(* Title: Tools/Compute_Oracle/am_interpreter.ML
ID: $Id$
Author: Steven Obua
*)
signature ABSTRACT_MACHINE =
sig
datatype term = Var of int | Const of int | App of term * term | Abs of term
datatype pattern = PVar | PConst of int * (pattern list)
type program
exception Compile of string;
val compile : (pattern * term) list -> program
exception Run of string;
val run : program -> term -> term
end
structure AM_Interpreter : ABSTRACT_MACHINE = struct
datatype term = Var of int | Const of int | App of term * term | Abs of term
datatype pattern = PVar | PConst of int * (pattern list)
datatype closure = CVar of int | CConst of int
| CApp of closure * closure | CAbs of closure
| Closure of (closure list) * closure
structure prog_struct = TableFun(type key = int*int val ord = prod_ord int_ord int_ord);
datatype program = Program of ((pattern * closure) list) prog_struct.table
datatype stack = SEmpty | SAppL of closure * stack | SAppR of closure * stack | SAbs of stack
exception Compile of string;
exception Run of string;
fun clos_of_term (Var x) = CVar x
| clos_of_term (Const c) = CConst c
| clos_of_term (App (u, v)) = CApp (clos_of_term u, clos_of_term v)
| clos_of_term (Abs u) = CAbs (clos_of_term u)
fun term_of_clos (CVar x) = Var x
| term_of_clos (CConst c) = Const c
| term_of_clos (CApp (u, v)) = App (term_of_clos u, term_of_clos v)
| term_of_clos (CAbs u) = Abs (term_of_clos u)
| term_of_clos (Closure (e, u)) = raise (Run "internal error: closure in normalized term found")
fun strip_closure args (CApp (a,b)) = strip_closure (b::args) a
| strip_closure args x = (x, args)
fun len_head_of_closure n (CApp (a,b)) = len_head_of_closure (n+1) a
| len_head_of_closure n x = (n, x)
(* earlier occurrence of PVar corresponds to higher de Bruijn index *)
fun pattern_match args PVar clos = SOME (clos::args)
| pattern_match args (PConst (c, patterns)) clos =
let
val (f, closargs) = strip_closure [] clos
in
case f of
CConst d =>
if c = d then
pattern_match_list args patterns closargs
else
NONE
| _ => NONE
end
and pattern_match_list args [] [] = SOME args
| pattern_match_list args (p::ps) (c::cs) =
(case pattern_match args p c of
NONE => NONE
| SOME args => pattern_match_list args ps cs)
| pattern_match_list _ _ _ = NONE
(* Returns true iff at most 0 .. (free-1) occur unbound. therefore check_freevars 0 t iff t is closed *)
fun check_freevars free (Var x) = x < free
| check_freevars free (Const c) = true
| check_freevars free (App (u, v)) = check_freevars free u andalso check_freevars free v
| check_freevars free (Abs m) = check_freevars (free+1) m
fun count_patternvars PVar = 1
| count_patternvars (PConst (_, ps)) = List.foldl (fn (p, count) => (count_patternvars p)+count) 0 ps
fun pattern_key (PConst (c, ps)) = (c, length ps)
| pattern_key _ = raise (Compile "pattern reduces to variable")
fun compile eqs =
let
val eqs = map (fn (p, r) => (check_freevars (count_patternvars p) r;
(pattern_key p, (p, clos_of_term r)))) eqs
in
Program (prog_struct.make (map (fn (k, a) => (k, [a])) eqs))
end
fun match_rules n [] clos = NONE
| match_rules n ((p,eq)::rs) clos =
case pattern_match [] p clos of
NONE => match_rules (n+1) rs clos
| SOME args => SOME (Closure (args, eq))
fun match_closure (Program prog) clos =
case len_head_of_closure 0 clos of
(len, CConst c) =>
(case prog_struct.lookup prog (c, len) of
NONE => NONE
| SOME rules => match_rules 0 rules clos)
| _ => NONE
fun lift n (c as (CConst _)) = c
| lift n (v as CVar m) = if m < n then v else CVar (m+1)
| lift n (CAbs t) = CAbs (lift (n+1) t)
| lift n (CApp (a,b)) = CApp (lift n a, lift n b)
| lift n (Closure (e, a)) = Closure (lift_env n e, lift (n+(length e)) a)
and lift_env n e = map (lift n) e
fun weak prog stack (Closure (e, CApp (a, b))) = weak prog (SAppL (Closure (e, b), stack)) (Closure (e, a))
| weak prog (SAppL (b, stack)) (Closure (e, CAbs m)) = weak prog stack (Closure (b::e, m))
| weak prog stack (Closure (e, CVar n)) = weak prog stack (List.nth (e, n) handle Subscript => (CVar (n-(length e))))
| weak prog stack (Closure (e, c as CConst _)) = weak prog stack c
| weak prog stack clos =
case match_closure prog clos of
NONE => weak_last prog stack clos
| SOME r => weak prog stack r
and weak_last prog (SAppR (a, stack)) b = weak prog stack (CApp (a,b))
| weak_last prog (s as (SAppL (b, stack))) a = weak prog (SAppR (a, stack)) b
| weak_last prog stack c = (stack, c)
fun strong prog stack (Closure (e, CAbs m)) =
let
val (stack', wnf) = weak prog SEmpty (Closure ((CVar 0)::(lift_env 0 e), m))
in
case stack' of
SEmpty => strong prog (SAbs stack) wnf
| _ => raise (Run "internal error in strong: weak failed")
end
| strong prog stack (clos as (CApp (u, v))) = strong prog (SAppL (v, stack)) u
| strong prog stack clos = strong_last prog stack clos
and strong_last prog (SAbs stack) m = strong prog stack (CAbs m)
| strong_last prog (SAppL (b, stack)) a = strong prog (SAppR (a, stack)) b
| strong_last prog (SAppR (a, stack)) b = strong_last prog stack (CApp (a, b))
| strong_last prog stack clos = (stack, clos)
fun run prog t =
let
val (stack, wnf) = weak prog SEmpty (Closure ([], clos_of_term t))
in
case stack of
SEmpty => (case strong prog SEmpty wnf of
(SEmpty, snf) => term_of_clos snf
| _ => raise (Run "internal error in run: strong failed"))
| _ => raise (Run "internal error in run: weak failed")
end
end
structure AbstractMachine = AM_Interpreter