--- a/src/HOL/Semiring_Normalization.thy Thu Sep 10 16:42:01 2015 +0200
+++ b/src/HOL/Semiring_Normalization.thy Thu Sep 10 16:44:17 2015 +0200
@@ -72,101 +72,120 @@
context comm_semiring_1
begin
-declaration \<open>
-let
- val rules = @{lemma
- "(a * m) + (b * m) = (a + b) * m"
- "(a * m) + m = (a + 1) * m"
- "m + (a * m) = (a + 1) * m"
- "m + m = (1 + 1) * m"
- "0 + a = a"
- "a + 0 = a"
- "a * b = b * a"
- "(a + b) * c = (a * c) + (b * c)"
- "0 * a = 0"
- "a * 0 = 0"
- "1 * a = a"
- "a * 1 = a"
- "(lx * ly) * (rx * ry) = (lx * rx) * (ly * ry)"
- "(lx * ly) * (rx * ry) = lx * (ly * (rx * ry))"
- "(lx * ly) * (rx * ry) = rx * ((lx * ly) * ry)"
- "(lx * ly) * rx = (lx * rx) * ly"
- "(lx * ly) * rx = lx * (ly * rx)"
- "lx * (rx * ry) = (lx * rx) * ry"
- "lx * (rx * ry) = rx * (lx * ry)"
- "(a + b) + (c + d) = (a + c) + (b + d)"
- "(a + b) + c = a + (b + c)"
- "a + (c + d) = c + (a + d)"
- "(a + b) + c = (a + c) + b"
- "a + c = c + a"
- "a + (c + d) = (a + c) + d"
- "(x ^ p) * (x ^ q) = x ^ (p + q)"
- "x * (x ^ q) = x ^ (Suc q)"
- "(x ^ q) * x = x ^ (Suc q)"
- "x * x = x\<^sup>2"
- "(x * y) ^ q = (x ^ q) * (y ^ q)"
- "(x ^ p) ^ q = x ^ (p * q)"
- "x ^ 0 = 1"
- "x ^ 1 = x"
- "x * (y + z) = (x * y) + (x * z)"
- "x ^ (Suc q) = x * (x ^ q)"
- "x ^ (2*n) = (x ^ n) * (x ^ n)"
- by (simp_all add: algebra_simps power_add power2_eq_square
- power_mult_distrib power_mult del: one_add_one)}
-in
+lemma semiring_normalization_rules:
+ "(a * m) + (b * m) = (a + b) * m"
+ "(a * m) + m = (a + 1) * m"
+ "m + (a * m) = (a + 1) * m"
+ "m + m = (1 + 1) * m"
+ "0 + a = a"
+ "a + 0 = a"
+ "a * b = b * a"
+ "(a + b) * c = (a * c) + (b * c)"
+ "0 * a = 0"
+ "a * 0 = 0"
+ "1 * a = a"
+ "a * 1 = a"
+ "(lx * ly) * (rx * ry) = (lx * rx) * (ly * ry)"
+ "(lx * ly) * (rx * ry) = lx * (ly * (rx * ry))"
+ "(lx * ly) * (rx * ry) = rx * ((lx * ly) * ry)"
+ "(lx * ly) * rx = (lx * rx) * ly"
+ "(lx * ly) * rx = lx * (ly * rx)"
+ "lx * (rx * ry) = (lx * rx) * ry"
+ "lx * (rx * ry) = rx * (lx * ry)"
+ "(a + b) + (c + d) = (a + c) + (b + d)"
+ "(a + b) + c = a + (b + c)"
+ "a + (c + d) = c + (a + d)"
+ "(a + b) + c = (a + c) + b"
+ "a + c = c + a"
+ "a + (c + d) = (a + c) + d"
+ "(x ^ p) * (x ^ q) = x ^ (p + q)"
+ "x * (x ^ q) = x ^ (Suc q)"
+ "(x ^ q) * x = x ^ (Suc q)"
+ "x * x = x\<^sup>2"
+ "(x * y) ^ q = (x ^ q) * (y ^ q)"
+ "(x ^ p) ^ q = x ^ (p * q)"
+ "x ^ 0 = 1"
+ "x ^ 1 = x"
+ "x * (y + z) = (x * y) + (x * z)"
+ "x ^ (Suc q) = x * (x ^ q)"
+ "x ^ (2*n) = (x ^ n) * (x ^ n)"
+ by (simp_all add: algebra_simps power_add power2_eq_square
+ power_mult_distrib power_mult del: one_add_one)
+
+local_setup \<open>
Semiring_Normalizer.declare @{thm comm_semiring_1_axioms}
- {semiring = ([@{cpat "?x + ?y"}, @{cpat "?x * ?y"}, @{cpat "?x ^ ?n"}, @{cpat 0}, @{cpat 1}],
- rules), ring = ([], []), field = ([], []), idom = [], ideal = []}
-end\<close>
+ {semiring = ([@{term "x + y"}, @{term "x * y"}, @{term "x ^ n"}, @{term 0}, @{term 1}],
+ @{thms semiring_normalization_rules}),
+ ring = ([], []),
+ field = ([], []),
+ idom = [],
+ ideal = []}
+\<close>
end
context comm_ring_1
begin
-declaration \<open>
-let
- val rules = @{lemma
- "- x = (- 1) * x"
- "x - y = x + (- y)"
- by simp_all}
-in
+lemma ring_normalization_rules:
+ "- x = (- 1) * x"
+ "x - y = x + (- y)"
+ by simp_all
+
+local_setup \<open>
Semiring_Normalizer.declare @{thm comm_ring_1_axioms}
- {semiring = Semiring_Normalizer.the_semiring @{context} @{thm comm_semiring_1_axioms},
- ring = ([@{cpat "?x - ?y"}, @{cpat "- ?x"}], rules), field = ([], []), idom = [], ideal = []}
-end\<close>
+ {semiring = ([@{term "x + y"}, @{term "x * y"}, @{term "x ^ n"}, @{term 0}, @{term 1}],
+ @{thms semiring_normalization_rules}),
+ ring = ([@{term "x - y"}, @{term "- x"}], @{thms ring_normalization_rules}),
+ field = ([], []),
+ idom = [],
+ ideal = []}
+\<close>
end
context comm_semiring_1_cancel_crossproduct
begin
-declaration \<open>Semiring_Normalizer.declare @{thm comm_semiring_1_cancel_crossproduct_axioms}
- {semiring = Semiring_Normalizer.the_semiring @{context} @{thm comm_semiring_1_axioms},
- ring = ([], []), field = ([], []), idom = @{thms crossproduct_noteq add_scale_eq_noteq}, ideal = []}\<close>
+local_setup \<open>
+ Semiring_Normalizer.declare @{thm comm_semiring_1_cancel_crossproduct_axioms}
+ {semiring = ([@{term "x + y"}, @{term "x * y"}, @{term "x ^ n"}, @{term 0}, @{term 1}],
+ @{thms semiring_normalization_rules}),
+ ring = ([], []),
+ field = ([], []),
+ idom = @{thms crossproduct_noteq add_scale_eq_noteq},
+ ideal = []}
+\<close>
end
context idom
begin
-declaration \<open>Semiring_Normalizer.declare @{thm idom_axioms}
- {semiring = Semiring_Normalizer.the_semiring @{context} @{thm comm_ring_1_axioms},
- ring = Semiring_Normalizer.the_ring @{context} @{thm comm_ring_1_axioms},
- field = ([], []), idom = @{thms crossproduct_noteq add_scale_eq_noteq},
- ideal = @{thms right_minus_eq add_0_iff}}\<close>
+local_setup \<open>
+ Semiring_Normalizer.declare @{thm idom_axioms}
+ {semiring = ([@{term "x + y"}, @{term "x * y"}, @{term "x ^ n"}, @{term 0}, @{term 1}],
+ @{thms semiring_normalization_rules}),
+ ring = ([@{term "x - y"}, @{term "- x"}], @{thms ring_normalization_rules}),
+ field = ([], []),
+ idom = @{thms crossproduct_noteq add_scale_eq_noteq},
+ ideal = @{thms right_minus_eq add_0_iff}}
+\<close>
end
context field
begin
-declaration \<open>Semiring_Normalizer.declare @{thm field_axioms}
- {semiring = Semiring_Normalizer.the_semiring @{context} @{thm idom_axioms},
- ring = Semiring_Normalizer.the_ring @{context} @{thm idom_axioms},
- field = ([@{cpat "?x / ?y"}, @{cpat "inverse ?x"}], @{thms divide_inverse inverse_eq_divide}),
- idom = Semiring_Normalizer.the_idom @{context} @{thm idom_axioms},
- ideal = Semiring_Normalizer.the_ideal @{context} @{thm idom_axioms}}\<close>
+local_setup \<open>
+ Semiring_Normalizer.declare @{thm field_axioms}
+ {semiring = ([@{term "x + y"}, @{term "x * y"}, @{term "x ^ n"}, @{term 0}, @{term 1}],
+ @{thms semiring_normalization_rules}),
+ ring = ([@{term "x - y"}, @{term "- x"}], @{thms ring_normalization_rules}),
+ field = ([@{term "x / y"}, @{term "inverse x"}], @{thms divide_inverse inverse_eq_divide}),
+ idom = @{thms crossproduct_noteq add_scale_eq_noteq},
+ ideal = @{thms right_minus_eq add_0_iff}}
+\<close>
end
--- a/src/HOL/Tools/semiring_normalizer.ML Thu Sep 10 16:42:01 2015 +0200
+++ b/src/HOL/Tools/semiring_normalizer.ML Thu Sep 10 16:44:17 2015 +0200
@@ -4,7 +4,7 @@
Normalization of expressions in semirings.
*)
-signature SEMIRING_NORMALIZER =
+signature SEMIRING_NORMALIZER =
sig
type entry
val match: Proof.context -> cterm -> entry option
@@ -13,8 +13,9 @@
val the_field: Proof.context -> thm -> cterm list * thm list
val the_idom: Proof.context -> thm -> thm list
val the_ideal: Proof.context -> thm -> thm list
- val declare: thm -> {semiring: cterm list * thm list, ring: cterm list * thm list,
- field: cterm list * thm list, idom: thm list, ideal: thm list} -> declaration
+ val declare: thm -> {semiring: term list * thm list, ring: term list * thm list,
+ field: term list * thm list, idom: thm list, ideal: thm list} ->
+ local_theory -> local_theory
val semiring_normalize_conv: Proof.context -> conv
val semiring_normalize_ord_conv: Proof.context -> (cterm -> cterm -> bool) -> conv
@@ -40,7 +41,7 @@
sub: Proof.context -> conv}
end
-structure Semiring_Normalizer: SEMIRING_NORMALIZER =
+structure Semiring_Normalizer: SEMIRING_NORMALIZER =
struct
(** data **)
@@ -76,7 +77,7 @@
fun match ctxt tm =
let
fun match_inst
- ({vars, semiring = (sr_ops, sr_rules),
+ ({vars, semiring = (sr_ops, sr_rules),
ring = (r_ops, r_rules), field = (f_ops, f_rules), idom, ideal},
fns) pat =
let
@@ -92,7 +93,7 @@
val idom' = map substT idom;
val ideal' = map substT ideal;
- val result = ({vars = vars', semiring = semiring',
+ val result = ({vars = vars', semiring = semiring',
ring = ring', field = field', idom = idom', ideal = ideal'}, fns);
in SOME result end
in (case try Thm.match (pat, tm) of
@@ -105,7 +106,7 @@
get_first (match_inst entry) (sr_ops @ r_ops @ f_ops);
in get_first match_struct (Data.get (Context.Proof ctxt)) end;
-
+
(* extra-logical functions *)
val semiring_norm_ss =
@@ -137,9 +138,9 @@
fun dest_const ct = ((case Thm.term_of ct of
Const (@{const_name Rings.divide},_) $ a $ b=>
Rat.rat_of_quotient (snd (HOLogic.dest_number a), snd (HOLogic.dest_number b))
- | Const (@{const_name Fields.inverse},_)$t =>
+ | Const (@{const_name Fields.inverse},_)$t =>
Rat.inv (Rat.rat_of_int (snd (HOLogic.dest_number t)))
- | t => Rat.rat_of_int (snd (HOLogic.dest_number t)))
+ | t => Rat.rat_of_int (snd (HOLogic.dest_number t)))
handle TERM _ => error "ring_dest_const")
fun mk_const cT x =
let val (a, b) = Rat.quotient_of_rat x
@@ -165,62 +166,71 @@
val idomN = "idom";
fun declare raw_key
- {semiring = raw_semiring, ring = raw_ring, field = raw_field, idom = raw_idom, ideal = raw_ideal}
- phi context =
+ {semiring = raw_semiring0, ring = raw_ring0, field = raw_field0, idom = raw_idom, ideal = raw_ideal}
+ lthy =
let
- val ctxt = Context.proof_of context;
- val key = Morphism.thm phi raw_key;
- fun morphism_ops_rules (ops, rules) = (map (Morphism.cterm phi) ops, Morphism.fact phi rules);
- val (sr_ops, sr_rules) = morphism_ops_rules raw_semiring;
- val (r_ops, r_rules) = morphism_ops_rules raw_ring;
- val (f_ops, f_rules) = morphism_ops_rules raw_field;
- val idom = Morphism.fact phi raw_idom;
- val ideal = Morphism.fact phi raw_ideal;
-
- fun check kind name xs n =
- null xs orelse length xs = n orelse
- error ("Expected " ^ string_of_int n ^ " " ^ kind ^ " for " ^ name);
- val check_ops = check "operations";
- val check_rules = check "rules";
- val _ =
- check_ops semiringN sr_ops 5 andalso
- check_rules semiringN sr_rules 36 andalso
- check_ops ringN r_ops 2 andalso
- check_rules ringN r_rules 2 andalso
- check_ops fieldN f_ops 2 andalso
- check_rules fieldN f_rules 2 andalso
- check_rules idomN idom 2;
+ val ctxt' = fold Variable.auto_fixes (fst raw_semiring0 @ fst raw_ring0 @ fst raw_field0) lthy;
+ val prepare_ops = apfst (Variable.export_terms ctxt' lthy #> map (Thm.cterm_of lthy));
+ val raw_semiring = prepare_ops raw_semiring0;
+ val raw_ring = prepare_ops raw_ring0;
+ val raw_field = prepare_ops raw_field0;
+ in
+ lthy |> Local_Theory.declaration {syntax = false, pervasive = false} (fn phi => fn context =>
+ let
+ val ctxt = Context.proof_of context;
+ val key = Morphism.thm phi raw_key;
+ fun transform_ops_rules (ops, rules) =
+ (map (Morphism.cterm phi) ops, Morphism.fact phi rules);
+ val (sr_ops, sr_rules) = transform_ops_rules raw_semiring;
+ val (r_ops, r_rules) = transform_ops_rules raw_ring;
+ val (f_ops, f_rules) = transform_ops_rules raw_field;
+ val idom = Morphism.fact phi raw_idom;
+ val ideal = Morphism.fact phi raw_ideal;
- val mk_meta = Local_Defs.meta_rewrite_rule ctxt;
- val sr_rules' = map mk_meta sr_rules;
- val r_rules' = map mk_meta r_rules;
- val f_rules' = map mk_meta f_rules;
+ fun check kind name xs n =
+ null xs orelse length xs = n orelse
+ error ("Expected " ^ string_of_int n ^ " " ^ kind ^ " for " ^ name);
+ val check_ops = check "operations";
+ val check_rules = check "rules";
+ val _ =
+ check_ops semiringN sr_ops 5 andalso
+ check_rules semiringN sr_rules 36 andalso
+ check_ops ringN r_ops 2 andalso
+ check_rules ringN r_rules 2 andalso
+ check_ops fieldN f_ops 2 andalso
+ check_rules fieldN f_rules 2 andalso
+ check_rules idomN idom 2;
+
+ val mk_meta = Local_Defs.meta_rewrite_rule ctxt;
+ val sr_rules' = map mk_meta sr_rules;
+ val r_rules' = map mk_meta r_rules;
+ val f_rules' = map mk_meta f_rules;
+
+ fun rule i = nth sr_rules' (i - 1);
- fun rule i = nth sr_rules' (i - 1);
-
- val (cx, cy) = Thm.dest_binop (hd sr_ops);
- val cz = rule 34 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
- val cn = rule 36 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
- val ((clx, crx), (cly, cry)) =
- rule 13 |> Thm.rhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop;
- val ((ca, cb), (cc, cd)) =
- rule 20 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop;
- val cm = rule 1 |> Thm.rhs_of |> Thm.dest_arg;
- val (cp, cq) = rule 26 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_arg;
+ val (cx, cy) = Thm.dest_binop (hd sr_ops);
+ val cz = rule 34 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
+ val cn = rule 36 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg;
+ val ((clx, crx), (cly, cry)) =
+ rule 13 |> Thm.rhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop;
+ val ((ca, cb), (cc, cd)) =
+ rule 20 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop;
+ val cm = rule 1 |> Thm.rhs_of |> Thm.dest_arg;
+ val (cp, cq) = rule 26 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_arg;
+
+ val vars = [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry];
- val vars = [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry];
-
- val semiring = (sr_ops, sr_rules');
- val ring = (r_ops, r_rules');
- val field = (f_ops, f_rules');
- val ideal' = map (Thm.symmetric o mk_meta) ideal
-
- in
- context
- |> Data.map (AList.update Thm.eq_thm (key,
- ({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal'},
- (if null f_ops then semiring_funs else field_funs))))
- end
+ val semiring = (sr_ops, sr_rules');
+ val ring = (r_ops, r_rules');
+ val field = (f_ops, f_rules');
+ val ideal' = map (Thm.symmetric o mk_meta) ideal
+ in
+ context
+ |> Data.map (AList.update Thm.eq_thm (key,
+ ({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal'},
+ (if null f_ops then semiring_funs else field_funs))))
+ end)
+ end;
(** auxiliary **)
@@ -255,7 +265,7 @@
fun zerone_conv ctxt cv =
zero1_numeral_conv ctxt then_conv cv then_conv numeral01_conv ctxt;
-val nat_add_ss = simpset_of
+val nat_add_ss = simpset_of
(put_simpset HOL_basic_ss @{context}
addsimps @{thms arith_simps} @ @{thms diff_nat_numeral} @ @{thms rel_simps}
@ @{thms if_False if_True Nat.add_0 add_Suc add_numeral_left Suc_eq_plus1}
@@ -308,9 +318,9 @@
end
| _ => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), true_tm, true_tm));
-val (divide_inverse, divide_tm, inverse_tm) =
- (case (f_ops, f_rules) of
- ([divide_pat, inverse_pat], [div_inv, _]) =>
+val (divide_inverse, divide_tm, inverse_tm) =
+ (case (f_ops, f_rules) of
+ ([divide_pat, inverse_pat], [div_inv, _]) =>
let val div_tm = funpow 2 Thm.dest_fun divide_pat
val inv_tm = Thm.dest_fun inverse_pat
in (div_inv, div_tm, inv_tm)
@@ -420,7 +430,7 @@
else
((let val (lopr,r) = Thm.dest_comb tm
val (opr,l) = Thm.dest_comb lopr
- in if opr aconvc pow_tm andalso is_number r then l
+ in if opr aconvc pow_tm andalso is_number r then l
else raise CTERM ("monomial_mul_conv",[tm]) end)
handle CTERM _ => tm) (* FIXME !? *)
fun vorder x y =
@@ -803,9 +813,9 @@
let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) r
in Thm.transitive th1 (polynomial_pow_conv ctxt (concl th1))
end
- else if opr aconvc divide_tm
+ else if opr aconvc divide_tm
then
- let val th1 = Thm.combination (Drule.arg_cong_rule opr (polynomial_conv ctxt l))
+ let val th1 = Thm.combination (Drule.arg_cong_rule opr (polynomial_conv ctxt l))
(polynomial_conv ctxt r)
val th2 = (Conv.rewr_conv divide_inverse then_conv polynomial_mul_conv ctxt)
(Thm.rhs_of th1)
@@ -846,7 +856,7 @@
(* various normalizing conversions *)
-fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal},
+fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal},
{conv, dest_const, mk_const, is_const}) ord =
let
val pow_conv =
@@ -862,14 +872,14 @@
({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal},
{conv = conv, dest_const = dest_const, mk_const = mk_const, is_const = is_const}) ord) ctxt;
-fun semiring_normalize_wrapper ctxt data =
+fun semiring_normalize_wrapper ctxt data =
semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;
fun semiring_normalize_ord_conv ctxt ord tm =
(case match ctxt tm of
NONE => Thm.reflexive tm
| SOME res => semiring_normalize_ord_wrapper ctxt res ord tm);
-
+
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt simple_cterm_ord;
end;