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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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