(* Title: Tools/Compute_Oracle/compute.ML ID: $Id: compute.ML,v 1.7 2007/10/27 16:38:42 obua Exp $ Author: Steven Obua *) signature COMPUTE = sig type computer type theorem type naming = int -> string datatype machine = BARRAS | BARRAS_COMPILED | HASKELL | SML (* Functions designated with a ! in front of them actually update the computer parameter *) exception Make of string val make : machine -> theory -> thm list -> computer val theory_of : computer -> theory val hyps_of : computer -> term list val shyps_of : computer -> sort list (* ! *) val update : computer -> thm list -> unit (* ! *) val discard : computer -> unit (* ! *) val set_naming : computer -> naming -> unit val naming_of : computer -> naming exception Compute of string val simplify : computer -> theorem -> thm val rewrite : computer -> cterm -> thm val make_theorem : computer -> thm -> string list -> theorem (* ! *) val instantiate : computer -> (string * cterm) list -> theorem -> theorem (* ! *) val evaluate_prem : computer -> int -> theorem -> theorem (* ! *) val modus_ponens : computer -> int -> thm -> theorem -> theorem val setup_compute : theory -> theory end structure Compute :> COMPUTE = struct open Report; datatype machine = BARRAS | BARRAS_COMPILED | HASKELL | SML (* Terms are mapped to integer codes *) structure Encode :> sig type encoding val empty : encoding val insert : term -> encoding -> int * encoding val lookup_code : term -> encoding -> int option val lookup_term : int -> encoding -> term option val remove_code : int -> encoding -> encoding val remove_term : term -> encoding -> encoding val fold : ((term * int) -> 'a -> 'a) -> encoding -> 'a -> 'a end = struct type encoding = int * (int Termtab.table) * (term Inttab.table) val empty = (0, Termtab.empty, Inttab.empty) fun insert t (e as (count, term2int, int2term)) = (case Termtab.lookup term2int t of NONE => (count, (count+1, Termtab.update_new (t, count) term2int, Inttab.update_new (count, t) int2term)) | SOME code => (code, e)) fun lookup_code t (_, term2int, _) = Termtab.lookup term2int t fun lookup_term c (_, _, int2term) = Inttab.lookup int2term c fun remove_code c (e as (count, term2int, int2term)) = (case lookup_term c e of NONE => e | SOME t => (count, Termtab.delete t term2int, Inttab.delete c int2term)) fun remove_term t (e as (count, term2int, int2term)) = (case lookup_code t e of NONE => e | SOME c => (count, Termtab.delete t term2int, Inttab.delete c int2term)) fun fold f (_, term2int, _) = Termtab.fold f term2int end exception Make of string; exception Compute of string; local fun make_constant t ty encoding = let val (code, encoding) = Encode.insert t encoding in (encoding, AbstractMachine.Const code) end in fun remove_types encoding t = case t of Var (_, ty) => make_constant t ty encoding | Free (_, ty) => make_constant t ty encoding | Const (_, ty) => make_constant t ty encoding | Abs (_, ty, t') => let val (encoding, t'') = remove_types encoding t' in (encoding, AbstractMachine.Abs t'') end | a $ b => let val (encoding, a) = remove_types encoding a val (encoding, b) = remove_types encoding b in (encoding, AbstractMachine.App (a,b)) end | Bound b => (encoding, AbstractMachine.Var b) end local fun type_of (Free (_, ty)) = ty | type_of (Const (_, ty)) = ty | type_of (Var (_, ty)) = ty | type_of _ = sys_error "infer_types: type_of error" in fun infer_types naming encoding = let fun infer_types _ bounds _ (AbstractMachine.Var v) = (Bound v, List.nth (bounds, v)) | infer_types _ bounds _ (AbstractMachine.Const code) = let val c = the (Encode.lookup_term code encoding) in (c, type_of c) end | infer_types level bounds _ (AbstractMachine.App (a, b)) = let val (a, aty) = infer_types level bounds NONE a val (adom, arange) = case aty of Type ("fun", [dom, range]) => (dom, range) | _ => sys_error "infer_types: function type expected" val (b, bty) = infer_types level bounds (SOME adom) b in (a $ b, arange) end | infer_types level bounds (SOME (ty as Type ("fun", [dom, range]))) (AbstractMachine.Abs m) = let val (m, _) = infer_types (level+1) (dom::bounds) (SOME range) m in (Abs (naming level, dom, m), ty) end | infer_types _ _ NONE (AbstractMachine.Abs m) = sys_error "infer_types: cannot infer type of abstraction" fun infer ty term = let val (term', _) = infer_types 0 [] (SOME ty) term in term' end in infer end end datatype prog = ProgBarras of AM_Interpreter.program | ProgBarrasC of AM_Compiler.program | ProgHaskell of AM_GHC.program | ProgSML of AM_SML.program fun machine_of_prog (ProgBarras _) = BARRAS | machine_of_prog (ProgBarrasC _) = BARRAS_COMPILED | machine_of_prog (ProgHaskell _) = HASKELL | machine_of_prog (ProgSML _) = SML structure Sorttab = TableFun(type key = sort val ord = Term.sort_ord) type naming = int -> string fun default_naming i = "v_" ^ Int.toString i datatype computer = Computer of (theory_ref * Encode.encoding * term list * unit Sorttab.table * prog * unit ref * naming) option ref fun theory_of (Computer (ref (SOME (rthy,_,_,_,_,_,_)))) = Theory.deref rthy fun hyps_of (Computer (ref (SOME (_,_,hyps,_,_,_,_)))) = hyps fun shyps_of (Computer (ref (SOME (_,_,_,shyptable,_,_,_)))) = Sorttab.keys (shyptable) fun shyptab_of (Computer (ref (SOME (_,_,_,shyptable,_,_,_)))) = shyptable fun stamp_of (Computer (ref (SOME (_,_,_,_,_,stamp,_)))) = stamp fun prog_of (Computer (ref (SOME (_,_,_,_,prog,_,_)))) = prog fun encoding_of (Computer (ref (SOME (_,encoding,_,_,_,_,_)))) = encoding fun set_encoding (Computer (r as ref (SOME (p1,encoding,p2,p3,p4,p5,p6)))) encoding' = (r := SOME (p1,encoding',p2,p3,p4,p5,p6)) fun naming_of (Computer (ref (SOME (_,_,_,_,_,_,n)))) = n fun set_naming (Computer (r as ref (SOME (p1,p2,p3,p4,p5,p6,naming)))) naming'= (r := SOME (p1,p2,p3,p4,p5,p6,naming')) fun ref_of (Computer r) = r datatype cthm = ComputeThm of term list * sort list * term fun thm2cthm th = let val {hyps, prop, tpairs, shyps, ...} = Thm.rep_thm th val _ = if not (null tpairs) then raise Make "theorems may not contain tpairs" else () in ComputeThm (hyps, shyps, prop) end fun make_internal machine thy stamp encoding raw_ths = let fun transfer (x:thm) = Thm.transfer thy x val ths = map (thm2cthm o Thm.strip_shyps o transfer) raw_ths fun thm2rule (encoding, hyptable, shyptable) th = let val (ComputeThm (hyps, shyps, prop)) = th val hyptable = fold (fn h => Termtab.update (h, ())) hyps hyptable val shyptable = fold (fn sh => Sorttab.update (sh, ())) shyps shyptable val (prems, prop) = (Logic.strip_imp_prems prop, Logic.strip_imp_concl prop) val (a, b) = Logic.dest_equals prop handle TERM _ => raise (Make "theorems must be meta-level equations (with optional guards)") val a = Envir.eta_contract a val b = Envir.eta_contract b val prems = map Envir.eta_contract prems val (encoding, left) = remove_types encoding a val (encoding, right) = remove_types encoding b fun remove_types_of_guard encoding g = (let val (t1, t2) = Logic.dest_equals g val (encoding, t1) = remove_types encoding t1 val (encoding, t2) = remove_types encoding t2 in (encoding, AbstractMachine.Guard (t1, t2)) end handle TERM _ => raise (Make "guards must be meta-level equations")) val (encoding, prems) = fold_rev (fn p => fn (encoding, ps) => let val (e, p) = remove_types_of_guard encoding p in (e, p::ps) end) prems (encoding, []) fun make_pattern encoding n vars (var as AbstractMachine.Abs _) = raise (Make "no lambda abstractions allowed in pattern") | make_pattern encoding n vars (var as AbstractMachine.Var _) = raise (Make "no bound variables allowed in pattern") | make_pattern encoding n vars (AbstractMachine.Const code) = (case the (Encode.lookup_term code encoding) of Var _ => ((n+1, Inttab.update_new (code, n) vars, AbstractMachine.PVar) handle Inttab.DUP _ => raise (Make "no duplicate variable in pattern allowed")) | _ => (n, vars, AbstractMachine.PConst (code, []))) | make_pattern encoding n vars (AbstractMachine.App (a, b)) = let val (n, vars, pa) = make_pattern encoding n vars a val (n, vars, pb) = make_pattern encoding n vars b in case pa of AbstractMachine.PVar => raise (Make "patterns may not start with a variable") | AbstractMachine.PConst (c, args) => (n, vars, AbstractMachine.PConst (c, args@[pb])) end (* Principally, a check should be made here to see if the (meta-) hyps contain any of the variables of the rule. As it is, all variables of the rule are schematic, and there are no schematic variables in meta-hyps, therefore this check can be left out. *) val (vcount, vars, pattern) = make_pattern encoding 0 Inttab.empty left val _ = (case pattern of AbstractMachine.PVar => raise (Make "patterns may not start with a variable") (* | AbstractMachine.PConst (_, []) => (print th; raise (Make "no parameter rewrite found"))*) | _ => ()) (* finally, provide a function for renaming the pattern bound variables on the right hand side *) fun rename level vars (var as AbstractMachine.Var _) = var | rename level vars (c as AbstractMachine.Const code) = (case Inttab.lookup vars code of NONE => c | SOME n => AbstractMachine.Var (vcount-n-1+level)) | rename level vars (AbstractMachine.App (a, b)) = AbstractMachine.App (rename level vars a, rename level vars b) | rename level vars (AbstractMachine.Abs m) = AbstractMachine.Abs (rename (level+1) vars m) fun rename_guard (AbstractMachine.Guard (a,b)) = AbstractMachine.Guard (rename 0 vars a, rename 0 vars b) in ((encoding, hyptable, shyptable), (map rename_guard prems, pattern, rename 0 vars right)) end val ((encoding, hyptable, shyptable), rules) = fold_rev (fn th => fn (encoding_hyptable, rules) => let val (encoding_hyptable, rule) = thm2rule encoding_hyptable th in (encoding_hyptable, rule::rules) end) ths ((encoding, Termtab.empty, Sorttab.empty), []) val prog = case machine of BARRAS => ProgBarras (AM_Interpreter.compile rules) | BARRAS_COMPILED => ProgBarrasC (AM_Compiler.compile rules) | HASKELL => ProgHaskell (AM_GHC.compile rules) | SML => ProgSML (AM_SML.compile rules) fun has_witness s = not (null (Sign.witness_sorts thy [] [s])) val shyptable = fold Sorttab.delete (filter has_witness (Sorttab.keys (shyptable))) shyptable in (Theory.check_thy thy, encoding, Termtab.keys hyptable, shyptable, prog, stamp, default_naming) end fun make machine thy raw_thms = Computer (ref (SOME (make_internal machine thy (ref ()) Encode.empty raw_thms))) fun update computer raw_thms = let val c = make_internal (machine_of_prog (prog_of computer)) (theory_of computer) (stamp_of computer) (encoding_of computer) raw_thms val _ = (ref_of computer) := SOME c in () end fun discard computer = let val _ = case prog_of computer of ProgBarras p => AM_Interpreter.discard p | ProgBarrasC p => AM_Compiler.discard p | ProgHaskell p => AM_GHC.discard p | ProgSML p => AM_SML.discard p val _ = (ref_of computer) := NONE in () end fun runprog (ProgBarras p) = AM_Interpreter.run p | runprog (ProgBarrasC p) = AM_Compiler.run p | runprog (ProgHaskell p) = AM_GHC.run p | runprog (ProgSML p) = AM_SML.run p (* ------------------------------------------------------------------------------------- *) (* An oracle for exporting theorems; must only be accessible from inside this structure! *) (* ------------------------------------------------------------------------------------- *) exception ExportThm of term list * sort list * term fun merge_hyps hyps1 hyps2 = let fun add hyps tab = fold (fn h => fn tab => Termtab.update (h, ()) tab) hyps tab in Termtab.keys (add hyps2 (add hyps1 Termtab.empty)) end fun add_shyps shyps tab = fold (fn h => fn tab => Sorttab.update (h, ()) tab) shyps tab fun merge_shyps shyps1 shyps2 = Sorttab.keys (add_shyps shyps2 (add_shyps shyps1 Sorttab.empty)) fun export_oracle (thy, ExportThm (hyps, shyps, prop)) = let val shyptab = add_shyps shyps Sorttab.empty fun delete s shyptab = Sorttab.delete s shyptab handle Sorttab.UNDEF _ => shyptab fun delete_term t shyptab = fold delete (Sorts.insert_term t []) shyptab fun has_witness s = not (null (Sign.witness_sorts thy [] [s])) val shyptab = fold Sorttab.delete (filter has_witness (Sorttab.keys (shyptab))) shyptab val shyps = if Sorttab.is_empty shyptab then [] else Sorttab.keys (fold delete_term (prop::hyps) shyptab) val _ = if not (null shyps) then raise Compute ("dangling sort hypotheses: "^(makestring shyps)) else () in fold_rev (fn hyp => fn p => Logic.mk_implies (hyp, p)) hyps prop end | export_oracle _ = raise Match val setup_compute = (fn thy => Theory.add_oracle ("compute", export_oracle) thy) fun export_thm thy hyps shyps prop = let val th = invoke_oracle_i thy "Compute_Oracle.compute" (thy, ExportThm (hyps, shyps, prop)) val hyps = map (fn h => assume (cterm_of thy h)) hyps in fold (fn h => fn p => implies_elim p h) hyps th end (* --------- Rewrite ----------- *) fun rewrite computer ct = let val {t=t',T=ty,thy=thy,...} = rep_cterm ct val _ = Theory.assert_super (theory_of computer) thy val naming = naming_of computer val (encoding, t) = remove_types (encoding_of computer) t' (*val _ = if (!print_encoding) then writeln (makestring ("encoding: ",Encode.fold (fn x => fn s => x::s) encoding [])) else ()*) val t = runprog (prog_of computer) t val t = infer_types naming encoding ty t val eq = Logic.mk_equals (t', t) in export_thm thy (hyps_of computer) (Sorttab.keys (shyptab_of computer)) eq end (* --------- Simplify ------------ *) datatype prem = EqPrem of AbstractMachine.term * AbstractMachine.term * Term.typ * int | Prem of AbstractMachine.term datatype theorem = Theorem of theory_ref * unit ref * (int * typ) Symtab.table * (AbstractMachine.term option) Inttab.table * prem list * AbstractMachine.term * term list * sort list exception ParamSimplify of computer * theorem fun make_theorem computer th vars = let val _ = Theory.assert_super (theory_of computer) (theory_of_thm th) val (ComputeThm (hyps, shyps, prop)) = thm2cthm th val encoding = encoding_of computer (* variables in the theorem are identified upfront *) fun collect_vars (Abs (_, _, t)) tab = collect_vars t tab | collect_vars (a $ b) tab = collect_vars b (collect_vars a tab) | collect_vars (Const _) tab = tab | collect_vars (Free _) tab = tab | collect_vars (Var ((s, i), ty)) tab = if List.find (fn x => x=s) vars = NONE then tab else (case Symtab.lookup tab s of SOME ((s',i'),ty') => if s' <> s orelse i' <> i orelse ty <> ty' then raise Compute ("make_theorem: variable name '"^s^"' is not unique") else tab | NONE => Symtab.update (s, ((s, i), ty)) tab) val vartab = collect_vars prop Symtab.empty fun encodevar (s, t as (_, ty)) (encoding, tab) = let val (x, encoding) = Encode.insert (Var t) encoding in (encoding, Symtab.update (s, (x, ty)) tab) end val (encoding, vartab) = Symtab.fold encodevar vartab (encoding, Symtab.empty) val varsubst = Inttab.make (map (fn (s, (x, _)) => (x, NONE)) (Symtab.dest vartab)) (* make the premises and the conclusion *) fun mk_prem encoding t = (let val (a, b) = Logic.dest_equals t val ty = type_of a val (encoding, a) = remove_types encoding a val (encoding, b) = remove_types encoding b val (eq, encoding) = Encode.insert (Const ("==", ty --> ty --> @{typ "prop"})) encoding in (encoding, EqPrem (a, b, ty, eq)) end handle TERM _ => let val (encoding, t) = remove_types encoding t in (encoding, Prem t) end) val (encoding, prems) = (fold_rev (fn t => fn (encoding, l) => case mk_prem encoding t of (encoding, t) => (encoding, t::l)) (Logic.strip_imp_prems prop) (encoding, [])) val (encoding, concl) = remove_types encoding (Logic.strip_imp_concl prop) val _ = set_encoding computer encoding in Theorem (Theory.check_thy (theory_of_thm th), stamp_of computer, vartab, varsubst, prems, concl, hyps, shyps) end fun theory_of_theorem (Theorem (rthy,_,_,_,_,_,_,_)) = Theory.deref rthy fun update_theory thy (Theorem (_,p0,p1,p2,p3,p4,p5,p6)) = Theorem (Theory.check_thy thy,p0,p1,p2,p3,p4,p5,p6) fun stamp_of_theorem (Theorem (_,s, _, _, _, _, _, _)) = s fun vartab_of_theorem (Theorem (_,_,vt,_,_,_,_,_)) = vt fun varsubst_of_theorem (Theorem (_,_,_,vs,_,_,_,_)) = vs fun update_varsubst vs (Theorem (p0,p1,p2,_,p3,p4,p5,p6)) = Theorem (p0,p1,p2,vs,p3,p4,p5,p6) fun prems_of_theorem (Theorem (_,_,_,_,prems,_,_,_)) = prems fun update_prems prems (Theorem (p0,p1,p2,p3,_,p4,p5,p6)) = Theorem (p0,p1,p2,p3,prems,p4,p5,p6) fun concl_of_theorem (Theorem (_,_,_,_,_,concl,_,_)) = concl fun hyps_of_theorem (Theorem (_,_,_,_,_,_,hyps,_)) = hyps fun update_hyps hyps (Theorem (p0,p1,p2,p3,p4,p5,_,p6)) = Theorem (p0,p1,p2,p3,p4,p5,hyps,p6) fun shyps_of_theorem (Theorem (_,_,_,_,_,_,_,shyps)) = shyps fun update_shyps shyps (Theorem (p0,p1,p2,p3,p4,p5,p6,_)) = Theorem (p0,p1,p2,p3,p4,p5,p6,shyps) fun check_compatible computer th s = if stamp_of computer <> stamp_of_theorem th then raise Compute (s^": computer and theorem are incompatible") else () fun instantiate computer insts th = let val _ = check_compatible computer th val thy = theory_of computer val vartab = vartab_of_theorem th fun rewrite computer t = let val naming = naming_of computer val (encoding, t) = remove_types (encoding_of computer) t val t = runprog (prog_of computer) t val _ = set_encoding computer encoding in t end fun assert_varfree vs t = if AbstractMachine.forall_consts (fn x => Inttab.lookup vs x = NONE) t then () else raise Compute "instantiate: assert_varfree failed" fun assert_closed t = if AbstractMachine.closed t then () else raise Compute "instantiate: not a closed term" fun compute_inst (s, ct) vs = let val _ = Theory.assert_super (theory_of_cterm ct) thy val ty = typ_of (ctyp_of_term ct) in (case Symtab.lookup vartab s of NONE => raise Compute ("instantiate: variable '"^s^"' not found in theorem") | SOME (x, ty') => (case Inttab.lookup vs x of SOME (SOME _) => raise Compute ("instantiate: variable '"^s^"' has already been instantiated") | SOME NONE => if ty <> ty' then raise Compute ("instantiate: wrong type for variable '"^s^"'") else let val t = rewrite computer (term_of ct) val _ = assert_varfree vs t val _ = assert_closed t in Inttab.update (x, SOME t) vs end | NONE => raise Compute "instantiate: internal error")) end val vs = fold compute_inst insts (varsubst_of_theorem th) in update_varsubst vs th end fun match_aterms subst = let exception no_match open AbstractMachine fun match subst (b as (Const c)) a = if a = b then subst else (case Inttab.lookup subst c of SOME (SOME a') => if a=a' then subst else raise no_match | SOME NONE => if AbstractMachine.closed a then Inttab.update (c, SOME a) subst else raise no_match | NONE => raise no_match) | match subst (b as (Var _)) a = if a=b then subst else raise no_match | match subst (App (u, v)) (App (u', v')) = match (match subst u u') v v' | match subst (Abs u) (Abs u') = match subst u u' | match subst _ _ = raise no_match in fn b => fn a => (SOME (match subst b a) handle no_match => NONE) end fun apply_subst vars_allowed subst = let open AbstractMachine fun app (t as (Const c)) = (case Inttab.lookup subst c of NONE => t | SOME (SOME t) => Computed t | SOME NONE => if vars_allowed then t else raise Compute "apply_subst: no vars allowed") | app (t as (Var _)) = t | app (App (u, v)) = App (app u, app v) | app (Abs m) = Abs (app m) in app end fun splicein n l L = List.take (L, n) @ l @ List.drop (L, n+1) fun evaluate_prem computer prem_no th = let val _ = check_compatible computer th val prems = prems_of_theorem th val varsubst = varsubst_of_theorem th fun run vars_allowed t = runprog (prog_of computer) (apply_subst vars_allowed varsubst t) in case List.nth (prems, prem_no) of Prem _ => raise Compute "evaluate_prem: no equality premise" | EqPrem (a, b, ty, _) => let val a' = run false a val b' = run true b in case match_aterms varsubst b' a' of NONE => let fun mk s = makestring (infer_types (naming_of computer) (encoding_of computer) ty s) val left = "computed left side: "^(mk a') val right = "computed right side: "^(mk b') in raise Compute ("evaluate_prem: cannot assign computed left to right hand side\n"^left^"\n"^right^"\n") end | SOME varsubst => update_prems (splicein prem_no [] prems) (update_varsubst varsubst th) end end fun prem2term (Prem t) = t | prem2term (EqPrem (a,b,_,eq)) = AbstractMachine.App (AbstractMachine.App (AbstractMachine.Const eq, a), b) fun modus_ponens computer prem_no th' th = let val _ = check_compatible computer th val thy = let val thy1 = theory_of_theorem th val thy2 = theory_of_thm th' in if Context.subthy (thy1, thy2) then thy2 else if Context.subthy (thy2, thy1) then thy1 else raise Compute "modus_ponens: theorems are not compatible with each other" end val th' = make_theorem computer th' [] val varsubst = varsubst_of_theorem th fun run vars_allowed t = runprog (prog_of computer) (apply_subst vars_allowed varsubst t) val prems = prems_of_theorem th val prem = run true (prem2term (List.nth (prems, prem_no))) val concl = run false (concl_of_theorem th') in case match_aterms varsubst prem concl of NONE => raise Compute "modus_ponens: conclusion does not match premise" | SOME varsubst => let val th = update_varsubst varsubst th val th = update_prems (splicein prem_no (prems_of_theorem th') prems) th val th = update_hyps (merge_hyps (hyps_of_theorem th) (hyps_of_theorem th')) th val th = update_shyps (merge_shyps (shyps_of_theorem th) (shyps_of_theorem th')) th in update_theory thy th end end fun simplify computer th = let val _ = check_compatible computer th val varsubst = varsubst_of_theorem th val encoding = encoding_of computer val naming = naming_of computer fun infer t = infer_types naming encoding @{typ "prop"} t fun run t = infer (runprog (prog_of computer) (apply_subst true varsubst t)) fun runprem p = run (prem2term p) val prop = Logic.list_implies (map runprem (prems_of_theorem th), run (concl_of_theorem th)) val hyps = merge_hyps (hyps_of computer) (hyps_of_theorem th) val shyps = merge_shyps (shyps_of_theorem th) (Sorttab.keys (shyptab_of computer)) in export_thm (theory_of_theorem th) hyps shyps prop end end