--- a/src/HOL/Tools/semiring_normalizer.ML Tue Apr 16 17:54:14 2013 +0200
+++ b/src/HOL/Tools/semiring_normalizer.ML Thu Apr 18 17:07:01 2013 +0200
@@ -27,10 +27,20 @@
val semiring_normalizers_conv: cterm list -> cterm list * thm list
-> cterm list * thm list -> cterm list * thm list ->
(cterm -> bool) * conv * conv * conv -> (cterm -> cterm -> bool) ->
- {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
+ {add: Proof.context -> conv,
+ mul: Proof.context -> conv,
+ neg: Proof.context -> conv,
+ main: Proof.context -> conv,
+ pow: Proof.context -> conv,
+ sub: Proof.context -> conv}
val semiring_normalizers_ord_wrapper: Proof.context -> entry ->
(cterm -> cterm -> bool) ->
- {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
+ {add: Proof.context -> conv,
+ mul: Proof.context -> conv,
+ neg: Proof.context -> conv,
+ main: Proof.context -> conv,
+ pow: Proof.context -> conv,
+ sub: Proof.context -> conv}
val setup: theory -> theory
end
@@ -177,9 +187,9 @@
handle TERM _ => error "ring_dest_const")),
mk_const = fn phi => fn cT => fn x => Numeral.mk_cnumber cT
(case Rat.quotient_of_rat x of (i, 1) => i | _ => error "int_of_rat: bad int"),
- conv = fn phi => fn _ => Simplifier.rewrite (HOL_basic_ss addsimps @{thms semiring_norm})
- then_conv Simplifier.rewrite (HOL_basic_ss addsimps
- @{thms numeral_1_eq_1})};
+ conv = fn phi => fn ctxt =>
+ Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps @{thms semiring_norm})
+ then_conv Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps @{thms numeral_1_eq_1})};
fun field_funs key =
let
@@ -208,7 +218,7 @@
{is_const = K numeral_is_const,
dest_const = K dest_const,
mk_const = mk_const,
- conv = K (K Numeral_Simprocs.field_comp_conv)}
+ conv = K Numeral_Simprocs.field_comp_conv}
end;
@@ -236,23 +246,26 @@
val dest_numeral = term_of #> HOLogic.dest_number #> snd;
val is_numeral = can dest_numeral;
-val numeral01_conv = Simplifier.rewrite
- (HOL_basic_ss addsimps [@{thm numeral_1_eq_1}]);
-val zero1_numeral_conv =
- Simplifier.rewrite (HOL_basic_ss addsimps [@{thm numeral_1_eq_1} RS sym]);
-fun zerone_conv cv = zero1_numeral_conv then_conv cv then_conv numeral01_conv;
+fun numeral01_conv ctxt =
+ Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_1_eq_1}]);
+
+fun zero1_numeral_conv ctxt =
+ Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_1_eq_1} RS sym]);
+
+fun zerone_conv ctxt cv =
+ zero1_numeral_conv ctxt then_conv cv then_conv numeral01_conv ctxt;
val natarith = [@{thm "numeral_plus_numeral"}, @{thm "diff_nat_numeral"},
@{thm "numeral_times_numeral"}, @{thm "numeral_eq_iff"},
@{thm "numeral_less_iff"}];
-val nat_add_conv =
- zerone_conv
- (Simplifier.rewrite
- (HOL_basic_ss
- addsimps @{thms arith_simps} @ natarith @ @{thms rel_simps}
- @ [@{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc},
- @{thm add_numeral_left}, @{thm Suc_eq_plus1}]
- @ map (fn th => th RS sym) @{thms numerals}));
+fun nat_add_conv ctxt =
+ zerone_conv ctxt
+ (Simplifier.rewrite
+ (put_simpset HOL_basic_ss ctxt
+ addsimps @{thms arith_simps} @ natarith @ @{thms rel_simps}
+ @ [@{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc},
+ @{thm add_numeral_left}, @{thm Suc_eq_plus1}]
+ @ map (fn th => th RS sym) @{thms numerals}));
val zeron_tm = @{cterm "0::nat"};
val onen_tm = @{cterm "1::nat"};
@@ -316,7 +329,7 @@
(* Also deals with "const * const", but both terms must involve powers of *)
(* the same variable, or both be constants, or behaviour may be incorrect. *)
- fun powvar_mul_conv tm =
+ fun powvar_mul_conv ctxt tm =
let
val (l,r) = dest_mul tm
in if is_semiring_constant l andalso is_semiring_constant r
@@ -328,16 +341,16 @@
((let val (rx,rn) = dest_pow r
val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29
val (tm1,tm2) = Thm.dest_comb(concl th1) in
- Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
+ Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)
handle CTERM _ =>
(let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31
val (tm1,tm2) = Thm.dest_comb(concl th1) in
- Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)) end)
+ Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)) end)
handle CTERM _ =>
((let val (rx,rn) = dest_pow r
val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30
val (tm1,tm2) = Thm.dest_comb(concl th1) in
- Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
+ Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)
handle CTERM _ => inst_thm [(cx,l)] pthm_32
))
@@ -353,7 +366,7 @@
(* Conversion for "(monomial)^n", where n is a numeral. *)
- val monomial_pow_conv =
+ fun monomial_pow_conv ctxt =
let
fun monomial_pow tm bod ntm =
if not(is_comb bod)
@@ -374,7 +387,7 @@
then
let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34
val (l,r) = Thm.dest_comb(concl th1)
- in Thm.transitive th1 (Drule.arg_cong_rule l (nat_add_conv r))
+ in Thm.transitive th1 (Drule.arg_cong_rule l (nat_add_conv ctxt r))
end
else
if opr aconvc mul_tm
@@ -405,7 +418,7 @@
end;
(* Multiplication of canonical monomials. *)
- val monomial_mul_conv =
+ fun monomial_mul_conv ctxt =
let
fun powvar tm =
if is_semiring_constant tm then one_tm
@@ -435,7 +448,7 @@
val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15
val (tm1,tm2) = Thm.dest_comb(concl th1)
val (tm3,tm4) = Thm.dest_comb tm1
- val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
+ val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2
val th3 = Thm.transitive th1 th2
val (tm5,tm6) = Thm.dest_comb(concl th3)
val (tm7,tm8) = Thm.dest_comb tm6
@@ -458,7 +471,7 @@
val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18
val (tm1,tm2) = Thm.dest_comb(concl th1)
val (tm3,tm4) = Thm.dest_comb tm1
- val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
+ val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2
in Thm.transitive th1 th2
end
else
@@ -480,7 +493,7 @@
let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21
val (tm1,tm2) = Thm.dest_comb(concl th1)
val (tm3,tm4) = Thm.dest_comb tm1
- in Thm.transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2)
+ in Thm.transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2)
end
else if ord > 0 then
let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22
@@ -493,7 +506,7 @@
handle CTERM _ =>
(let val vr = powvar r
val ord = vorder vl vr
- in if ord = 0 then powvar_mul_conv tm
+ in if ord = 0 then powvar_mul_conv ctxt tm
else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09
else Thm.reflexive tm
end)) end))
@@ -502,7 +515,7 @@
end;
(* Multiplication by monomial of a polynomial. *)
- val polynomial_monomial_mul_conv =
+ fun polynomial_monomial_mul_conv ctxt =
let
fun pmm_conv tm =
let val (l,r) = dest_mul tm
@@ -511,10 +524,11 @@
val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37
val (tm1,tm2) = Thm.dest_comb(concl th1)
val (tm3,tm4) = Thm.dest_comb tm1
- val th2 = Thm.combination (Drule.arg_cong_rule tm3 (monomial_mul_conv tm4)) (pmm_conv tm2)
+ val th2 =
+ Thm.combination (Drule.arg_cong_rule tm3 (monomial_mul_conv ctxt tm4)) (pmm_conv tm2)
in Thm.transitive th1 th2
end)
- handle CTERM _ => monomial_mul_conv tm)
+ handle CTERM _ => monomial_mul_conv ctxt tm)
end
in pmm_conv
end;
@@ -592,7 +606,7 @@
(* Addition of two polynomials. *)
-val polynomial_add_conv =
+fun polynomial_add_conv ctxt =
let
fun dezero_rule th =
let
@@ -690,25 +704,25 @@
(* Multiplication of two polynomials. *)
-val polynomial_mul_conv =
+fun polynomial_mul_conv ctxt =
let
fun pmul tm =
let val (l,r) = dest_mul tm
in
- if not(is_add l) then polynomial_monomial_mul_conv tm
+ if not(is_add l) then polynomial_monomial_mul_conv ctxt tm
else
if not(is_add r) then
let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09
- in Thm.transitive th1 (polynomial_monomial_mul_conv(concl th1))
+ in Thm.transitive th1 (polynomial_monomial_mul_conv ctxt (concl th1))
end
else
let val (a,b) = dest_add l
val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10
val (tm1,tm2) = Thm.dest_comb(concl th1)
val (tm3,tm4) = Thm.dest_comb tm1
- val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv tm4)
+ val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv ctxt tm4)
val th3 = Thm.transitive th1 (Thm.combination th2 (pmul tm2))
- in Thm.transitive th3 (polynomial_add_conv (concl th3))
+ in Thm.transitive th3 (polynomial_add_conv ctxt (concl th3))
end
end
in fn tm =>
@@ -724,12 +738,12 @@
(* Power of polynomial (optimized for the monomial and trivial cases). *)
-fun num_conv n =
- nat_add_conv (Thm.apply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
+fun num_conv ctxt n =
+ nat_add_conv ctxt (Thm.apply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
|> Thm.symmetric;
-val polynomial_pow_conv =
+fun polynomial_pow_conv ctxt =
let
fun ppow tm =
let val (l,n) = dest_pow tm
@@ -737,52 +751,52 @@
if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35
else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36
else
- let val th1 = num_conv n
+ let val th1 = num_conv ctxt n
val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38
val (tm1,tm2) = Thm.dest_comb(concl th2)
val th3 = Thm.transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2))
val th4 = Thm.transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3
- in Thm.transitive th4 (polynomial_mul_conv (concl th4))
+ in Thm.transitive th4 (polynomial_mul_conv ctxt (concl th4))
end
end
in fn tm =>
- if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv tm
+ if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv ctxt tm
end;
(* Negation. *)
-fun polynomial_neg_conv tm =
+fun polynomial_neg_conv ctxt tm =
let val (l,r) = Thm.dest_comb tm in
if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else
let val th1 = inst_thm [(cx',r)] neg_mul
val th2 = Thm.transitive th1 (Conv.arg1_conv semiring_mul_conv (concl th1))
- in Thm.transitive th2 (polynomial_monomial_mul_conv (concl th2))
+ in Thm.transitive th2 (polynomial_monomial_mul_conv ctxt (concl th2))
end
end;
(* Subtraction. *)
-fun polynomial_sub_conv tm =
+fun polynomial_sub_conv ctxt tm =
let val (l,r) = dest_sub tm
val th1 = inst_thm [(cx',l),(cy',r)] sub_add
val (tm1,tm2) = Thm.dest_comb(concl th1)
- val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv tm2)
- in Thm.transitive th1 (Thm.transitive th2 (polynomial_add_conv (concl th2)))
+ val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv ctxt tm2)
+ in Thm.transitive th1 (Thm.transitive th2 (polynomial_add_conv ctxt (concl th2)))
end;
(* Conversion from HOL term. *)
-fun polynomial_conv tm =
+fun polynomial_conv ctxt tm =
if is_semiring_constant tm then semiring_add_conv tm
else if not(is_comb tm) then Thm.reflexive tm
else
let val (lopr,r) = Thm.dest_comb tm
in if lopr aconvc neg_tm then
- let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
- in Thm.transitive th1 (polynomial_neg_conv (concl th1))
+ let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r)
+ in Thm.transitive th1 (polynomial_neg_conv ctxt (concl th1))
end
else if lopr aconvc inverse_tm then
- let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
+ let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r)
in Thm.transitive th1 (semiring_mul_conv (concl th1))
end
else
@@ -791,14 +805,14 @@
let val (opr,l) = Thm.dest_comb lopr
in if opr aconvc pow_tm andalso is_numeral r
then
- let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv l)) r
- in Thm.transitive th1 (polynomial_pow_conv (concl th1))
+ 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
then
- let val th1 = Thm.combination (Drule.arg_cong_rule opr (polynomial_conv l))
- (polynomial_conv r)
- val th2 = (Conv.rewr_conv divide_inverse then_conv polynomial_mul_conv)
+ 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)
in Thm.transitive th1 th2
end
@@ -806,10 +820,11 @@
if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm
then
let val th1 =
- Thm.combination (Drule.arg_cong_rule opr (polynomial_conv l)) (polynomial_conv r)
- val f = if opr aconvc add_tm then polynomial_add_conv
- else if opr aconvc mul_tm then polynomial_mul_conv
- else polynomial_sub_conv
+ Thm.combination
+ (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) (polynomial_conv ctxt r)
+ val f = if opr aconvc add_tm then polynomial_add_conv ctxt
+ else if opr aconvc mul_tm then polynomial_mul_conv ctxt
+ else polynomial_sub_conv ctxt
in Thm.transitive th1 (f (concl th1))
end
else Thm.reflexive tm
@@ -826,8 +841,10 @@
end;
val nat_exp_ss =
- HOL_basic_ss addsimps (@{thms eval_nat_numeral} @ @{thms nat_arith} @ @{thms arith_simps} @ @{thms rel_simps})
- addsimps [@{thm Let_def}, @{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc}];
+ simpset_of
+ (put_simpset HOL_basic_ss @{context}
+ addsimps (@{thms eval_nat_numeral} @ @{thms nat_arith} @ @{thms arith_simps} @ @{thms rel_simps})
+ addsimps [@{thm Let_def}, @{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc}]);
fun simple_cterm_ord t u = Term_Ord.term_ord (term_of t, term_of u) = LESS;
@@ -838,15 +855,17 @@
{conv, dest_const, mk_const, is_const}) ord =
let
val pow_conv =
- Conv.arg_conv (Simplifier.rewrite nat_exp_ss)
+ Conv.arg_conv (Simplifier.rewrite (put_simpset nat_exp_ss ctxt))
then_conv Simplifier.rewrite
- (HOL_basic_ss addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
+ (put_simpset HOL_basic_ss ctxt addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
then_conv conv ctxt
val dat = (is_const, conv ctxt, conv ctxt, pow_conv)
in semiring_normalizers_conv vars semiring ring field dat ord end;
fun semiring_normalize_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, {conv, dest_const, mk_const, is_const}) ord =
- #main (semiring_normalizers_ord_wrapper ctxt ({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);
+ #main (semiring_normalizers_ord_wrapper ctxt
+ ({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 =
semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;