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Started work on a bi-directional type checking algorithm for sail
based on Mark and Neel's typechecker for minisail in idl
repository. It's a bit different though, because we are working with
the unmodified sail AST, and not in let normal-form.
Currently, we can check a fragment of sail that includes pattern
matching (in both function clauses and switch statements), numeric
constraints (but not set constraints), function application, casts
between numeric types, assignments to local mutable variables,
sequential blocks, and (implicit) let expressions.
For example, we can correctly typecheck the following program:
val forall Nat 'n, Nat 'm. ([:'n + 20:], [:'m:]) -> [:'n + 20 + 'm:] effect pure plus
val forall Nat 'n, 'n <= -10. [:'n:] -> [:'n:] effect pure minus_ten_id
val forall Nat 'n, 'n >= 10. [:'n:] -> [:'n:] effect pure ten_id
val forall Nat 'N, 'N >= 63. [|10:'N|] -> [|10:'N|] effect pure branch
function forall Nat 'N, 'N >= 63. [|10:'N|] branch x =
{
switch x {
case ([|10:30|]) y -> y
case ([:31:]) _ -> sizeof 'N
case ([|31:40|]) _ -> plus(60,3)
}
}
and branch (([|51:63|]) _) = ten_id(sizeof 'N)
The typechecker has been set up so it can produce derivation trees for
the typing judgements and constraints, so for the above program we
have:
Checking function branch
Adding local binding x :: range<10, 'N>
| Check { switch x { case (range<10, 30>) y -> y case (atom<31>) _ -> sizeof 'N case (range<31, 40>) _ -> plus(60, 3)} } <= range<10, 'N>
| | Check switch x { case (range<10, 30>) y -> y case (atom<31>) _ -> sizeof 'N case (range<31, 40>) _ -> plus(60, 3)} <= range<10, 'N>
| | | Infer x => range<10, 'N>
| | Subset 'N >= 63 |- {'fv1 | 10 <= 'fv1 & 'fv1 <= 30} {'fv0 | 10 <= 'fv0 & 'fv0 <= 'N}
| | Adding local binding y :: range<10, 30>
| | | Check y <= range<10, 'N>
| | | | Infer y => range<10, 30>
| | | Subset 'N >= 63 |- {'fv4 | 10 <= 'fv4 & 'fv4 <= 30} {'fv3 | 10 <= 'fv3 & 'fv3 <= 'N}
| | Subset 'N >= 63 |- {'fv7 | 31 <= 'fv7 & 'fv7 <= 31} {'fv6 | 10 <= 'fv6 & 'fv6 <= 'N}
| | | Check sizeof 'N <= range<10, 'N>
| | | | Infer sizeof 'N => atom<'N>
| | | Subset 'N >= 63 |- {'fv10 | 'N <= 'fv10 & 'fv10 <= 'N} {'fv9 | 10 <= 'fv9 & 'fv9 <= 'N}
| | Subset 'N >= 63 |- {'fv13 | 31 <= 'fv13 & 'fv13 <= 40} {'fv12 | 10 <= 'fv12 & 'fv12 <= 'N}
| | | Check plus(60, 3) <= range<10, 'N>
| | | | | Infer 60 => atom<60>
| | | | | Infer 3 => atom<3>
| | | | Infer plus(60, 3) => atom<((60 - 20) + (20 + 3))>
| | | Subset 'N >= 63 |- {'fv20 | ((60 - 20) + (20 + 3)) <= 'fv20 & 'fv20 <= ((60 - 20) + (20 + 3))} {'fv19 | 10 <= 'fv19 & 'fv19 <= 'N}
Subset 'N >= 63 |- {'fv23 | 51 <= 'fv23 & 'fv23 <= 63} {'fv22 | 10 <= 'fv22 & 'fv22 <= 'N}
| Check ten_id(sizeof 'N) <= range<10, 'N>
| | | Infer sizeof 'N => atom<'N>
| | Prove 'N >= 63 |- 'N >= 10
| | Infer ten_id(sizeof 'N) => atom<'N>
| Subset 'N >= 63 |- {'fv28 | 'N <= 'fv28 & 'fv28 <= 'N} {'fv27 | 10 <= 'fv27 & 'fv27 <= 'N}
Judgements are displayed in the order they occur - inference steps go
inwards bottom up, while checking steps go outwards top-down. The
subtyping rules from Mark and Neel's check_sub rule all are verified
using the Z3 constraint solver.
I have been a set of tests in test/typecheck which aim to exhaustively
test all the code paths in the typechecker, adding new tests everytime
I add support for a new construct.
The new checker is turned on using the -new_typecheck option, and can
be tested (from the toplevel sail directory) by running:
test/typecheck/run_tests.sh -new_typecheck
(currently passes 32/32)
and compared to the old typechecker by
test/typecheck/run_tests.sh
(currently passes 21/32)
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