Lazy Lambda Interpreter

O — CPS language with general recursion

Article

Untyped Lazy Interpreter

The motivation for building an interpreter that can run on L1 cache sizes (limited to 64KB of code and data) is based on success of LuaJIT, V8, HotSpot, and vector lanaguages such as K and J. If we can build a really fast VM for such interpreter (compact aligned bytecode) and make it stick to L1 sizes with enabled AVX instruction set then it can outperform any reasonable alternative.

This approach was chosen for building O-CPS interpreter in Rust. Following results were achieved in factorial (5) and ackerman function (3,4) benchmarks, and that's even without bytecode VM implementation! Next step to improvement.

Rust 0 Java 3 PyPy 8 O-CPS 291 Python 537 K 756 Erlang 10699/1806/436/9 LuaJIT 33856
akkerman_k 635 ns/iter (+/- 73) akkerman_rust 8,968 ns/iter (+/- 322)

The key challenge here was that O-CPS implementation was made in Rust's flavour of linear types. Thus lambda interpreter as an internal language of cartesian closed category was written in a language with linear types and lifetimes as an internal language of symmetric monoidal categories. Such an exercise will definitely increase your confidence in linear types.

Built-in Vectorization by Rust

(&AST::Atom(Atom::Value(Value::$vec(ref l))), &AST::Atom(Atom::Value(Value::$vec(ref r)))) => { let a: Vec<$atype> = l.iter() .zip(r) .map(|(l,r)| dyad_map_expr!(l,$op,r,$atom)) .collect::>(); Ok( AST::Atom(Atom::Value(Value::$r_vec(a))) ) }, objdump ./target/release/o -d | grep mulpd 223f1: c5 f5 59 0c d3 vmulpd (%rbx,%rdx,8),%ymm1,%ymm1 223f6: c5 dd 59 64 d3 20 vmulpd 0x20(%rbx,%rdx,8),%ymm4,%ymm4 22416: c5 f5 59 4c d3 40 vmulpd 0x40(%rbx,%rdx,8),%ymm1,%ymm1 2241c: c5 dd 59 64 d3 60 vmulpd 0x60(%rbx,%rdx,8),%ymm4,%ymm4 2264d: c5 f5 59 0c d3 vmulpd (%rbx,%rdx,8),%ymm1,%ymm1 22652: c5 e5 59 5c d3 20 vmulpd 0x20(%rbx,%rdx,8),%ymm3,%ymm3

AST

data Value = Nil | SymbolInt (a: u16) | SequenceInt (a: u16) | Number (a: i64) | Float (a: f64) | VecNumber (Vec i64) | VecFloat (Vec f64) data Scalar = Nil | Any | List (a: AST) | Dict (a: AST) | Call (a b: AST) | Assign (a b: AST) | Cond (a b c: AST) | Lambda (otree: Option NodeId) (a b: AST) | Yield (c: Context) | Value (v: Value) | Name (s: String) data AST = Atom (a: Scalar) | Vector (a: Vec AST) data Lazy = Defer (otree: NodeId) (a: AST) (cont: Cont) | Continuation (otree: NodeId) (a: AST) (cont: Cont) | Return (a: AST) | Start data Cont = Expressions (ast: AST) Option (vec: Iter AST) (cont: Cont) | Assign (ast: AST) (cont: Cont) | Cond (c,d: AST) (cont: Cont) | Func (a,b,c: AST) (cont: Cont) | List (acc: Vec AST) (vec: Iter AST) (i: Nat) (cont: Cont) | Call (a: AST) (i: Nat) (cont: Cont) | Return | Intercore (m: Message) (cont: Cont) | Yield (cont: Cont)

O-CPS Interpreter

E: V | A | C NC: ";" = [] | ";" m:NL = m FC: ";" = [] | ";" m:FL = m EC: ";" = [] | ";" m:EL = m NL: NAME | o:NAME m:NC = Cons o m FL: E | o:E | m:FC = Cons o m EL: E | EC | o:E m:EC = Cons o m C: N | c:N a:C = Call c a N: NAME | S | HEX | L | F L: "(" ")" = [] | "([" c:NL "]" m:FL ")" = Table c m | "(" l:EL ")" = List l F: "{" "}" = Lambda [] [] [] | "{[" c:NL "]" m:EL "}" = Lambda [] c m | "{" m:EL "}" = Lambda [] [] m lazy n (Assign n b) e k = D n b (ContAssign n k) n (Cond v a l) e k = D n v (ContCond l r k) n (List l) e k = eve n l e k n (Call c a) e k = D n a (ContCall c k) n (Name s) e k = cont (lookup n s e) k n (Lambda _ x y) e k = cont ((Lambda n x y) n) k evf n (Lambda c x y) a e k = cont (y (if (= c []) n c)) (ContFunc x a k) n (Name s) a e k = lookup n s e eve n (Cons a d) e k = D n a (ContExpr d k) n Nil e k = cont n Nil e k n a e k = D n a k emr (Dict x) e k = R Dict (rev x) (Cons x y) e k = R Dict (Cons (rev x) (rev x)) a e k = R a run D n a e k = lazy n a e k R a = a cont n (Dict v) e (ContCall c k) = evf n c v e k n x e (ContCall c k) = evf n c x e k n x e (ContFunc s a k) = eve (e.define_args s (rev a)) v k n False e (ContCond l r k) = D n r k n True e (ContCond l r k) = D n l k n x e (ContCond l r k) = D n x (ContCond l r k) n x e (ContAssign (Name s) k) = eve n (e.define s x) k n x e (ContExpr (Cons a d) k) = eve n (Cons a d) k n x e (ContExpr r k) = cont n x k n x e ContRet = emr x e k