--- a/src/HOL/HOLCF/Tools/fixrec.ML Tue Nov 30 14:01:49 2010 -0800
+++ b/src/HOL/HOLCF/Tools/fixrec.ML Tue Nov 30 14:21:57 2010 -0800
@@ -13,23 +13,23 @@
val add_matchers: (string * string) list -> theory -> theory
val fixrec_simp_tac: Proof.context -> int -> tactic
val setup: theory -> theory
-end;
+end
structure Fixrec :> FIXREC =
struct
-open HOLCF_Library;
+open HOLCF_Library
-infixr 6 ->>;
-infix -->>;
-infix 9 `;
+infixr 6 ->>
+infix -->>
+infix 9 `
-val def_cont_fix_eq = @{thm def_cont_fix_eq};
-val def_cont_fix_ind = @{thm def_cont_fix_ind};
+val def_cont_fix_eq = @{thm def_cont_fix_eq}
+val def_cont_fix_ind = @{thm def_cont_fix_ind}
-fun fixrec_err s = error ("fixrec definition error:\n" ^ s);
+fun fixrec_err s = error ("fixrec definition error:\n" ^ s)
fun fixrec_eq_err thy s eq =
- fixrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
+ fixrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq))
(*************************************************************************)
(***************************** building types ****************************)
@@ -39,19 +39,19 @@
fun binder_cfun (Type(@{type_name cfun},[T, U])) = T :: binder_cfun U
| binder_cfun (Type(@{type_name "fun"},[T, U])) = T :: binder_cfun U
- | binder_cfun _ = [];
+ | binder_cfun _ = []
fun body_cfun (Type(@{type_name cfun},[T, U])) = body_cfun U
| body_cfun (Type(@{type_name "fun"},[T, U])) = body_cfun U
- | body_cfun T = T;
+ | body_cfun T = T
fun strip_cfun T : typ list * typ =
- (binder_cfun T, body_cfun T);
+ (binder_cfun T, body_cfun T)
in
fun matcherT (T, U) =
- body_cfun T ->> (binder_cfun T -->> U) ->> U;
+ body_cfun T ->> (binder_cfun T -->> U) ->> U
end
@@ -59,21 +59,21 @@
(***************************** building terms ****************************)
(*************************************************************************)
-val mk_trp = HOLogic.mk_Trueprop;
+val mk_trp = HOLogic.mk_Trueprop
(* splits a cterm into the right and lefthand sides of equality *)
-fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t);
+fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t)
(* similar to Thm.head_of, but for continuous application *)
fun chead_of (Const(@{const_name Rep_cfun},_)$f$t) = chead_of f
- | chead_of u = u;
+ | chead_of u = u
-infix 0 ==; val (op ==) = Logic.mk_equals;
-infix 1 ===; val (op ===) = HOLogic.mk_eq;
+infix 0 == val (op ==) = Logic.mk_equals
+infix 1 === val (op ===) = HOLogic.mk_eq
fun mk_mplus (t, u) =
let val mT = Term.fastype_of t
- in Const(@{const_name Fixrec.mplus}, mT ->> mT ->> mT) ` t ` u end;
+ in Const(@{const_name Fixrec.mplus}, mT ->> mT ->> mT) ` t ` u end
fun mk_run t =
let
@@ -85,7 +85,7 @@
Const(@{const_name Rep_cfun}, _) $
Const(@{const_name Fixrec.succeed}, _) $ u => u
| _ => run ` t
- end;
+ end
(*************************************************************************)
@@ -94,26 +94,26 @@
structure FixrecUnfoldData = Generic_Data
(
- type T = thm Symtab.table;
- val empty = Symtab.empty;
- val extend = I;
- fun merge data : T = Symtab.merge (K true) data;
-);
+ type T = thm Symtab.table
+ val empty = Symtab.empty
+ val extend = I
+ fun merge data : T = Symtab.merge (K true) data
+)
local
fun name_of (Const (n, T)) = n
| name_of (Free (n, T)) = n
- | name_of t = raise TERM ("Fixrec.add_unfold: lhs not a constant", [t]);
+ | name_of t = raise TERM ("Fixrec.add_unfold: lhs not a constant", [t])
val lhs_name =
- name_of o head_of o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of;
+ name_of o head_of o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of
in
val add_unfold : attribute =
Thm.declaration_attribute
- (fn th => FixrecUnfoldData.map (Symtab.insert (K true) (lhs_name th, th)));
+ (fn th => FixrecUnfoldData.map (Symtab.insert (K true) (lhs_name th, th)))
end
@@ -122,73 +122,73 @@
(spec : (Attrib.binding * term) list)
(lthy : local_theory) =
let
- val thy = ProofContext.theory_of lthy;
- val names = map (Binding.name_of o fst o fst) fixes;
- val all_names = space_implode "_" names;
- val (lhss, rhss) = ListPair.unzip (map (dest_eqs o snd) spec);
- val functional = lambda_tuple lhss (mk_tuple rhss);
- val fixpoint = mk_fix (mk_cabs functional);
+ val thy = ProofContext.theory_of lthy
+ val names = map (Binding.name_of o fst o fst) fixes
+ val all_names = space_implode "_" names
+ val (lhss, rhss) = ListPair.unzip (map (dest_eqs o snd) spec)
+ val functional = lambda_tuple lhss (mk_tuple rhss)
+ val fixpoint = mk_fix (mk_cabs functional)
val cont_thm =
let
- val prop = mk_trp (mk_cont functional);
+ val prop = mk_trp (mk_cont functional)
fun err _ = error (
- "Continuity proof failed; please check that cont2cont rules\n" ^
+ "Continuity proof failed please check that cont2cont rules\n" ^
"or simp rules are configured for all non-HOLCF constants.\n" ^
"The error occurred for the goal statement:\n" ^
- Syntax.string_of_term lthy prop);
- val rules = Cont2ContData.get lthy;
- val fast_tac = SOLVED' (REPEAT_ALL_NEW (match_tac rules));
- val slow_tac = SOLVED' (simp_tac (simpset_of lthy));
- val tac = fast_tac 1 ORELSE slow_tac 1 ORELSE err;
+ Syntax.string_of_term lthy prop)
+ val rules = Cont2ContData.get lthy
+ val fast_tac = SOLVED' (REPEAT_ALL_NEW (match_tac rules))
+ val slow_tac = SOLVED' (simp_tac (simpset_of lthy))
+ val tac = fast_tac 1 ORELSE slow_tac 1 ORELSE err
in
Goal.prove lthy [] [] prop (K tac)
- end;
+ end
fun one_def (l as Free(n,_)) r =
let val b = Long_Name.base_name n
in ((Binding.name (b^"_def"), []), r) end
- | one_def _ _ = fixrec_err "fixdefs: lhs not of correct form";
+ | one_def _ _ = fixrec_err "fixdefs: lhs not of correct form"
fun defs [] _ = []
| defs (l::[]) r = [one_def l r]
- | defs (l::ls) r = one_def l (mk_fst r) :: defs ls (mk_snd r);
- val fixdefs = defs lhss fixpoint;
+ | defs (l::ls) r = one_def l (mk_fst r) :: defs ls (mk_snd r)
+ val fixdefs = defs lhss fixpoint
val (fixdef_thms : (term * (string * thm)) list, lthy) = lthy
- |> fold_map Local_Theory.define (map (apfst fst) fixes ~~ fixdefs);
- fun pair_equalI (thm1, thm2) = @{thm Pair_equalI} OF [thm1, thm2];
- val tuple_fixdef_thm = foldr1 pair_equalI (map (snd o snd) fixdef_thms);
- val P = Var (("P", 0), map Term.fastype_of lhss ---> HOLogic.boolT);
- val predicate = lambda_tuple lhss (list_comb (P, lhss));
+ |> fold_map Local_Theory.define (map (apfst fst) fixes ~~ fixdefs)
+ fun pair_equalI (thm1, thm2) = @{thm Pair_equalI} OF [thm1, thm2]
+ val tuple_fixdef_thm = foldr1 pair_equalI (map (snd o snd) fixdef_thms)
+ val P = Var (("P", 0), map Term.fastype_of lhss ---> HOLogic.boolT)
+ val predicate = lambda_tuple lhss (list_comb (P, lhss))
val tuple_induct_thm = (def_cont_fix_ind OF [tuple_fixdef_thm, cont_thm])
|> Drule.instantiate' [] [SOME (Thm.cterm_of thy predicate)]
- |> Local_Defs.unfold lthy @{thms split_paired_all split_conv split_strict};
+ |> Local_Defs.unfold lthy @{thms split_paired_all split_conv split_strict}
val tuple_unfold_thm = (def_cont_fix_eq OF [tuple_fixdef_thm, cont_thm])
- |> Local_Defs.unfold lthy @{thms split_conv};
+ |> Local_Defs.unfold lthy @{thms split_conv}
fun unfolds [] thm = []
| unfolds (n::[]) thm = [(n, thm)]
| unfolds (n::ns) thm = let
- val thmL = thm RS @{thm Pair_eqD1};
- val thmR = thm RS @{thm Pair_eqD2};
- in (n, thmL) :: unfolds ns thmR end;
- val unfold_thms = unfolds names tuple_unfold_thm;
+ val thmL = thm RS @{thm Pair_eqD1}
+ val thmR = thm RS @{thm Pair_eqD2}
+ in (n, thmL) :: unfolds ns thmR end
+ val unfold_thms = unfolds names tuple_unfold_thm
val induct_note : Attrib.binding * Thm.thm list =
let
- val thm_name = Binding.qualify true all_names (Binding.name "induct");
+ val thm_name = Binding.qualify true all_names (Binding.name "induct")
in
((thm_name, []), [tuple_induct_thm])
- end;
+ end
fun unfold_note (name, thm) : Attrib.binding * Thm.thm list =
let
- val thm_name = Binding.qualify true name (Binding.name "unfold");
- val src = Attrib.internal (K add_unfold);
+ val thm_name = Binding.qualify true name (Binding.name "unfold")
+ val src = Attrib.internal (K add_unfold)
in
((thm_name, [src]), [thm])
- end;
+ end
val (thmss, lthy) = lthy
- |> fold_map Local_Theory.note (induct_note :: map unfold_note unfold_thms);
+ |> fold_map Local_Theory.note (induct_note :: map unfold_note unfold_thms)
in
(lthy, names, fixdef_thms, map snd unfold_thms)
- end;
+ end
(*************************************************************************)
(*********** monadic notation and pattern matching compilation ***********)
@@ -196,14 +196,14 @@
structure FixrecMatchData = Theory_Data
(
- type T = string Symtab.table;
- val empty = Symtab.empty;
- val extend = I;
- fun merge data = Symtab.merge (K true) data;
-);
+ type T = string Symtab.table
+ val empty = Symtab.empty
+ val extend = I
+ fun merge data = Symtab.merge (K true) data
+)
(* associate match functions with pattern constants *)
-fun add_matchers ms = FixrecMatchData.map (fold Symtab.update ms);
+fun add_matchers ms = FixrecMatchData.map (fold Symtab.update ms)
fun taken_names (t : term) : bstring list =
let
@@ -211,10 +211,10 @@
| taken (Free(a,_) , bs) = insert (op =) a bs
| taken (f $ u , bs) = taken (f, taken (u, bs))
| taken (Abs(a,_,t), bs) = taken (t, insert (op =) a bs)
- | taken (_ , bs) = bs;
+ | taken (_ , bs) = bs
in
taken (t, [])
- end;
+ end
(* builds a monadic term for matching a pattern *)
(* returns (rhs, free variable, used varnames) *)
@@ -244,87 +244,87 @@
| _ => raise TERM ("fixrec: invalid pattern ", [p])
in
comp_pat pat rhs taken
- end;
+ end
(* builds a monadic term for matching a function definition pattern *)
(* returns (constant, (vars, matcher)) *)
fun compile_lhs match_name pat rhs vs taken =
case pat of
Const(@{const_name Rep_cfun}, _) $ f $ x =>
- let val (rhs', v, taken') = compile_pat match_name x rhs taken;
+ let val (rhs', v, taken') = compile_pat match_name x rhs taken
in compile_lhs match_name f rhs' (v::vs) taken' end
| Free(_,_) => (pat, (vs, rhs))
| Const(_,_) => (pat, (vs, rhs))
| _ => fixrec_err ("invalid function pattern: "
- ^ ML_Syntax.print_term pat);
+ ^ ML_Syntax.print_term pat)
fun strip_alls t =
- if Logic.is_all t then strip_alls (snd (Logic.dest_all t)) else t;
+ if Logic.is_all t then strip_alls (snd (Logic.dest_all t)) else t
fun compile_eq match_name eq =
let
- val (lhs,rhs) = dest_eqs (Logic.strip_imp_concl (strip_alls eq));
+ val (lhs,rhs) = dest_eqs (Logic.strip_imp_concl (strip_alls eq))
in
compile_lhs match_name lhs (mk_succeed rhs) [] (taken_names eq)
- end;
+ end
(* this is the pattern-matching compiler function *)
fun compile_eqs match_name eqs =
let
val (consts, matchers) =
- ListPair.unzip (map (compile_eq match_name) eqs);
+ ListPair.unzip (map (compile_eq match_name) eqs)
val const =
case distinct (op =) consts of
[n] => n
- | _ => fixrec_err "all equations in block must define the same function";
+ | _ => fixrec_err "all equations in block must define the same function"
val vars =
case distinct (op = o pairself length) (map fst matchers) of
[vars] => vars
- | _ => fixrec_err "all equations in block must have the same arity";
+ | _ => fixrec_err "all equations in block must have the same arity"
(* rename so all matchers use same free variables *)
- fun rename (vs, t) = Term.subst_free (filter_out (op =) (vs ~~ vars)) t;
- val rhs = big_lambdas vars (mk_run (foldr1 mk_mplus (map rename matchers)));
+ fun rename (vs, t) = Term.subst_free (filter_out (op =) (vs ~~ vars)) t
+ val rhs = big_lambdas vars (mk_run (foldr1 mk_mplus (map rename matchers)))
in
mk_trp (const === rhs)
- end;
+ end
(*************************************************************************)
(********************** Proving associated theorems **********************)
(*************************************************************************)
-fun eta_tac i = CONVERSION Thm.eta_conversion i;
+fun eta_tac i = CONVERSION Thm.eta_conversion i
fun fixrec_simp_tac ctxt =
let
- val tab = FixrecUnfoldData.get (Context.Proof ctxt);
- val ss = Simplifier.simpset_of ctxt;
+ val tab = FixrecUnfoldData.get (Context.Proof ctxt)
+ val ss = Simplifier.simpset_of ctxt
fun concl t =
if Logic.is_all t then concl (snd (Logic.dest_all t))
- else HOLogic.dest_Trueprop (Logic.strip_imp_concl t);
+ else HOLogic.dest_Trueprop (Logic.strip_imp_concl t)
fun tac (t, i) =
let
val (c, T) =
- (dest_Const o head_of o chead_of o fst o HOLogic.dest_eq o concl) t;
- val unfold_thm = the (Symtab.lookup tab c);
- val rule = unfold_thm RS @{thm ssubst_lhs};
+ (dest_Const o head_of o chead_of o fst o HOLogic.dest_eq o concl) t
+ val unfold_thm = the (Symtab.lookup tab c)
+ val rule = unfold_thm RS @{thm ssubst_lhs}
in
CHANGED (rtac rule i THEN eta_tac i THEN asm_simp_tac ss i)
end
in
SUBGOAL (fn ti => the_default no_tac (try tac ti))
- end;
+ end
(* proves a block of pattern matching equations as theorems, using unfold *)
fun make_simps ctxt (unfold_thm, eqns : (Attrib.binding * term) list) =
let
- val ss = Simplifier.simpset_of ctxt;
- val rule = unfold_thm RS @{thm ssubst_lhs};
- val tac = rtac rule 1 THEN eta_tac 1 THEN asm_simp_tac ss 1;
- fun prove_term t = Goal.prove ctxt [] [] t (K tac);
- fun prove_eqn (bind, eqn_t) = (bind, prove_term eqn_t);
+ val ss = Simplifier.simpset_of ctxt
+ val rule = unfold_thm RS @{thm ssubst_lhs}
+ val tac = rtac rule 1 THEN eta_tac 1 THEN asm_simp_tac ss 1
+ fun prove_term t = Goal.prove ctxt [] [] t (K tac)
+ fun prove_eqn (bind, eqn_t) = (bind, prove_term eqn_t)
in
map prove_eqn eqns
- end;
+ end
(*************************************************************************)
(************************* Main fixrec function **************************)
@@ -339,54 +339,54 @@
(raw_spec' : (bool * (Attrib.binding * 'b)) list)
(lthy : local_theory) =
let
- val (skips, raw_spec) = ListPair.unzip raw_spec';
+ val (skips, raw_spec) = ListPair.unzip raw_spec'
val (fixes : ((binding * typ) * mixfix) list,
spec : (Attrib.binding * term) list) =
- fst (prep_spec raw_fixes raw_spec lthy);
+ fst (prep_spec raw_fixes raw_spec lthy)
val chead_of_spec =
- chead_of o fst o dest_eqs o Logic.strip_imp_concl o strip_alls o snd;
+ chead_of o fst o dest_eqs o Logic.strip_imp_concl o strip_alls o snd
fun name_of (Free (n, _)) = n
- | name_of t = fixrec_err ("unknown term");
- val all_names = map (name_of o chead_of_spec) spec;
- val names = distinct (op =) all_names;
+ | name_of t = fixrec_err ("unknown term")
+ val all_names = map (name_of o chead_of_spec) spec
+ val names = distinct (op =) all_names
fun block_of_name n =
map_filter
(fn (m,eq) => if m = n then SOME eq else NONE)
- (all_names ~~ (spec ~~ skips));
- val blocks = map block_of_name names;
+ (all_names ~~ (spec ~~ skips))
+ val blocks = map block_of_name names
- val matcher_tab = FixrecMatchData.get (ProofContext.theory_of lthy);
+ val matcher_tab = FixrecMatchData.get (ProofContext.theory_of lthy)
fun match_name c =
case Symtab.lookup matcher_tab c of SOME m => m
- | NONE => fixrec_err ("unknown pattern constructor: " ^ c);
+ | NONE => fixrec_err ("unknown pattern constructor: " ^ c)
- val matches = map (compile_eqs match_name) (map (map (snd o fst)) blocks);
- val spec' = map (pair Attrib.empty_binding) matches;
+ val matches = map (compile_eqs match_name) (map (map (snd o fst)) blocks)
+ val spec' = map (pair Attrib.empty_binding) matches
val (lthy, cnames, fixdef_thms, unfold_thms) =
- add_fixdefs fixes spec' lthy;
+ add_fixdefs fixes spec' lthy
- val blocks' = map (map fst o filter_out snd) blocks;
+ val blocks' = map (map fst o filter_out snd) blocks
val simps : (Attrib.binding * thm) list list =
- map (make_simps lthy) (unfold_thms ~~ blocks');
+ map (make_simps lthy) (unfold_thms ~~ blocks')
fun mk_bind n : Attrib.binding =
(Binding.qualify true n (Binding.name "simps"),
- [Attrib.internal (K Simplifier.simp_add)]);
+ [Attrib.internal (K Simplifier.simp_add)])
val simps1 : (Attrib.binding * thm list) list =
- map (fn (n,xs) => (mk_bind n, map snd xs)) (names ~~ simps);
+ map (fn (n,xs) => (mk_bind n, map snd xs)) (names ~~ simps)
val simps2 : (Attrib.binding * thm list) list =
- map (apsnd (fn thm => [thm])) (flat simps);
+ map (apsnd (fn thm => [thm])) (flat simps)
val (_, lthy) = lthy
- |> fold_map Local_Theory.note (simps1 @ simps2);
+ |> fold_map Local_Theory.note (simps1 @ simps2)
in
lthy
- end;
+ end
in
-val add_fixrec = gen_fixrec Specification.check_spec;
-val add_fixrec_cmd = gen_fixrec Specification.read_spec;
+val add_fixrec = gen_fixrec Specification.check_spec
+val add_fixrec_cmd = gen_fixrec Specification.read_spec
-end; (* local *)
+end (* local *)
(*************************************************************************)
@@ -395,23 +395,23 @@
val opt_thm_name' : (bool * Attrib.binding) parser =
Parse.$$$ "(" -- Parse.$$$ "unchecked" -- Parse.$$$ ")" >> K (true, Attrib.empty_binding)
- || Parse_Spec.opt_thm_name ":" >> pair false;
+ || Parse_Spec.opt_thm_name ":" >> pair false
val spec' : (bool * (Attrib.binding * string)) parser =
- opt_thm_name' -- Parse.prop >> (fn ((a, b), c) => (a, (b, c)));
+ opt_thm_name' -- Parse.prop >> (fn ((a, b), c) => (a, (b, c)))
val alt_specs' : (bool * (Attrib.binding * string)) list parser =
- let val unexpected = Scan.ahead (Parse.name || Parse.$$$ "[" || Parse.$$$ "(");
- in Parse.enum1 "|" (spec' --| Scan.option (unexpected -- Parse.!!! (Parse.$$$ "|"))) end;
+ let val unexpected = Scan.ahead (Parse.name || Parse.$$$ "[" || Parse.$$$ "(")
+ in Parse.enum1 "|" (spec' --| Scan.option (unexpected -- Parse.!!! (Parse.$$$ "|"))) end
val _ =
Outer_Syntax.local_theory "fixrec" "define recursive functions (HOLCF)" Keyword.thy_decl
(Parse.fixes -- (Parse.where_ |-- Parse.!!! alt_specs')
- >> (fn (fixes, specs) => add_fixrec_cmd fixes specs));
+ >> (fn (fixes, specs) => add_fixrec_cmd fixes specs))
val setup =
Method.setup @{binding fixrec_simp}
(Scan.succeed (SIMPLE_METHOD' o fixrec_simp_tac))
- "pattern prover for fixrec constants";
+ "pattern prover for fixrec constants"
-end;
+end