} {g : A -> A} g ~ lam(x. g x)] {
auto;
assert [=(g; lam(x.g x); A -> A)];
aux { ext; auto; reduce; auto };
hyp-subst -> #3 [h. h ~ _]; auto
}. | computational-eta : [{A:U{i}} {g : A -> A} g ~ lam(x. g x)] | {
auto;
assert [=(g; lam(x.g x); A -> A)];
aux { ext; auto; reduce; auto };
hyp-subst -> #3 [h. h ~ _]; auto
}. | theorem | computational-eta | example | example/computational-equality.jonprl | [] | [
"assert"
] | null | 15 | 20 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
computational-eta-tac {
@{ [f : A -> A |- ceq(f; lam(x. f x))] =>
cut-lemma <computational-eta>;
elim <computational-eta> [A]; auto;
@{ [H : {g : A -> A} g ~ lam(x. g x) |- _] =>
elim <H> [f]; auto
}
}
}. | computational-eta-tac | {
@{ [f : A -> A |- ceq(f; lam(x. f x))] =>
cut-lemma <computational-eta>;
elim <computational-eta> [A]; auto;
@{ [H : {g : A -> A} g ~ lam(x. g x) |- _] =>
elim <H> [f]; auto
}
}
}. | tactic | computational-eta-tac | example | example/computational-equality.jonprl | [] | [
"ceq",
"computational-eta"
] | null | 22 | 30 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
fix-is-fix-point : [{A:U{i}} {f : A -> A} fix(f) ~ f fix(f)] {
auto;
csubst [f ~ lam(x.f x)] [h. fix(h) ~ _];
aux {computational-eta-tac};
step;
csubst [lam(x.f x) ~ f] [h. h fix(h) ~ _];
aux {csymmetry; computational-eta-tac};
auto
}. | fix-is-fix-point : [{A:U{i}} {f : A -> A} fix(f) ~ f fix(f)] | {
auto;
csubst [f ~ lam(x.f x)] [h. fix(h) ~ _];
aux {computational-eta-tac};
step;
csubst [lam(x.f x) ~ f] [h. h fix(h) ~ _];
aux {csymmetry; computational-eta-tac};
auto
}. | theorem | fix-is-fix-point | example | example/computational-equality.jonprl | [] | [
"computational-eta-tac"
] | null | 32 | 41 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
transitive : [
{a:base} {b:base} {c:base}
=(a;b;base)
=> =(b;c;base)
=> =(a;b;base)
] {
auto;
elim #4;
elim #5;
chyp-subst → #6 [h. h ~ c];
chyp-subst ← #7 [h. b ~ h];
auto
}. | transitive : [
{a:base} {b:base} {c:base}
=(a;b;base)
=> =(b;c;base)
=> =(a;b;base)
] | {
auto;
elim #4;
elim #5;
chyp-subst → #6 [h. h ~ c];
chyp-subst ← #7 [h. b ~ h];
auto
}. | theorem | transitive | example | example/computational-equality.jonprl | [] | [] | null | 43 | 55 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
complex : (1; 1; 2; 0; 1). | complex : (1; 1; 2; 0; 1). | operator | complex | example | example/computational-equality.jonprl | [] | [] | null | 57 | 57 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
complex-ceq : [
complex(x.x; x.unit; x.y.y; <>; x.<>)
~ complex(x.spread(<x,x>; x._.x); x.unit; x.y.y; <>; x.<>)
] {
auto; reduce; auto
}. | complex-ceq : [
complex(x.x; x.unit; x.y.y; <>; x.<>)
~ complex(x.spread(<x,x>; x._.x); x.unit; x.y.y; <>; x.<>)
] | {
auto; reduce; auto
}. | theorem | complex-ceq | example | example/computational-equality.jonprl | [] | [
"complex"
] | null | 59 | 64 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
top : (). | top : (). | operator | top | example | example/conats.jonprl | [] | [] | null | 1 | 1 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[top] =def= [void => void]. | [top] | =def= [void => void]. | definition | top | example | example/conats.jonprl | [] | [] | null | 2 | 2 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
top-is-top :
[{x:base} {y:base} =(x; y; top)] {
unfold <top>; auto
}. | top-is-top :
[{x:base} {y:base} =(x; y; top)] | {
unfold <top>; auto
}. | theorem | top-is-top | example | example/conats.jonprl | [] | [
"top"
] | null | 4 | 7 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
corec : (1). | corec : (1). | operator | corec | example | example/conats.jonprl | [] | [] | null | 9 | 9 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[corec(x.F[x])] =def= [{n:nat} natrec(n; top; _.x. F[x])]. | [corec(x.F[x])] | =def= [{n:nat} natrec(n; top; _.x. F[x])]. | definition | corec | example | example/conats.jonprl | [] | [
"top"
] | null | 10 | 10 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
conatF : (0). | conatF : (0). | operator | conatF | example | example/conats.jonprl | [] | [] | null | 12 | 12 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[conatF(X)] =def= [unit + X]. | [conatF(X)] | =def= [unit + X]. | definition | conatF | example | example/conats.jonprl | [] | [] | null | 13 | 13 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
conat : (). | conat : (). | operator | conat | example | example/conats.jonprl | [] | [] | null | 16 | 16 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[conat] =def= [corec(R. conatF(R))]. | [conat] | =def= [corec(R. conatF(R))]. | definition | conat | example | example/conats.jonprl | [] | [
"conatF",
"corec"
] | null | 17 | 17 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
czero : (). | czero : (). | operator | czero | example | example/conats.jonprl | [] | [] | null | 19 | 19 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[czero] =def= [inl(<>)]. | [czero] | =def= [inl(<>)]. | definition | czero | example | example/conats.jonprl | [] | [] | null | 20 | 20 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
csucc : (0). | csucc : (0). | operator | csucc | example | example/conats.jonprl | [] | [] | null | 22 | 22 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[csucc(M)] =def= [inr(M)]. | [csucc(M)] | =def= [inr(M)]. | definition | csucc | example | example/conats.jonprl | [] | [] | null | 23 | 23 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
Y : (1). | Y : (1). | operator | Y | example | example/conats.jonprl | [] | [] | null | 25 | 25 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Y(z.f[z])] =def= [lam(x.f[x x]) lam(x.f [(x x)])]. | [Y(z.f[z])] | =def= [lam(x.f[x x]) lam(x.f [(x x)])]. | definition | Y | example | example/conats.jonprl | [] | [] | null | 26 | 26 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
omega : (). | omega : (). | operator | omega | example | example/conats.jonprl | [] | [] | null | 28 | 28 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[omega] =def= [Y(x.csucc(x))]. | [omega] | =def= [Y(x.csucc(x))]. | definition | omega | example | example/conats.jonprl | [] | [
"csucc"
] | null | 29 | 29 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
instantiate-hyp {
@{ [H : P => Q, H' : P |- _] => elim <H> [H'] }
}. | instantiate-hyp | {
@{ [H : P => Q, H' : P |- _] => elim <H> [H'] }
}. | tactic | instantiate-hyp | example | example/conats.jonprl | [] | [] | null | 31 | 33 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
refl-from-trans {
@{ [H : =(y; x; P) |- =(x;x; P)] => hyp-subst <- <H> [h.=(h;h;_)] };
}. | refl-from-trans | {
@{ [H : =(y; x; P) |- =(x;x; P)] => hyp-subst <- <H> [h.=(h;h;_)] };
}. | tactic | refl-from-trans | example | example/conats.jonprl | [] | [] | null | 35 | 37 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
conat-wf-overture {
*{ unfold <corec conat czero csucc conatF top omega unit Y> }; auto;
@{ [n:nat |- _] => elim <n>; thin <n> };
reduce 1; auto
}. | conat-wf-overture | {
*{ unfold <corec conat czero csucc conatF top omega unit Y> }; auto;
@{ [n:nat |- _] => elim <n>; thin <n> };
reduce 1; auto
}. | tactic | conat-wf-overture | example | example/conats.jonprl | [] | [
"conat",
"conatF",
"corec",
"csucc",
"czero",
"omega",
"top"
] | null | 39 | 43 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
zero-wf : [member(czero; conat)] {
conat-wf-overture
}. | zero-wf : [member(czero; conat)] | {
conat-wf-overture
}. | theorem | zero-wf | example | example/conats.jonprl | [] | [
"conat",
"conat-wf-overture",
"czero",
"member"
] | null | 45 | 47 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
succ-wf : [{x:conat} member(csucc(x); conat)] {
conat-wf-overture;
instantiate-hyp; auto;
refl-from-trans; auto
}. | succ-wf : [{x:conat} member(csucc(x); conat)] | {
conat-wf-overture;
instantiate-hyp; auto;
refl-from-trans; auto
}. | theorem | succ-wf | example | example/conats.jonprl | [] | [
"conat",
"conat-wf-overture",
"csucc",
"instantiate-hyp",
"member",
"refl-from-trans"
] | null | 49 | 53 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
omega-wf : [member(omega; conat)] {
conat-wf-overture;
csubst [ceq(lam(x.inr(x x)) lam(x.inr(x x));
inr(lam(x.inr(x x)) lam(x.inr(x x))))]
[h.=(h;h;_)];
[step, reduce 1]; auto
}. | omega-wf : [member(omega; conat)] | {
conat-wf-overture;
csubst [ceq(lam(x.inr(x x)) lam(x.inr(x x));
inr(lam(x.inr(x x)) lam(x.inr(x x))))]
[h.=(h;h;_)];
[step, reduce 1]; auto
}. | theorem | omega-wf | example | example/conats.jonprl | [] | [
"ceq",
"conat",
"conat-wf-overture",
"member",
"omega"
] | null | 55 | 61 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
20 "∈" := member. | 20 "∈" := member. | notation | member | example | example/container.jonprl | [] | [] | null | 1 | 1 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
20 "⇓" := has-value. | 20 "⇓" := has-value. | notation | has-value | example | example/container.jonprl | [] | [] | null | 2 | 2 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
has-value-wf : [{M:base} M ⇓ ∈ U{i}] {
unfold <has-value>; auto
}. | has-value-wf : [{M:base} M ⇓ ∈ U{i}] | {
unfold <has-value>; auto
}. | theorem | has-value-wf | example | example/container.jonprl | [] | [
"has-value"
] | null | 4 | 6 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-decode : (0). | nat-decode : (0). | operator | nat-decode | example | example/container.jonprl | [] | [] | null | 10 | 10 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[nat-decode(x)] =def= [
match x {
"ze" => void
| "su" => unit
| _ => bot
}
]. | [nat-decode(x)] | =def= [
match x {
"ze" => void
| "su" => unit
| _ => bot
}
]. | definition | nat-decode | example | example/container.jonprl | [] | [
"su",
"ze"
] | null | 11 | 17 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-code : (). | nat-code : (). | operator | nat-code | example | example/container.jonprl | [] | [] | null | 19 | 19 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[nat-code] =def= [{a : atom | nat-decode(a) ⇓}]. | [nat-code] | =def= [{a : atom | nat-decode(a) ⇓}]. | definition | nat-code | example | example/container.jonprl | [] | [
"nat-decode"
] | null | 20 | 20 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-sig : (). | nat-sig : (). | operator | nat-sig | example | example/container.jonprl | [] | [] | null | 22 | 22 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[nat-sig] =def= [x : nat-code ◃ nat-decode(x)]. | [nat-sig] | =def= [x : nat-code ◃ nat-decode(x)]. | definition | nat-sig | example | example/container.jonprl | [] | [
"nat-code",
"nat-decode"
] | null | 23 | 23 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-code-wf : [nat-code ∈ U{i}] {
unfold <nat-code has-value>; auto
}. | nat-code-wf : [nat-code ∈ U{i}] | {
unfold <nat-code has-value>; auto
}. | theorem | nat-code-wf | example | example/container.jonprl | [] | [
"has-value",
"nat-code"
] | null | 25 | 27 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-decode-wf : [{a:nat-code} nat-decode(a) ∈ U{i}] {
intro @i; auto;
unfold <nat-decode nat-code>; auto;
elim #1;
unfold <nat-decode>;
assert [bot ⇓];
aux { chyp-subst <- #4; auto };
bot-div #6
}. | nat-decode-wf : [{a:nat-code} nat-decode(a) ∈ U{i}] | {
intro @i; auto;
unfold <nat-decode nat-code>; auto;
elim #1;
unfold <nat-decode>;
assert [bot ⇓];
aux { chyp-subst <- #4; auto };
bot-div #6
}. | theorem | nat-decode-wf | example | example/container.jonprl | [] | [
"assert",
"nat-code",
"nat-decode"
] | null | 31 | 39 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat-sig-wf : [nat-sig ∈ container{i}] {
unfold <nat-sig nat-code nat-decode has-value>; auto;
elim #1;
assert [bot ⇓];
aux {chyp-subst <- #4 [h. h ⇓]; auto;};
bot-div #6
}. | nat-sig-wf : [nat-sig ∈ container{i}] | {
unfold <nat-sig nat-code nat-decode has-value>; auto;
elim #1;
assert [bot ⇓];
aux {chyp-subst <- #4 [h. h ⇓]; auto;};
bot-div #6
}. | theorem | nat-sig-wf | example | example/container.jonprl | [] | [
"assert",
"has-value",
"nat-code",
"nat-decode",
"nat-sig"
] | null | 43 | 49 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat' : (). | nat' : (). | operator | nat' | example | example/container.jonprl | [] | [] | null | 53 | 53 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[nat'] =def= [wtree(nat-sig)]. | [nat'] | =def= [wtree(nat-sig)]. | definition | nat' | example | example/container.jonprl | [] | [
"nat-sig"
] | null | 54 | 54 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat'-wf : [nat' ∈ U{i}] {
unfold <nat'>; auto
}. | nat'-wf : [nat' ∈ U{i}] | {
unfold <nat'>; auto
}. | theorem | nat'-wf | example | example/container.jonprl | [] | [
"nat'"
] | null | 56 | 58 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
ze-code-wf : ["ze" ∈ nat-code] {
unfold <nat-code has-value nat-decode>;
auto; reduce; auto ; auto
}. | ze-code-wf : ["ze" ∈ nat-code] | {
unfold <nat-code has-value nat-decode>;
auto; reduce; auto ; auto
}. | theorem | ze-code-wf | example | example/container.jonprl | [] | [
"has-value",
"nat-code",
"nat-decode",
"ze"
] | null | 62 | 65 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
su-code-wf : ["su" ∈ nat-code] {
unfold <nat-code has-value nat-decode>;
auto; reduce; auto ; auto
}. | su-code-wf : ["su" ∈ nat-code] | {
unfold <nat-code has-value nat-decode>;
auto; reduce; auto ; auto
}. | theorem | su-code-wf | example | example/container.jonprl | [] | [
"has-value",
"nat-code",
"nat-decode",
"su"
] | null | 67 | 70 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
ze : (). | ze : (). | operator | ze | example | example/container.jonprl | [] | [] | null | 76 | 76 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[ze] =def= [sup("ze" ^ <>)]. | [ze] | =def= [sup("ze" ^ <>)]. | definition | ze | example | example/container.jonprl | [] | [] | null | 77 | 77 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
su : (0). | su : (0). | operator | su | example | example/container.jonprl | [] | [] | null | 79 | 79 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[su(N)] =def= [sup("su" ^ N)]. | [su(N)] | =def= [sup("su" ^ N)]. | definition | su | example | example/container.jonprl | [] | [] | null | 80 | 80 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
ze-wf : [ze ∈ nat'] {
unfold <ze nat' nat-sig>; auto; reduce; auto;
unfold <nat-decode>; reduce; auto
}. | ze-wf : [ze ∈ nat'] | {
unfold <ze nat' nat-sig>; auto; reduce; auto;
unfold <nat-decode>; reduce; auto
}. | theorem | ze-wf | example | example/container.jonprl | [] | [
"nat'",
"nat-decode",
"nat-sig",
"ze"
] | null | 82 | 85 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
su-wf : [{N:nat'} su(N) ∈ nat'] {
intro @i; auto;
unfold <su nat'>;
auto; reduce; auto; auto;
unfold <nat-sig>; reduce; auto
}. | su-wf : [{N:nat'} su(N) ∈ nat'] | {
intro @i; auto;
unfold <su nat'>;
auto; reduce; auto; auto;
unfold <nat-sig>; reduce; auto
}. | theorem | su-wf | example | example/container.jonprl | [] | [
"nat'",
"nat-sig",
"su"
] | null | 89 | 94 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
nat'-elim-test : [nat' -> atom] {
intro @i; auto;
unfold <nat'>;
elim #1; unfold <nat-sig>; reduce;
witness [a];
unfold <nat-code>; auto
}. | nat'-elim-test : [nat' -> atom] | {
intro @i; auto;
unfold <nat'>;
elim #1; unfold <nat-sig>; reduce;
witness [a];
unfold <nat-code>; auto
}. | theorem | nat'-elim-test | example | example/container.jonprl | [] | [
"nat'",
"nat-code",
"nat-sig"
] | null | 98 | 104 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
50 "↓" := squash. | 50 "↓" := squash. | notation | squash | example | example/identity-types.jonprl | [] | [] | null | 3 | 3 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
rel : (0). | rel : (0). | operator | rel | example | example/identity-types.jonprl | [] | [] | null | 5 | 5 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[rel(A)] =def= [A -> A -> U{i}]. | [rel(A)] | =def= [A -> A -> U{i}]. | definition | rel | example | example/identity-types.jonprl | [] | [] | null | 6 | 6 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
rel-wf : [{A:U{i}} rel(A) ∈ U{i'}] {
unfold <rel>; auto
}. | rel-wf : [{A:U{i}} rel(A) ∈ U{i'}] | {
unfold <rel>; auto
}. | theorem | rel-wf | example | example/identity-types.jonprl | [] | [
"rel"
] | null | 8 | 10 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-reflexive : (0;0). | is-reflexive : (0;0). | operator | is-reflexive | example | example/identity-types.jonprl | [] | [] | null | 24 | 24 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[is-reflexive(A;R)] =def= [(a:A) R a a]. | [is-reflexive(A;R)] | =def= [(a:A) R a a]. | definition | is-reflexive | example | example/identity-types.jonprl | [] | [] | null | 25 | 25 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-symmetric : (0;0). | is-symmetric : (0;0). | operator | is-symmetric | example | example/identity-types.jonprl | [] | [] | null | 27 | 27 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[is-symmetric(A;R)] =def= [(a:A) (b:A) R a b -> R b a]. | [is-symmetric(A;R)] | =def= [(a:A) (b:A) R a b -> R b a]. | definition | is-symmetric | example | example/identity-types.jonprl | [] | [] | null | 28 | 28 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-transitive : (0;0). | is-transitive : (0;0). | operator | is-transitive | example | example/identity-types.jonprl | [] | [] | null | 30 | 30 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[is-transitive(A;R)] =def= [(a:A) (b:A) (c:A) R a b -> R b c -> R a c]. | [is-transitive(A;R)] | =def= [(a:A) (b:A) (c:A) R a b -> R b c -> R a c]. | definition | is-transitive | example | example/identity-types.jonprl | [] | [] | null | 31 | 31 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-reflexive-wf : [{A:U{i}} {R:rel(A)} is-reflexive(A;R) ∈ U{i}] {
unfold <is-reflexive rel>;
auto
}. | is-reflexive-wf : [{A:U{i}} {R:rel(A)} is-reflexive(A;R) ∈ U{i}] | {
unfold <is-reflexive rel>;
auto
}. | theorem | is-reflexive-wf | example | example/identity-types.jonprl | [] | [
"is-reflexive",
"rel"
] | null | 33 | 36 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-symmetric-wf : [{A:U{i}} {R:rel(A)} is-symmetric(A;R) ∈ U{i}] {
unfold <is-symmetric rel>; auto
}. | is-symmetric-wf : [{A:U{i}} {R:rel(A)} is-symmetric(A;R) ∈ U{i}] | {
unfold <is-symmetric rel>; auto
}. | theorem | is-symmetric-wf | example | example/identity-types.jonprl | [] | [
"is-symmetric",
"rel"
] | null | 38 | 40 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
is-transitive-wf : [{A:U{i}} {R:rel(A)} is-transitive(A;R) ∈ U{i}] {
unfold <is-transitive rel>; auto
}. | is-transitive-wf : [{A:U{i}} {R:rel(A)} is-transitive(A;R) ∈ U{i}] | {
unfold <is-transitive rel>; auto
}. | theorem | is-transitive-wf | example | example/identity-types.jonprl | [] | [
"is-transitive",
"rel"
] | null | 42 | 44 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
J-principle : (0;0;0). | J-principle : (0;0;0). | operator | J-principle | example | example/identity-types.jonprl | [] | [] | null | 51 | 51 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[J-principle(A; R; Refl)] =def= [
(M:A) (C : (y:A) R M y -> U{i})
C M (Refl M) -> (N:A) (P : R M N) C N P
]. | [J-principle(A; R; Refl)] | =def= [
(M:A) (C : (y:A) R M y -> U{i})
C M (Refl M) -> (N:A) (P : R M N) C N P
]. | definition | J-principle | example | example/identity-types.jonprl | [] | [] | null | 52 | 55 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
J-principle-wf : [{A:U{i}} {R:rel(A)} {Refl : is-reflexive(A; R)} J-principle(A; R; Refl) ∈ U{i'}] {
auto; unfold <J-principle>;
intro @i; auto;
unfold <is-reflexive>; auto
}. | J-principle-wf : [{A:U{i}} {R:rel(A)} {Refl : is-reflexive(A; R)} J-principle(A; R; Refl) ∈ U{i'}] | {
auto; unfold <J-principle>;
intro @i; auto;
unfold <is-reflexive>; auto
}. | theorem | J-principle-wf | example | example/identity-types.jonprl | [] | [
"J-principle",
"is-reflexive",
"rel"
] | null | 57 | 61 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
identity-type : (0). | identity-type : (0). | operator | identity-type | example | example/identity-types.jonprl | [] | [] | null | 65 | 65 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[identity-type(A)] =def= [
(R : rel(A))
* (Refl : is-reflexive(A; R))
* J-principle(A; R; Refl)
]. | [identity-type(A)] | =def= [
(R : rel(A))
* (Refl : is-reflexive(A; R))
* J-principle(A; R; Refl)
]. | definition | identity-type | example | example/identity-types.jonprl | [] | [
"J-principle",
"is-reflexive",
"rel"
] | null | 66 | 70 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
identity-type-wf : [{A:U{i}} identity-type(A) ∈ U{i'}] {
unfold <identity-type>; auto;
cum @i; auto
}. | identity-type-wf : [{A:U{i}} identity-type(A) ∈ U{i'}] | {
unfold <identity-type>; auto;
cum @i; auto
}. | theorem | identity-type-wf | example | example/identity-types.jonprl | [] | [
"identity-type"
] | null | 73 | 76 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
id-rel : (0). | id-rel : (0). | operator | id-rel | example | example/identity-types.jonprl | [] | [] | null | 85 | 85 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[id-rel(I)] =def= [fst(I)]. | [id-rel(I)] | =def= [fst(I)]. | definition | id-rel | example | example/identity-types.jonprl | [] | [
"fst"
] | null | 86 | 86 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
id-refl : (0). | id-refl : (0). | operator | id-refl | example | example/identity-types.jonprl | [] | [] | null | 88 | 88 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[id-refl(I)] =def= [fst(snd(I))]. | [id-refl(I)] | =def= [fst(snd(I))]. | definition | id-refl | example | example/identity-types.jonprl | [] | [
"fst",
"snd"
] | null | 89 | 89 | true | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
id-J : (0). | id-J : (0). | operator | id-J | example | example/identity-types.jonprl | [] | [] | null | 91 | 91 | false | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
End of preview. Expand in Data Studio
JonPRL
Declarations from JonPRL, a Nuprl-family proof refinement logic for computational type theory.
Source
- Repository: https://github.com/jonsterling/JonPRL
- Commit:
f937a5461955fff8cb22331ecb6fdeae8df636d5 - Files: 53
- License: other
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Verbatim declaration with the leading keyword removed: signature and body/proof joined |
| statement | string | Signature with the leading keyword removed (verbatim slice) |
| proof | string | theorem/tactic: the { .. } tactic block; definition: the =def= .. body; empty otherwise |
| type | string | theorem, operator, definition, notation, or tactic |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | Unused; always empty |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Unused; always null |
| line_start | int | First source line |
| line_end | int | Last source line |
| has_proof | bool | Whether a proof block was captured |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
Statistics
- Entries: 847
- With proof: 541 (63.9%)
- With docstring: 0 (0.0%)
- Libraries: 7
By type
| Type | Count |
|---|---|
| theorem | 253 |
| operator | 244 |
| definition | 242 |
| notation | 62 |
| tactic | 46 |
Example
bottom-diverges : [ ¬ bot ⇓ ] {
unfold <not implies>;
intro; aux {auto; unfold <has-value>; auto};
bot-div #1
}.
- type: theorem | symbolic_name:
bottom-diverges| example/approx.jonprl:13
Use
Statement and proof are available both joined (fact) and split (statement, proof) for
proof-term modeling, autoformalization, retrieval, and dependency analysis via deps.
Citation
@misc{jonprl_dataset,
title = {JonPRL},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/jonsterling/JonPRL, commit f937a5461955},
url = {https://huggingface.co/datasets/phanerozoic/JonPRL}
}
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