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