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README
Sit: sizeirrelevant types
A prototype dependentlytyped language with sized natural numbers
Sit parses and typechecks .agda
that conform to the Sit language syntax.
Syntax (excerpt):
 Lexical stuff
 Single line comment
{ Block comment }
;  End of declaration (mandatory)
f_x'1  identifiers start with a letter, then have letters, digits, _ and '
 Declarations
x : T ;  type signature
x = t ;  definition
open import M ;  ignored, for Agda compatibility
 Sit specifics
oo  infinity size
i + 1  successor size
Nat a  type of natural numbers below size a
zero a  number zero (a is size annotation)
suc a n  successor of n (a is size annotation)
forall .i > T  irrelevant size quantification
forall ..i > T  relevant size quantification
fix T t n  recursive function over natural numbers
 T: return type
 t: functional
 n: natural number argument
\{ (zero _) > t; (suc _ x) > u }  case distinction function
 Inherited Agda syntax
U > T  nondependent function type
(x y z : U) > T  dependent function type
\ x y z > t  lambdaabstraction
t u  application
Set  first universe
Set1  second universe
Set a  universe of level a
Limitations
Sit only understands a tiny subset of the Agda language.
Sit does not understand layout, instead each declaration has to be terminated with
comment ;
.
Installation
Requires GHC and cabal, for instance via the Haskell Platform. In a shell, type
cabal install
Test
In a shell, type
Sit.bin test/Test.agda
Example
This is the addition function in Sit:
 Addition of natural numbers
plus : forall .i > Nat i > Nat oo > Nat oo ;
plus = \ i x y >
fix (\ i x > Nat oo)
(\ _ f > \
{ (zero _) > y
; (suc _ x) > suc oo (f x)
})
x