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Notes on a possible type system for GRIN
LLVM is a typed intermediate language. GRIN has to be typed to harness the full power of LLVM. The GRIN type system must be expressive enough to
- embed the LLVM type system
- type the GRIN programs during transformations (at any stage)
- describe the type of GRIN transformations (type preserving and well typed)
The result of the Heap-Points-To (HPT) analysis can be seen as a type environment. In this setting the HPT analysis is the type inference algorithm.
e.g. HPT result for a GRIN program
Heap
1 -> {CInt[{T_Int64}]}
2 -> {CInt[{T_Int64}]}
3 -> {CInt[{T_Int64}]
,Fadd[{1},{2}]}
Env
a -> {1}
b -> {2}
b' -> {T_Int64}
m -> {1}
m' -> {T_Int64}
n -> {2}
n' -> {T_Int64}
q -> {1,2,3}
r' -> {T_Int64}
t1 -> {1}
t2 -> {2}
t3 -> {3}
v -> {CInt[{T_Int64}]
,Fadd[{1},{2}]}
w -> {CInt[{T_Int64}]}
x'1 -> {T_Int64}
Function
_prim_int_add :: {T_Int64}
-> {T_Int64}
-> {T_Int64}
_prim_int_print :: {T_Int64}
-> {T_Unit}
add :: {1}
-> {2}
-> {CInt[{T_Int64}]}
eval :: {1,2,3}
-> {CInt[{T_Int64}]
,Fadd[{1},{2}]}
grinMain :: {T_Unit}
GRIN source program
grinMain =
t1 <- store (CInt 1)
t2 <- store (CInt 10000)
t3 <- store (Fadd t1 t2)
(CInt r') <- eval t3
_prim_int_print r'
add m n =
(CInt m') <- eval m
(CInt n') <- eval n
b' <- _prim_int_add m' n'
pure (CInt b')
eval q =
v <- fetch q
case v of
(CInt x'1) -> pure v
(Fadd a b) -> w <- add a b
update q w
pure w
Notes
A builtin dependent type function should be enough for full GRIN expressivity.
prj :: Tag -> Int -> a
OR
prjNode :: {Node A, ..., Node Z} -> Tag -> Node Tag
prjItem :: Node Tag -> Int -> a