2.3 KiB
date: 2022-07-12 title: a few undocumented beluga features tags: [computer, beluga, cool languages] toc: true summary: | some undocumented features i found while looking through the source code of the proof language beluga. ...
several of these are in the examples, just not in the documentation. but some of them i did find while looking through the parser.
unicode
you can call your context variables Γ
and it works just fine.
you can also use →
and ⇒
and ⊢
if they are legible in the font you're
using.
block values in substitutions
a lot of the time you have a variable typed like
\[Γ, b : block (x : term, t : oft x A[..]) ⊢ ty]
,
but you actually need a
\[Γ, x : term, t : oft x A[..] ⊢ ty]
,
with the block flattened out. or vice versa.
or you want to substitute the block more conveniently.
for this purpose, there is actually a block literal syntax <a; b; c>
usable
in substitutions:
let [Γ, b : block (x : term, t : oft x A[..]) ⊢ X] = blah in
[Γ, x : term, t : oft x A[..] ⊢ X[.., <x; t>]]
% but equivalent to this, but clearer (imo)
let [Γ, block (x : term, t : oft x A[..]) ⊢ X[.., b.x, b.t]] = blah in
[Γ, x : term, t : oft x A[..] ⊢ X]
explicit binders before patterns
sometimes in a case expression, the type of the pattern variables is too hard for beluga to work out on its own. in this case you get an error message about a stuck unification problem.
most of the time you can get out of this by writing the types of some variables explicitly. the syntax is like a forall-type:
case [Γ ⊢ #p] of
| {#p : [Γ ⊢ term]}
[Γ, y : term ⊢ #p[..]] ⇒ ?body
mutual recursion
of course this exists. but it's not mentioned anywhere in the documentation for some reason. the syntax is this:
LF term : type = …
and elim : type = …;
rec eval-term : (Γ : ctx) [Γ ⊢ term] → [Γ ⊢ value] = …
and rec eval-elim : (Γ : ctx) [Γ ⊢ elim] → [Γ ⊢ value] = …;
inductive ReduceTerm : (Γ : ctx) [Γ ⊢ term] → ctype = …
and inductive ReduceElim : (Γ : ctx) [Γ ⊢ elim] → ctype = …;
two rec
s! which is because you can mix rec
/proof
, or
inductive
/coinductive
/stratified
, within a block.