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content/lambda-mmm(実用版).md

@@ -83,4 +83,86 @@ $$
 &\frac{E^n \vdash e_c \Downarrow n \quad n \leqq0\ E^n \vdash e_e\ \Downarrow v\ }{E^n \vdash\ if (e_c)\ e_t\ else\ e_t \Downarrow v }\ &\textrm{[E-IFFALSE]}\\
 &\frac{E^n \vdash e_1 \Downarrow cls(\lambda x_c.e_c, E^n_c) E^n \vdash e_2 \Downarrow v_2\ E^n_c,\ x_c \mapsto v_2 \vdash e_c \Downarrow v }{E^n \vdash\ e_1\ e_2 \Downarrow v }\ &\textrm{[E-APP]}
 \end{gathered}
+
 $$
+
+## 実用スモールステップ意味論
+
+アイデア：クロージャ呼び出しとそれ以外の関数呼び出し（グローバルに登録されたものと即時呼び出しされるものとか）を分けよう
+
+OCamlでの疑似コード（未完成）
+
+```Ocaml
+type expr = NumLit of float
+          | Var of string
+          | App of expr * expr
+          | Lam of string * expr
+          | Delay of int * expr * expr
+          | Feed of string * expr
+          | Quote of expr
+          | Splice of expr
+          | Tuple of expr list
+          | Proj of expr * int
+type bound = string * value
+and env = bound list
+and value = Real of float
+           | OpenFn of string * expr * int
+           | Closure of string * expr * env
+           | Code of expr
+type state = float list
+type stage = int
+type stateptr = int
+
+let lookup: string->env->value =
+ fun name env -> let finder = fun (n,v) -> n == name in
+ let (_n,v) = List.find finder env in
+ v
+
+
+
+let rec contain_freevars: string -> expr -> env -> bool = 
+ ...
+
+
+let states = ... in
+let stateptr = 0 in
+let rec eval : stage -> expr -> env -> value = 
+  fun stage e env -> match e with
+| Var(name) ->
+  lookup env name
+| Lam(x,e) ->
+  if contains_freevar(e) then OpenFn(x,e,statesize e)
+  else Closure(x,e,env)
+| App(ef,ea) ->
+  let va = eval stage ea env in
+  let vf = eval stage ef env in
+  match vf with
+   | OpenFn(x,e,size)-> let r = eval stage e ((x,va)::env) in
+   shift stateptr size;
+   r
+   | Closure(x,e,cenv) -> eval stage e ((x,va)::cenv)
+| Delay(n,et,ev) ->
+ let v = eval stage ev env in
+ let vt = eval stage et env in
+ update_ringbuf state stateptr v vt
+| Feed(x,e)->
+ let size = statesize e in
+ let last = getstate state stateptr in
+ let current = eval stage e ((x,last)::env)
+ state[stateptr] := current;
+ last
+| Quote(e)->
+  rebuild stage+1 e env
+| Splice(e)->
+  let v = rebuild stage-1 e env
+  match v with
+  | Code(e) -> eval e env
+  _-> raise
+and rebuild : stage -> expr -> env =
+fun stage e env -> 
+ if stage == 0 then eval e env
+ else Code(e)
+
+
+```
+