author | haftmann |
Fri, 19 Oct 2007 16:20:27 +0200 | |
changeset 25101 | cae0f68b693b |
parent 25098 | 1ec53c9ae71a |
child 25167 | 0fd59d8e2bad |
permissions | -rw-r--r-- |
24590 | 1 |
(* Title: Tools/nbe.ML |
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ID: $Id$ |
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Authors: Klaus Aehlig, LMU Muenchen; Tobias Nipkow, Florian Haftmann, TU Muenchen |
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Normalization by evaluation, based on generic code generator. |
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*) |
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signature NBE = |
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sig |
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val norm_conv: cterm -> thm |
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val norm_term: theory -> term -> term |
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datatype Univ = |
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Const of string * Univ list (*named (uninterpreted) constants*) |
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| Free of string * Univ list |
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| DFree of string (*free (uninterpreted) dictionary parameters*) |
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| BVar of int * Univ list |
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| Abs of (int * (Univ list -> Univ)) * Univ list; |
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val free: string -> Univ (*free (uninterpreted) variables*) |
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val app: Univ -> Univ -> Univ (*explicit application*) |
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val abs: int -> (Univ list -> Univ) -> Univ |
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(*abstractions as closures*) |
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val univs_ref: (unit -> Univ list) ref |
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val lookup_fun: string -> Univ |
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val trace: bool ref |
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val setup: theory -> theory |
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end; |
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structure Nbe: NBE = |
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struct |
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(* generic non-sense *) |
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val trace = ref false; |
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fun tracing f x = if !trace then (Output.tracing (f x); x) else x; |
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(** the semantical universe **) |
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(* |
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Functions are given by their semantical function value. To avoid |
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trouble with the ML-type system, these functions have the most |
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generic type, that is "Univ list -> Univ". The calling convention is |
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that the arguments come as a list, the last argument first. In |
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other words, a function call that usually would look like |
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f x_1 x_2 ... x_n or f(x_1,x_2, ..., x_n) |
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would be in our convention called as |
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f [x_n,..,x_2,x_1] |
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Moreover, to handle functions that are still waiting for some |
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arguments we have additionally a list of arguments collected to far |
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and the number of arguments we're still waiting for. |
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*) |
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datatype Univ = |
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Const of string * Univ list (*named (uninterpreted) constants*) |
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| Free of string * Univ list (*free variables*) |
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| DFree of string (*free (uninterpreted) dictionary parameters*) |
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| BVar of int * Univ list (*bound named variables*) |
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| Abs of (int * (Univ list -> Univ)) * Univ list |
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(*abstractions as closures*); |
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(* constructor functions *) |
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fun free v = Free (v, []); |
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fun abs n f = Abs ((n, f), []); |
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fun app (Abs ((1, f), xs)) x = f (x :: xs) |
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| app (Abs ((n, f), xs)) x = Abs ((n - 1, f), x :: xs) |
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| app (Const (name, args)) x = Const (name, x :: args) |
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| app (Free (name, args)) x = Free (name, x :: args) |
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| app (BVar (name, args)) x = BVar (name, x :: args); |
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(* universe graph *) |
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type univ_gr = Univ option Graph.T; |
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val compiled : univ_gr -> string -> bool = can o Graph.get_node; |
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(* sandbox communication *) |
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val univs_ref = ref (fn () => [] : Univ list); |
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local |
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val gr_ref = ref NONE : univ_gr option ref; |
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fun compile gr raw_s = NAMED_CRITICAL "nbe" (fn () => |
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let |
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val _ = univs_ref := (fn () => []); |
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val s = "Nbe.univs_ref := " ^ raw_s; |
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val _ = tracing (fn () => "\n--- generated code:\n" ^ s) (); |
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val _ = gr_ref := SOME gr; |
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val _ = use_text "" (Output.tracing o enclose "\n---compiler echo:\n" "\n---\n", |
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Output.tracing o enclose "\n--- compiler echo (with error):\n" "\n---\n") |
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(!trace) s; |
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val _ = gr_ref := NONE; |
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in !univs_ref end); |
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in |
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fun lookup_fun s = NAMED_CRITICAL "nbe" (fn () => case ! gr_ref |
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of NONE => error "compile_univs" |
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| SOME gr => the (Graph.get_node gr s)); |
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fun compile_univs gr ([], _) = [] |
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| compile_univs gr (cs, raw_s) = cs ~~ compile gr raw_s (); |
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end; (*local*) |
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(** assembling and compiling ML code from terms **) |
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(* abstract ML syntax *) |
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infix 9 `$` `$$`; |
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fun e1 `$` e2 = "(" ^ e1 ^ " " ^ e2 ^ ")"; |
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fun e `$$` [] = e |
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| e `$$` es = "(" ^ e ^ " " ^ space_implode " " es ^ ")"; |
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fun ml_abs v e = "(fn " ^ v ^ " => " ^ e ^ ")"; |
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fun ml_Val v s = "val " ^ v ^ " = " ^ s; |
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fun ml_cases t cs = |
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"(case " ^ t ^ " of " ^ space_implode " | " (map (fn (p, t) => p ^ " => " ^ t) cs) ^ ")"; |
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fun ml_Let ds e = "let\n" ^ space_implode "\n" ds ^ " in " ^ e ^ " end"; |
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fun ml_list es = "[" ^ commas es ^ "]"; |
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val ml_delay = ml_abs "()" |
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fun ml_fundefs ([(name, [([], e)])]) = |
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"val " ^ name ^ " = " ^ e ^ "\n" |
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| ml_fundefs (eqs :: eqss) = |
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let |
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fun fundef (name, eqs) = |
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let |
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fun eqn (es, e) = name ^ " " ^ space_implode " " es ^ " = " ^ e |
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in space_implode "\n | " (map eqn eqs) end; |
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in |
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(prefix "fun " o fundef) eqs :: map (prefix "and " o fundef) eqss |
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|> space_implode "\n" |
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|> suffix "\n" |
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end; |
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(* nbe specific syntax *) |
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local |
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val prefix = "Nbe."; |
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val name_const = prefix ^ "Const"; |
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val name_free = prefix ^ "free"; |
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val name_dfree = prefix ^ "DFree"; |
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val name_abs = prefix ^ "abs"; |
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val name_app = prefix ^ "app"; |
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val name_lookup_fun = prefix ^ "lookup_fun"; |
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in |
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fun nbe_const c ts = |
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name_const `$` ("(" ^ ML_Syntax.print_string c ^ ", " ^ ml_list ts ^ ")"); |
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fun nbe_fun c = "c_" ^ translate_string (fn "." => "_" | c => c) c; |
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fun nbe_free v = name_free `$` ML_Syntax.print_string v; |
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fun nbe_dfree v = name_dfree `$` ML_Syntax.print_string v; |
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fun nbe_dict v n = "d_" ^ v ^ "_" ^ string_of_int n; |
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fun nbe_bound v = "v_" ^ v; |
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fun nbe_apps e es = |
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Library.foldr (fn (s, e) => name_app `$$` [e, s]) (es, e); |
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fun nbe_abss 0 f = f `$` ml_list [] |
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| nbe_abss n f = name_abs `$$` [string_of_int n, f]; |
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fun nbe_lookup c = ml_Val (nbe_fun c) (name_lookup_fun `$` ML_Syntax.print_string c); |
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val nbe_value = "value"; |
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end; |
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open BasicCodeThingol; |
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(* greetings to Tarski *) |
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fun assemble_idict (DictConst (inst, dss)) = |
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nbe_apps (nbe_fun inst) ((maps o map) assemble_idict dss) |
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| assemble_idict (DictVar (supers, (v, (n, _)))) = |
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fold (fn super => nbe_apps (nbe_fun super) o single) supers (nbe_dict v n); |
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fun assemble_iterm is_fun num_args = |
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let |
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fun of_iterm t = |
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let |
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val (t', ts) = CodeThingol.unfold_app t |
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in of_iapp t' (fold (cons o of_iterm) ts []) end |
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and of_iconst c ts = case num_args c |
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of SOME n => if n <= length ts |
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then let val (args2, args1) = chop (length ts - n) ts |
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in nbe_apps (nbe_fun c `$` ml_list args1) args2 |
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end else nbe_const c ts |
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| NONE => if is_fun c then nbe_apps (nbe_fun c) ts |
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else nbe_const c ts |
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and of_iapp (IConst (c, (dss, _))) ts = of_iconst c |
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(ts @ rev ((maps o map) assemble_idict dss)) |
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| of_iapp (IVar v) ts = nbe_apps (nbe_bound v) ts |
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| of_iapp ((v, _) `|-> t) ts = |
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nbe_apps (nbe_abss 1 (ml_abs (ml_list [nbe_bound v]) (of_iterm t))) ts |
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| of_iapp (ICase (((t, _), cs), t0)) ts = |
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nbe_apps (ml_cases (of_iterm t) (map (pairself of_iterm) cs |
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@ [("_", of_iterm t0)])) ts |
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in of_iterm end; |
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fun assemble_fun gr num_args (c, (vs, eqns)) = |
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let |
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val assemble_arg = assemble_iterm (K false) (K NONE); |
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val assemble_rhs = assemble_iterm (is_some o Graph.get_node gr) num_args; |
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val dict_params = maps (fn (v, sort) => map_index (nbe_dict v o fst) sort) vs |
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|> rev; |
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fun assemble_eqn (args, rhs) = |
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([ml_list (map assemble_arg (rev args) @ dict_params)], assemble_rhs rhs); |
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val default_params = map nbe_bound (Name.invent_list [] "a" ((the o num_args) c)); |
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val default_eqn = ([ml_list default_params], nbe_const c default_params); |
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in map assemble_eqn eqns @ [default_eqn] end; |
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fun assemble_eqnss gr ([], deps) = ([], "") |
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| assemble_eqnss gr (eqnss, deps) = |
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let |
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val cs = map fst eqnss; |
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val num_args = cs ~~ map (fn (_, (vs, (args, rhs) :: _)) => |
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length (maps snd vs) + length args) eqnss; |
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val bind_deps = map nbe_lookup (filter (is_some o Graph.get_node gr) deps); |
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val bind_locals = ml_fundefs (map nbe_fun cs ~~ map |
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(assemble_fun gr (AList.lookup (op =) num_args)) eqnss); |
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val result = ml_list (map (fn (c, n) => nbe_abss n (nbe_fun c)) num_args) |
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|> ml_delay; |
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in (cs, ml_Let (bind_deps @ [bind_locals]) result) end; |
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fun eqns_of_stmt (_, CodeThingol.Fun (_, [])) = |
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[] |
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| eqns_of_stmt (const, CodeThingol.Fun ((vs, _), eqns)) = |
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[(const, (vs, map fst eqns))] |
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| eqns_of_stmt (_, CodeThingol.Datatypecons _) = |
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[] |
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| eqns_of_stmt (_, CodeThingol.Datatype _) = |
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[] |
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| eqns_of_stmt (class, CodeThingol.Class (v, (superclasses, classops))) = |
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let |
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val names = map snd superclasses @ map fst classops; |
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val params = Name.invent_list [] "d" (length names); |
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fun mk (k, name) = |
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(name, ([(v, [])], |
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[([IConst (class, ([], [])) `$$ map IVar params], IVar (nth params k))])); |
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in map_index mk names end |
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| eqns_of_stmt (_, CodeThingol.Classrel _) = |
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[] |
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| eqns_of_stmt (_, CodeThingol.Classparam _) = |
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[] |
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| eqns_of_stmt (inst, CodeThingol.Classinst ((class, (_, arities)), (superinsts, instops))) = |
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[(inst, (arities, [([], IConst (class, ([], [])) `$$ |
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map (fn (_, (_, (inst, dicts))) => IConst (inst, (dicts, []))) superinsts |
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@ map (IConst o snd o fst) instops)]))]; |
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fun compile_stmts stmts_deps = |
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let |
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val names = map (fst o fst) stmts_deps; |
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val names_deps = map (fn ((name, _), deps) => (name, deps)) stmts_deps; |
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val eqnss = maps (eqns_of_stmt o fst) stmts_deps; |
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val compiled_deps = names_deps |> maps snd |> distinct (op =) |> subtract (op =) names; |
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fun compile gr = (eqnss, compiled_deps) |> assemble_eqnss gr |> compile_univs gr |> rpair gr; |
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in |
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fold (fn name => Graph.new_node (name, NONE)) names |
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#> fold (fn (name, deps) => fold (curry Graph.add_edge name) deps) names_deps |
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#> compile |
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#-> fold (fn (name, univ) => Graph.map_node name (K (SOME univ))) |
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end; |
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fun ensure_stmts code = |
277 |
let |
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fun add_stmts names gr = if exists (compiled gr) names then gr else gr |
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|> compile_stmts (map (fn name => ((name, Graph.get_node code name), |
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Graph.imm_succs code name)) names); |
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in fold_rev add_stmts (Graph.strong_conn code) end; |
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fun assemble_eval gr (((vs, ty), t), deps) = |
284 |
let |
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val frees = CodeThingol.fold_unbound_varnames (insert (op =)) t []; |
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val bind_deps = map nbe_lookup (filter (is_some o Graph.get_node gr) deps); |
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val dict_params = maps (fn (v, sort) => map_index (nbe_dict v o fst) sort) vs |
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|> rev; |
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val bind_value = ml_fundefs [(nbe_value, |
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[([ml_list (map nbe_bound frees @ dict_params)], |
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assemble_iterm (is_some o Graph.get_node gr) (K NONE) t)])]; |
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val result = ml_list [nbe_value `$` ml_list |
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(map nbe_free frees @ map nbe_dfree dict_params)] |
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|> ml_delay; |
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in ([nbe_value], ml_Let (bind_deps @ [bind_value]) result) end; |
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297 |
fun eval_term gr = |
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assemble_eval gr |
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#> compile_univs gr |
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#> the_single |
301 |
#> snd; |
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303 |
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(** evaluation **) |
24155 | 305 |
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(* reification *) |
24155 | 307 |
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308 |
fun term_of_univ thy t = |
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309 |
let |
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fun take_until f [] = [] |
311 |
| take_until f (x::xs) = if f x then [] else x :: take_until f xs; |
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312 |
fun is_dict (Const (c, _)) = |
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(is_some o CodeName.class_rev thy) c |
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314 |
orelse (is_some o CodeName.classrel_rev thy) c |
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315 |
orelse (is_some o CodeName.instance_rev thy) c |
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316 |
| is_dict (DFree _) = true |
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317 |
| is_dict _ = false; |
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fun of_apps bounds (t, ts) = |
319 |
fold_map (of_univ bounds) ts |
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320 |
#>> (fn ts' => list_comb (t, rev ts')) |
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321 |
and of_univ bounds (Const (name, ts)) typidx = |
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322 |
let |
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25101 | 323 |
val ts' = take_until is_dict ts; |
24423
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overloaded definitions accompanied by explicit constants
haftmann
parents:
24381
diff
changeset
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324 |
val SOME c = CodeName.const_rev thy name; |
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overloaded definitions accompanied by explicit constants
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325 |
val T = Code.default_typ thy c; |
24155 | 326 |
val T' = map_type_tvar (fn ((v, i), S) => TypeInfer.param (typidx + i) (v, S)) T; |
327 |
val typidx' = typidx + maxidx_of_typ T' + 1; |
|
25101 | 328 |
in of_apps bounds (Term.Const (c, T'), ts') typidx' end |
24155 | 329 |
| of_univ bounds (Free (name, ts)) typidx = |
330 |
of_apps bounds (Term.Free (name, dummyT), ts) typidx |
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331 |
| of_univ bounds (BVar (name, ts)) typidx = |
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332 |
of_apps bounds (Bound (bounds - name - 1), ts) typidx |
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333 |
| of_univ bounds (t as Abs _) typidx = |
|
334 |
typidx |
|
335 |
|> of_univ (bounds + 1) (app t (BVar (bounds, []))) |
|
336 |
|-> (fn t' => pair (Term.Abs ("u", dummyT, t'))) |
|
337 |
in of_univ 0 t 0 |> fst end; |
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338 |
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25101 | 339 |
(* function store *) |
340 |
||
341 |
structure Nbe_Functions = CodeDataFun |
|
342 |
( |
|
343 |
type T = univ_gr; |
|
344 |
val empty = Graph.empty; |
|
345 |
fun merge _ = Graph.merge (K true); |
|
346 |
fun purge _ NONE _ = Graph.empty |
|
347 |
| purge NONE _ _ = Graph.empty |
|
348 |
| purge (SOME thy) (SOME cs) gr = |
|
349 |
let |
|
350 |
val cs_exisiting = |
|
351 |
map_filter (CodeName.const_rev thy) (Graph.keys gr); |
|
352 |
val dels = (Graph.all_preds gr |
|
353 |
o map (CodeName.const thy) |
|
354 |
o filter (member (op =) cs_exisiting) |
|
355 |
) cs; |
|
356 |
in Graph.del_nodes dels gr end; |
|
357 |
); |
|
358 |
||
359 |
(* compilation, evaluation and reification *) |
|
360 |
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361 |
fun compile_eval thy code vs_ty_t deps = |
|
362 |
(vs_ty_t, deps) |
|
363 |
|> eval_term (Nbe_Functions.change thy (ensure_stmts code)) |
|
364 |
|> term_of_univ thy; |
|
365 |
||
24155 | 366 |
(* evaluation with type reconstruction *) |
367 |
||
24381 | 368 |
fun eval thy code t vs_ty_t deps = |
24155 | 369 |
let |
24347 | 370 |
val ty = type_of t; |
24155 | 371 |
fun subst_Frees [] = I |
372 |
| subst_Frees inst = |
|
373 |
Term.map_aterms (fn (t as Term.Free (s, _)) => the_default t (AList.lookup (op =) inst s) |
|
374 |
| t => t); |
|
375 |
val anno_vars = |
|
376 |
subst_Frees (map (fn (s, T) => (s, Term.Free (s, T))) (Term.add_frees t [])) |
|
377 |
#> subst_Vars (map (fn (ixn, T) => (ixn, Var (ixn, T))) (Term.add_vars t [])) |
|
24347 | 378 |
fun constrain t = |
24680 | 379 |
singleton (Syntax.check_terms (ProofContext.init thy)) (TypeInfer.constrain ty t); |
24155 | 380 |
fun check_tvars t = if null (Term.term_tvars t) then t else |
381 |
error ("Illegal schematic type variables in normalized term: " |
|
382 |
^ setmp show_types true (Sign.string_of_term thy) t); |
|
383 |
in |
|
25101 | 384 |
compile_eval thy code vs_ty_t deps |
24155 | 385 |
|> tracing (fn t => "Normalized:\n" ^ setmp show_types true Display.raw_string_of_term t) |
386 |
|> anno_vars |
|
387 |
|> tracing (fn t => "Vars typed:\n" ^ setmp show_types true Display.raw_string_of_term t) |
|
388 |
|> constrain |
|
389 |
|> tracing (fn t => "Types inferred:\n" ^ setmp show_types true Display.raw_string_of_term t) |
|
25101 | 390 |
|> tracing (fn t => "---\n") |
24155 | 391 |
|> check_tvars |
392 |
end; |
|
393 |
||
394 |
(* evaluation oracle *) |
|
395 |
||
24839 | 396 |
exception Norm of CodeThingol.code * term |
24381 | 397 |
* (CodeThingol.typscheme * CodeThingol.iterm) * string list; |
24155 | 398 |
|
24839 | 399 |
fun norm_oracle (thy, Norm (code, t, vs_ty_t, deps)) = |
24381 | 400 |
Logic.mk_equals (t, eval thy code t vs_ty_t deps); |
24155 | 401 |
|
24839 | 402 |
fun norm_invoke thy code t vs_ty_t deps = |
403 |
Thm.invoke_oracle_i thy "HOL.norm" (thy, Norm (code, t, vs_ty_t, deps)); |
|
24283 | 404 |
(*FIXME get rid of hardwired theory name*) |
24155 | 405 |
|
24839 | 406 |
fun norm_conv ct = |
24155 | 407 |
let |
408 |
val thy = Thm.theory_of_cterm ct; |
|
24381 | 409 |
fun conv code vs_ty_t deps ct = |
24155 | 410 |
let |
411 |
val t = Thm.term_of ct; |
|
24839 | 412 |
in norm_invoke thy code t vs_ty_t deps end; |
24219 | 413 |
in CodePackage.eval_conv thy conv ct end; |
24155 | 414 |
|
24839 | 415 |
fun norm_term thy = |
416 |
let |
|
417 |
fun invoke code vs_ty_t deps t = |
|
418 |
eval thy code t vs_ty_t deps; |
|
419 |
in CodePackage.eval_term thy invoke #> Code.postprocess_term thy end; |
|
420 |
||
24155 | 421 |
(* evaluation command *) |
422 |
||
423 |
fun norm_print_term ctxt modes t = |
|
424 |
let |
|
425 |
val thy = ProofContext.theory_of ctxt; |
|
24839 | 426 |
val t' = norm_term thy t; |
427 |
val ty' = Term.type_of t'; |
|
24634 | 428 |
val p = PrintMode.with_modes modes (fn () => |
24920 | 429 |
Pretty.block [Pretty.quote (Syntax.pretty_term ctxt t'), Pretty.fbrk, |
430 |
Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt ty')]) (); |
|
24155 | 431 |
in Pretty.writeln p end; |
432 |
||
433 |
||
434 |
(** Isar setup **) |
|
435 |
||
24508
c8b82fec6447
replaced ProofContext.read_term/prop by general Syntax.read_term/prop;
wenzelm
parents:
24493
diff
changeset
|
436 |
fun norm_print_term_cmd (modes, s) state = |
24155 | 437 |
let val ctxt = Toplevel.context_of state |
24508
c8b82fec6447
replaced ProofContext.read_term/prop by general Syntax.read_term/prop;
wenzelm
parents:
24493
diff
changeset
|
438 |
in norm_print_term ctxt modes (Syntax.read_term ctxt s) end; |
24155 | 439 |
|
24839 | 440 |
val setup = Theory.add_oracle ("norm", norm_oracle) |
24155 | 441 |
|
442 |
local structure P = OuterParse and K = OuterKeyword in |
|
443 |
||
444 |
val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) []; |
|
445 |
||
24867 | 446 |
val _ = |
24155 | 447 |
OuterSyntax.improper_command "normal_form" "normalize term by evaluation" K.diag |
448 |
(opt_modes -- P.typ >> (Toplevel.keep o norm_print_term_cmd)); |
|
449 |
||
450 |
end; |
|
451 |
||
452 |
end; |