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 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
easy-with-fiat2 : [void] | {
elim #1
}. | theorem | easy-with-fiat2 | example | example/resource.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
easy-with-fiat3 : [void] | {
intro
}. | theorem | easy-with-fiat3 | example | example/resource.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
easy-with-fiat4 : [void] | {
eq-cd
}. | theorem | easy-with-fiat4 | example | example/resource.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
easy-with-fiat5 : [void] | {
resource my-custom-resource
}. | theorem | easy-with-fiat5 | example | example/resource.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
set-squash : (0). | operator | set-squash | example | example/squash.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
7 "↓" := set-squash. | notation | set-squash | example | example/squash.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[↓ A] | =def= [{_:unit | A}]. | definition | ↓ | example | example/squash.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
set-squash-wf : [{A:U{i}} member(↓ A; U{i})] | {
unfold <set-squash>; auto
}. | theorem | set-squash-wf | example | example/squash.jonprl | [] | [
"member",
"set-squash"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
set-squash-intro : [{A:U{i}} A -> ↓ A] | {
unfold <set-squash>; auto
}. | theorem | set-squash-intro | example | example/squash.jonprl | [] | [
"set-squash"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
reflexive : [{A : U{i}} subtype_rel(A; A)] | {
auto; unfold <id>; auto
}. | theorem | reflexive | example | example/subtype.jonprl | [] | [
"subtype_rel"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
unsquash | {
@{ [ |- squash(T) ] =>
assert [T] <h>;
[ id
, witness [lam(_.<>) h];
unfold <squash>;
auto;
fail
]
}
}. | tactic | unsquash | example | example/subtype.jonprl | [] | [
"assert",
"squash"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
subtype_rel_wf :
[ {A : U{i}}{B : U{i}} member(subtype_rel(A;B);U{i}) ] | {
auto;unfold <subtype_rel member>;eq-eq-base;unfold <bunion id>;
[ auto
, csubst [ceq(lam(x.x);lam(x.snd(x)) pair(inr(<>);lam(x.x)))] [h.=(h;h;_)];
aux { unfold <snd>; reduce 2; auto }; auto;
focus 0 #{ reduce 1; auto };
elim <x>; reduce 1; auto
, csubst [ceq(lam(x.x);lam(x.snd(x)) pair(inr(<>);lam... | theorem | subtype_rel_wf | example | example/subtype.jonprl | [] | [
"bunion",
"ceq",
"member",
"snd",
"subtype_rel"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
subtype_rel_eq :
[ {A : U{i}}{B : U{i}}{x : A}{y : A} subtype_rel(A;B) -> =(x;y;A) -> =(x;y;B) ] | {
auto;
unfold <subtype_rel id>;
assert [=(lam(x.x)x;lam(x.x)y;B)] <h>;
aux { eq-cd [A -> B]; unfold <member> };
reduce; auto
}. | theorem | subtype_rel_eq | example | example/subtype.jonprl | [] | [
"assert",
"member",
"subtype_rel"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
subtype_rel_reflexive : [{A : U{i}} subtype_rel(A; A)] | {
auto;unfold <id>;eq-cd;auto
}. | theorem | subtype_rel_reflexive | example | example/subtype.jonprl | [] | [
"subtype_rel"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
subtype_rel_trans : [{A : U{i}}{B : U{i}}{C : U{i}}
subtype_rel(A; B) => subtype_rel(B; C) => subtype_rel(A; C)] | {
auto;
[ unfold <id>;eq-cd;[id,auto];
cut-lemma <subtype_rel_eq>;
elim #7 [A]; aux { auto };
elim #8 [B]; aux { auto };
elim #10 [p]; aux { auto };
elim #12 [p]; aux { auto };
elim #14 [x]; aux { auto; unfold <subtype_rel member id>; auto };
elim #16 [<>]; aux { auto };
elim #7 [B];... | theorem | subtype_rel_trans | example | example/subtype.jonprl | [] | [
"member",
"subtype_rel",
"subtype_rel_eq"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
constructor | {
(!{intro #0; auto} | !{intro #1; auto})
}. | tactic | constructor | example | example/sums.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
constructor2 | {
(!{intro #0; auto; constructor} | !{intro #1; auto; constructor})
}. | tactic | constructor2 | example | example/sums.jonprl | [] | [
"constructor"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
elims | {
*{ @{ [H : P + Q |- _] => elim <H>; thin <H>
| [H : void |- _] => elim <H>
| [H : P |- P] => hypothesis <H>
}
}
}. | tactic | elims | example | example/sums.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
auto-sums | {
auto; elims; constructor2
}. | tactic | auto-sums | example | example/sums.jonprl | [] | [
"constructor2",
"elims"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
commutative : [{A:U{i}} {B:U{i}} iff(A + B; B + A)] | {
auto-sums
}. | theorem | commutative | example | example/sums.jonprl | [] | [
"auto-sums",
"iff"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
plus-assoc : [{A:U{i}} {B:U{i}} {C:U{i}} iff(A + (B + C); (A + B) + C)] | {
auto-sums
}. | theorem | plus-assoc | example | example/sums.jonprl | [] | [
"auto-sums",
"iff"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
void-idr : [{A:U{i}} iff(A + void; A)] | {
auto-sums
}. | theorem | void-idr | example | example/sums.jonprl | [] | [
"auto-sums",
"iff"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
void-idl : [{A:U{i}} iff(void + A; A)] | {
auto-sums
}. | theorem | void-idl | example | example/sums.jonprl | [] | [
"auto-sums",
"iff"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
tautology-step | {
@{ [H : P |- P] => hypothesis <H>
| [|- unit] => unfold <unit>;auto
| [|- P * Q] => intro
| [|- P -> Q] => intro
| [|- P => Q] => intro
| [H : void |- _] => elim <H>
| [H : (x : P) * _ |- _] => elim <H>; thin <H>
| [H : P + Q |- _] => elim <H>; thin <H>
| [H : (x : P) _, H' : P |- _] => elim... | tactic | tautology-step | example | example/tautology.jonprl | [] | [
"member"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
tautology | {
*{ tautology-step }
}. | tactic | tautology | example | example/tautology.jonprl | [] | [
"tautology-step"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
example : [{P:U{i}} {Q:U{i}} (P + Q + void) * (P -> Q) -> unit * Q] | {
tautology
}. | theorem | example | example | example/tautology.jonprl | [] | [
"tautology"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
50 "¬" := not. | notation | not | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
option-wf : [{A:U{i}} A? ∈ U{i}] | {
unfold <option>; auto
}. | theorem | option-wf | example | example/telescopes.jonprl | [] | [
"option"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
telescope-sig : (). | operator | telescope-sig | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[telescope-sig] | =def= [A : U{i}? <: decide(A; A'.A'; _.void)]. | definition | telescope-sig | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
telescope-sig-wf : [telescope-sig ∈ container{i'}] | {
unfold <telescope-sig>; auto;
[ unfold <option>; auto
, unfold <option>; elim #1; reduce; auto
]
}. | theorem | telescope-sig-wf | example | example/telescopes.jonprl | [] | [
"option",
"telescope-sig"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
telescope : (). | operator | telescope | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[telescope] | =def= [wtree(telescope-sig)]. | definition | telescope | example | example/telescopes.jonprl | [] | [
"telescope-sig"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
telescope-wf : [telescope ∈ U{i'}] | {
unfold <telescope>; unfold <member>;
eq-cd @i'; auto
}. | theorem | telescope-wf | example | example/telescopes.jonprl | [] | [
"member",
"telescope"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
t-nil : (). | operator | t-nil | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[t-nil] | =def= [sup(none ^ <>)]. | definition | t-nil | example | example/telescopes.jonprl | [] | [
"none"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
t-nil-wf : [t-nil ∈ telescope] | {
unfold <t-nil telescope telescope-sig>; auto; reduce;
unfold <none option>; reduce; auto
}. | theorem | t-nil-wf | example | example/telescopes.jonprl | [] | [
"none",
"option",
"t-nil",
"telescope",
"telescope-sig"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
t-snoc : (0;1). | operator | t-snoc | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
<- 10 "#" := t-snoc. | notation | t-snoc | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[A # a. T[a]] | =def= [sup(some(A) ^ a.T[a])]. | definition | A | example | example/telescopes.jonprl | [] | [
"some"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
t-snoc-wf : [{A:U{i}} {T:A -> telescope} (A # a.T a) ∈ telescope] | {
auto; intro @i'; auto;
unfold <t-snoc some telescope telescope-sig option>;
*{ auto; reduce }
}. | theorem | t-snoc-wf | example | example/telescopes.jonprl | [] | [
"option",
"some",
"t-snoc",
"telescope",
"telescope-sig"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
t-prod : (0). | operator | t-prod | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[t-prod(T)] | =def= [
wtree-rec(T; shape.po.ih.
decide(shape; A. (x:A) * ih x; var.unit)
)
]. | definition | t-prod | example | example/telescopes.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
test : [<"hi", zero, <>> ∈ t-prod(atom # match { "hi" => nat # _.t-nil | _ => t-nil })] | {
unfold <t-prod t-snoc t-nil some none>;
*{ reduce; auto };
eq-cd [telescope-sig, _.U{i}];
unfold <telescope-sig option>;
*{ reduce; auto };
elim #2; reduce; auto
}. | theorem | test | example | example/telescopes.jonprl | [] | [
"none",
"option",
"some",
"t-nil",
"t-prod",
"t-snoc",
"telescope-sig"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
Top : (). | operator | Top | example | example/top.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[Top] | =def= [void => void]. | definition | Top | example | example/top.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
anything-in-top : [{E:base} member(E; Top)] | {
unfold <Top>; auto
}. | theorem | anything-in-top | example | example/top.jonprl | [] | [
"Top",
"member"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
top-singleton : [{E:Top} {F:Top} =(E; F; Top)] | {
unfold <Top>; auto
}. | theorem | top-singleton | example | example/top.jonprl | [] | [
"Top"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
sym : [{A:U{i}} {M:A} {N:A} =(M; N; A) => =(N; M; A)] | {
auto; trace "Here's a quick message\n\twith escapes";
symmetry; auto
}. | theorem | sym | example | example/trace.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
unique : (0;1). | operator | unique | example | example/unique.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[unique(A; x.B[x])] | =def= [
(x:A) * {_ : B[x] | {y:A} B[y] => =(x;y;A)}
]. | definition | unique | example | example/unique.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
isContr : (0). | operator | isContr | example | example/unique.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[isContr(A)] | =def= [{x:A | {y:A} =(x; y; A)}]. | definition | isContr | example | example/unique.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
abort-unique : [{A:U{i}} unique(void -> A; _. unit)] | {
unfold <unique>; auto;
intro [lam(x. x)]; auto;unfold <unit>; auto;
ext; auto
}. | theorem | abort-unique | example | example/unique.jonprl | [] | [
"unique"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
void-fun-contr : [{A : U{i}} isContr(void -> A)] | {
unfold <isContr>; auto;
intro [lam(x. x)]; auto;
ext; auto
}. | theorem | void-fun-contr | example | example/unique.jonprl | [] | [
"isContr"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
lower : [U{i} -> U{i'}] | {
auto; witness [void]; auto
}. | theorem | lower | example | example/universe-levels.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
higher : [U{i'} -> U{i''}] | {
lemma <lower>
}. | theorem | higher | example | example/universe-levels.jonprl | [] | [
"lower"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
autoRed | {
reduce; *{auto; reduce}
}. | tactic | autoRed | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
cmp : (0;0). | operator | cmp | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
pairF : (0;0). | operator | pairF | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
pairFp : (0;0). | operator | pairFp | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
diag : (). | operator | diag | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
bang : (0). | operator | bang | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[cmp(g;f)] | =def= [lam(x. g (f x))]. | definition | cmp | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[pairF(f;g)] | =def= [lam(x. pair(f x; g x))]. | definition | pairF | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[pairFp(f;g)] | =def= [lam(x. pairF(f fst(x); g snd(x)))]. | definition | pairFp | example | example/yoga.jonprl | [] | [
"fst",
"pairF",
"snd"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[bang(v)] | =def= [lam(_. v)]. | definition | bang | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[diag] | =def= [pairF(id; id)]. | definition | diag | example | example/yoga.jonprl | [] | [
"pairF"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
CTT : (). | operator | CTT | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
Paths : (0). | operator | Paths | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
Yo : (0). | operator | Yo | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
oY : (0). | operator | oY | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[CTT] | =def= [lam(A.lam(B. A -> B))]. | definition | CTT | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Paths(A)] | =def= [lam(x.lam(y. =(x;y;A)))]. | definition | Paths | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Yo(B)] | =def= [lam(A. A -> B)]. | definition | Yo | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[oY(A)] | =def= [lam(B. A -> B)]. | definition | oY | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
End : (0;1). | operator | End | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
Coend : (0;1). | operator | Coend | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[End(X;x.P[x])] | =def= [(x:X) P[x]]. | definition | End | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Coend(X;x.P[x])] | =def= [(x:X) * P[x]]. | definition | Coend | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Ran(X;cat;hom;g;h)] | =def= [lam(a. End(X; x. hom (cat a (g x)) (h x)))]. | definition | Ran | example | example/yoga.jonprl | [] | [
"End",
"hom"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Lan(X;cat;ten;g;h)] | =def= [lam(a. Coend(X; x. ten (h x) (cat (g x) a)))]. | definition | Lan | example | example/yoga.jonprl | [] | [
"Coend"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
Psh : (0). | operator | Psh | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[Psh(X)] | =def= [X -> U{i}]. | definition | Psh | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
Hom : (). | operator | Hom | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
Ten : (). | operator | Ten | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
LowerShriek : (0;0;0). | operator | LowerShriek | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
UpperShriek : (0;0;0). | operator | UpperShriek | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
UpperStar : (0;0;0). | operator | UpperStar | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
LowerStar : (0;0;0). | operator | LowerStar | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
[Hom] | =def= [lam(A.lam(B. A -> B))]. | definition | Hom | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[Ten] | =def= [lam(A.lam(B. A * B))]. | definition | Ten | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[LowerShriek(X;Y;f)] | =def= [lam(φ.lam(x. Lan(X;Paths(Y);Ten;f;φ) x))]. | definition | LowerShriek | example | example/yoga.jonprl | [] | [
"Lan",
"Paths",
"Ten"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[UpperShriek(X;Y;f)] | =def= [lam(φ.lam(x. φ (f x)))]. | definition | UpperShriek | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[UpperStar(X;Y;f)] | =def= [UpperShriek(X;Y;f)]. | definition | UpperStar | example | example/yoga.jonprl | [] | [
"UpperShriek"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
[LowerStar(X;Y;f)] | =def= [lam(φ.lam(x. Ran(X;Paths(Y);Hom;f;φ) x))]. | definition | LowerStar | example | example/yoga.jonprl | [] | [
"Hom",
"Paths",
"Ran"
] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | |
contract : (). | operator | contract | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
Equals : (0;0). | operator | Equals | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
element : (0;0). | operator | element | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 | ||
implies : (0;0). | operator | implies | example | example/yoga.jonprl | [] | [] | https://github.com/jonsterling/JonPRL | f937a5461955fff8cb22331ecb6fdeae8df636d5 |
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