# HG changeset patch # User bulwahn # Date 1246366506 -7200 # Node ID 4e03a2cdf61163378de8cdc71e028b74d3847f84 # Parent e3de75d3b8987f38d40a01ae2cdf10daad9a8aec# Parent 3b08dcd74229cfaa77f8934e8136f7b9fa6981e6 merged diff -r e3de75d3b898 -r 4e03a2cdf611 Admin/launch4j/README --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Admin/launch4j/README Tue Jun 30 14:55:06 2009 +0200 @@ -0,0 +1,5 @@ +Cross-platform Java executable wrapper +====================================== + +* http://launch4j.sourceforge.net + diff -r e3de75d3b898 -r 4e03a2cdf611 Admin/launch4j/isabelle.ico Binary file Admin/launch4j/isabelle.ico has changed diff -r e3de75d3b898 -r 4e03a2cdf611 Admin/launch4j/isabelle.xml --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Admin/launch4j/isabelle.xml Tue Jun 30 14:55:06 2009 +0200 @@ -0,0 +1,23 @@ + + true + gui + lib/classes/isabelle-scala.jar + Isabelle.exe + + + + normal + http://java.com/download + + false + false + + isabelle.ico + + + 1.6.0 + + preferJre + -Disabelle.home="%EXEDIR%" + + \ No newline at end of file diff -r e3de75d3b898 -r 4e03a2cdf611 NEWS --- a/NEWS Tue Jun 30 14:54:30 2009 +0200 +++ b/NEWS Tue Jun 30 14:55:06 2009 +0200 @@ -73,7 +73,7 @@ approximation method. * "approximate" supports now arithmetic expressions as boundaries of intervals and implements -interval splitting. +interval splitting and taylor series expansion. *** ML *** diff -r e3de75d3b898 -r 4e03a2cdf611 doc-src/Codegen/Thy/document/Introduction.tex --- a/doc-src/Codegen/Thy/document/Introduction.tex Tue Jun 30 14:54:30 2009 +0200 +++ b/doc-src/Codegen/Thy/document/Introduction.tex Tue Jun 30 14:55:06 2009 +0200 @@ -249,9 +249,9 @@ \hspace*{0pt}dequeue (AQueue [] []) = (Nothing,~AQueue [] []);\\ \hspace*{0pt}dequeue (AQueue xs (y :~ys)) = (Just y,~AQueue xs ys);\\ \hspace*{0pt}dequeue (AQueue (v :~va) []) =\\ -\hspace*{0pt} ~(let {\char123}\\ +\hspace*{0pt} ~let {\char123}\\ \hspace*{0pt} ~~~(y :~ys) = rev (v :~va);\\ -\hspace*{0pt} ~{\char125}~in (Just y,~AQueue [] ys) );\\ +\hspace*{0pt} ~{\char125}~in (Just y,~AQueue [] ys);\\ \hspace*{0pt}\\ \hspace*{0pt}enqueue ::~forall a.~a -> Queue a -> Queue a;\\ \hspace*{0pt}enqueue x (AQueue xs ys) = AQueue (x :~xs) ys;\\ diff -r e3de75d3b898 -r 4e03a2cdf611 doc-src/Codegen/Thy/document/Program.tex --- a/doc-src/Codegen/Thy/document/Program.tex Tue Jun 30 14:54:30 2009 +0200 +++ b/doc-src/Codegen/Thy/document/Program.tex Tue Jun 30 14:55:06 2009 +0200 @@ -966,9 +966,9 @@ \noindent% \hspace*{0pt}strict{\char95}dequeue ::~forall a.~Queue a -> (a,~Queue a);\\ \hspace*{0pt}strict{\char95}dequeue (AQueue xs []) =\\ -\hspace*{0pt} ~(let {\char123}\\ +\hspace*{0pt} ~let {\char123}\\ \hspace*{0pt} ~~~(y :~ys) = rev xs;\\ -\hspace*{0pt} ~{\char125}~in (y,~AQueue [] ys) );\\ +\hspace*{0pt} ~{\char125}~in (y,~AQueue [] ys);\\ \hspace*{0pt}strict{\char95}dequeue (AQueue xs (y :~ys)) = (y,~AQueue xs ys);% \end{isamarkuptext}% \isamarkuptrue% diff -r e3de75d3b898 -r 4e03a2cdf611 doc-src/Codegen/Thy/examples/Example.hs --- a/doc-src/Codegen/Thy/examples/Example.hs Tue Jun 30 14:54:30 2009 +0200 +++ b/doc-src/Codegen/Thy/examples/Example.hs Tue Jun 30 14:55:06 2009 +0200 @@ -23,9 +23,9 @@ dequeue (AQueue [] []) = (Nothing, AQueue [] []); dequeue (AQueue xs (y : ys)) = (Just y, AQueue xs ys); dequeue (AQueue (v : va) []) = - (let { + let { (y : ys) = rev (v : va); - } in (Just y, AQueue [] ys) ); + } in (Just y, AQueue [] ys); enqueue :: forall a. a -> Queue a -> Queue a; enqueue x (AQueue xs ys) = AQueue (x : xs) ys; diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Decision_Procs/Approximation.thy --- a/src/HOL/Decision_Procs/Approximation.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Decision_Procs/Approximation.thy Tue Jun 30 14:55:06 2009 +0200 @@ -2069,8 +2069,7 @@ | Atom nat | Num float -fun interpret_floatarith :: "floatarith \ real list \ real" -where +fun interpret_floatarith :: "floatarith \ real list \ real" where "interpret_floatarith (Add a b) vs = (interpret_floatarith a vs) + (interpret_floatarith b vs)" | "interpret_floatarith (Minus a) vs = - (interpret_floatarith a vs)" | "interpret_floatarith (Mult a b) vs = (interpret_floatarith a vs) * (interpret_floatarith b vs)" | @@ -2117,7 +2116,6 @@ and "interpret_floatarith (Num (Float 1 0)) vs = 1" and "interpret_floatarith (Num (Float (number_of a) 0)) vs = number_of a" by auto - subsection "Implement approximation function" fun lift_bin' :: "(float * float) option \ (float * float) option \ (float \ float \ float \ float \ (float * float)) \ (float * float) option" where @@ -2632,6 +2630,576 @@ shows "interpret_form f xs" using approx_form_aux[OF _ bounded_by_None] assms by auto +subsection {* Implementing Taylor series expansion *} + +fun isDERIV :: "nat \ floatarith \ real list \ bool" where +"isDERIV x (Add a b) vs = (isDERIV x a vs \ isDERIV x b vs)" | +"isDERIV x (Mult a b) vs = (isDERIV x a vs \ isDERIV x b vs)" | +"isDERIV x (Minus a) vs = isDERIV x a vs" | +"isDERIV x (Inverse a) vs = (isDERIV x a vs \ interpret_floatarith a vs \ 0)" | +"isDERIV x (Cos a) vs = isDERIV x a vs" | +"isDERIV x (Arctan a) vs = isDERIV x a vs" | +"isDERIV x (Min a b) vs = False" | +"isDERIV x (Max a b) vs = False" | +"isDERIV x (Abs a) vs = False" | +"isDERIV x Pi vs = True" | +"isDERIV x (Sqrt a) vs = (isDERIV x a vs \ interpret_floatarith a vs > 0)" | +"isDERIV x (Exp a) vs = isDERIV x a vs" | +"isDERIV x (Ln a) vs = (isDERIV x a vs \ interpret_floatarith a vs > 0)" | +"isDERIV x (Power a 0) vs = True" | +"isDERIV x (Power a (Suc n)) vs = isDERIV x a vs" | +"isDERIV x (Num f) vs = True" | +"isDERIV x (Atom n) vs = True" + +fun DERIV_floatarith :: "nat \ floatarith \ floatarith" where +"DERIV_floatarith x (Add a b) = Add (DERIV_floatarith x a) (DERIV_floatarith x b)" | +"DERIV_floatarith x (Mult a b) = Add (Mult a (DERIV_floatarith x b)) (Mult (DERIV_floatarith x a) b)" | +"DERIV_floatarith x (Minus a) = Minus (DERIV_floatarith x a)" | +"DERIV_floatarith x (Inverse a) = Minus (Mult (DERIV_floatarith x a) (Inverse (Power a 2)))" | +"DERIV_floatarith x (Cos a) = Minus (Mult (Cos (Add (Mult Pi (Num (Float 1 -1))) (Minus a))) (DERIV_floatarith x a))" | +"DERIV_floatarith x (Arctan a) = Mult (Inverse (Add (Num 1) (Power a 2))) (DERIV_floatarith x a)" | +"DERIV_floatarith x (Min a b) = Num 0" | +"DERIV_floatarith x (Max a b) = Num 0" | +"DERIV_floatarith x (Abs a) = Num 0" | +"DERIV_floatarith x Pi = Num 0" | +"DERIV_floatarith x (Sqrt a) = (Mult (Inverse (Mult (Sqrt a) (Num 2))) (DERIV_floatarith x a))" | +"DERIV_floatarith x (Exp a) = Mult (Exp a) (DERIV_floatarith x a)" | +"DERIV_floatarith x (Ln a) = Mult (Inverse a) (DERIV_floatarith x a)" | +"DERIV_floatarith x (Power a 0) = Num 0" | +"DERIV_floatarith x (Power a (Suc n)) = Mult (Num (Float (int (Suc n)) 0)) (Mult (Power a n) (DERIV_floatarith x a))" | +"DERIV_floatarith x (Num f) = Num 0" | +"DERIV_floatarith x (Atom n) = (if x = n then Num 1 else Num 0)" + +lemma DERIV_chain'': "\DERIV g (f x) :> E ; DERIV f x :> D; x' = E * D \ \ + DERIV (\x. g (f x)) x :> x'" using DERIV_chain' by auto + +lemma DERIV_cong: "\ DERIV f x :> X ; X = X' \ \ DERIV f x :> X'" by simp + +lemma DERIV_floatarith: + assumes "n < length vs" + assumes isDERIV: "isDERIV n f (vs[n := x])" + shows "DERIV (\ x'. interpret_floatarith f (vs[n := x'])) x :> + interpret_floatarith (DERIV_floatarith n f) (vs[n := x])" + (is "DERIV (?i f) x :> _") +using isDERIV proof (induct f arbitrary: x) + case (Add a b) thus ?case by (auto intro: DERIV_add) +next case (Mult a b) thus ?case by (auto intro!: DERIV_mult[THEN DERIV_cong]) +next case (Minus a) thus ?case by (auto intro!: DERIV_minus[THEN DERIV_cong]) +next case (Inverse a) thus ?case + by (auto intro!: DERIV_inverse_fun[THEN DERIV_cong] DERIV_inverse[THEN DERIV_cong] + simp add: algebra_simps power2_eq_square) +next case (Cos a) thus ?case + by (auto intro!: DERIV_chain''[of cos "?i a"] + DERIV_cos[THEN DERIV_cong] + simp del: interpret_floatarith.simps(5) + simp add: interpret_floatarith_sin interpret_floatarith.simps(5)[of a]) +next case (Arctan a) thus ?case + by (auto intro!: DERIV_chain''[of arctan "?i a"] DERIV_arctan[THEN DERIV_cong]) +next case (Exp a) thus ?case + by (auto intro!: DERIV_chain''[of exp "?i a"] DERIV_exp[THEN DERIV_cong]) +next case (Power a n) thus ?case + by (cases n, auto intro!: DERIV_power_Suc[THEN DERIV_cong] + simp del: power_Suc simp add: real_eq_of_nat) +next case (Sqrt a) thus ?case + by (auto intro!: DERIV_chain''[of sqrt "?i a"] DERIV_real_sqrt[THEN DERIV_cong]) +next case (Ln a) thus ?case + by (auto intro!: DERIV_chain''[of ln "?i a"] DERIV_ln[THEN DERIV_cong] + simp add: divide_inverse) +next case (Atom i) thus ?case using `n < length vs` by auto +qed auto + +declare approx.simps[simp del] + +fun isDERIV_approx :: "nat \ nat \ floatarith \ (float * float) option list \ bool" where +"isDERIV_approx prec x (Add a b) vs = (isDERIV_approx prec x a vs \ isDERIV_approx prec x b vs)" | +"isDERIV_approx prec x (Mult a b) vs = (isDERIV_approx prec x a vs \ isDERIV_approx prec x b vs)" | +"isDERIV_approx prec x (Minus a) vs = isDERIV_approx prec x a vs" | +"isDERIV_approx prec x (Inverse a) vs = + (isDERIV_approx prec x a vs \ (case approx prec a vs of Some (l, u) \ 0 < l \ u < 0 | None \ False))" | +"isDERIV_approx prec x (Cos a) vs = isDERIV_approx prec x a vs" | +"isDERIV_approx prec x (Arctan a) vs = isDERIV_approx prec x a vs" | +"isDERIV_approx prec x (Min a b) vs = False" | +"isDERIV_approx prec x (Max a b) vs = False" | +"isDERIV_approx prec x (Abs a) vs = False" | +"isDERIV_approx prec x Pi vs = True" | +"isDERIV_approx prec x (Sqrt a) vs = + (isDERIV_approx prec x a vs \ (case approx prec a vs of Some (l, u) \ 0 < l | None \ False))" | +"isDERIV_approx prec x (Exp a) vs = isDERIV_approx prec x a vs" | +"isDERIV_approx prec x (Ln a) vs = + (isDERIV_approx prec x a vs \ (case approx prec a vs of Some (l, u) \ 0 < l | None \ False))" | +"isDERIV_approx prec x (Power a 0) vs = True" | +"isDERIV_approx prec x (Power a (Suc n)) vs = isDERIV_approx prec x a vs" | +"isDERIV_approx prec x (Num f) vs = True" | +"isDERIV_approx prec x (Atom n) vs = True" + +lemma isDERIV_approx: + assumes "bounded_by xs vs" + and isDERIV_approx: "isDERIV_approx prec x f vs" + shows "isDERIV x f xs" +using isDERIV_approx proof (induct f) + case (Inverse a) + then obtain l u where approx_Some: "Some (l, u) = approx prec a vs" + and *: "0 < l \ u < 0" + by (cases "approx prec a vs", auto) + with approx[OF `bounded_by xs vs` approx_Some] + have "interpret_floatarith a xs \ 0" unfolding less_float_def by auto + thus ?case using Inverse by auto +next + case (Ln a) + then obtain l u where approx_Some: "Some (l, u) = approx prec a vs" + and *: "0 < l" + by (cases "approx prec a vs", auto) + with approx[OF `bounded_by xs vs` approx_Some] + have "0 < interpret_floatarith a xs" unfolding less_float_def by auto + thus ?case using Ln by auto +next + case (Sqrt a) + then obtain l u where approx_Some: "Some (l, u) = approx prec a vs" + and *: "0 < l" + by (cases "approx prec a vs", auto) + with approx[OF `bounded_by xs vs` approx_Some] + have "0 < interpret_floatarith a xs" unfolding less_float_def by auto + thus ?case using Sqrt by auto +next + case (Power a n) thus ?case by (cases n, auto) +qed auto + +lemma bounded_by_update_var: + assumes "bounded_by xs vs" and "vs ! i = Some (l, u)" + and bnd: "x \ { real l .. real u }" + shows "bounded_by (xs[i := x]) vs" +proof (cases "i < length xs") + case False thus ?thesis using `bounded_by xs vs` by auto +next + let ?xs = "xs[i := x]" + case True hence "i < length ?xs" by auto +{ fix j + assume "j < length vs" + have "case vs ! j of None \ True | Some (l, u) \ ?xs ! j \ { real l .. real u }" + proof (cases "vs ! j") + case (Some b) + thus ?thesis + proof (cases "i = j") + case True + thus ?thesis using `vs ! i = Some (l, u)` Some and bnd `i < length ?xs` + by auto + next + case False + thus ?thesis using `bounded_by xs vs`[THEN bounded_byE, OF `j < length vs`] Some + by auto + qed + qed auto } + thus ?thesis unfolding bounded_by_def by auto +qed + +lemma isDERIV_approx': + assumes "bounded_by xs vs" + and vs_x: "vs ! x = Some (l, u)" and X_in: "X \ { real l .. real u }" + and approx: "isDERIV_approx prec x f vs" + shows "isDERIV x f (xs[x := X])" +proof - + note bounded_by_update_var[OF `bounded_by xs vs` vs_x X_in] approx + thus ?thesis by (rule isDERIV_approx) +qed + +lemma DERIV_approx: + assumes "n < length xs" and bnd: "bounded_by xs vs" + and isD: "isDERIV_approx prec n f vs" + and app: "Some (l, u) = approx prec (DERIV_floatarith n f) vs" (is "_ = approx _ ?D _") + shows "\x. real l \ x \ x \ real u \ + DERIV (\ x. interpret_floatarith f (xs[n := x])) (xs!n) :> x" + (is "\ x. _ \ _ \ DERIV (?i f) _ :> _") +proof (rule exI[of _ "?i ?D (xs!n)"], rule conjI[OF _ conjI]) + let "?i f x" = "interpret_floatarith f (xs[n := x])" + from approx[OF bnd app] + show "real l \ ?i ?D (xs!n)" and "?i ?D (xs!n) \ real u" + using `n < length xs` by auto + from DERIV_floatarith[OF `n < length xs`, of f "xs!n"] isDERIV_approx[OF bnd isD] + show "DERIV (?i f) (xs!n) :> (?i ?D (xs!n))" by simp +qed + +fun lift_bin :: "(float * float) option \ (float * float) option \ (float \ float \ float \ float \ (float * float) option) \ (float * float) option" where +"lift_bin (Some (l1, u1)) (Some (l2, u2)) f = f l1 u1 l2 u2" | +"lift_bin a b f = None" + +lemma lift_bin: + assumes lift_bin_Some: "Some (l, u) = lift_bin a b f" + obtains l1 u1 l2 u2 + where "a = Some (l1, u1)" + and "b = Some (l2, u2)" + and "f l1 u1 l2 u2 = Some (l, u)" +using assms by (cases a, simp, cases b, simp, auto) + +fun approx_tse where +"approx_tse prec n 0 c k f bs = approx prec f bs" | +"approx_tse prec n (Suc s) c k f bs = + (if isDERIV_approx prec n f bs then + lift_bin (approx prec f (bs[n := Some (c,c)])) + (approx_tse prec n s c (Suc k) (DERIV_floatarith n f) bs) + (\ l1 u1 l2 u2. approx prec + (Add (Atom 0) + (Mult (Inverse (Num (Float (int k) 0))) + (Mult (Add (Atom (Suc (Suc 0))) (Minus (Num c))) + (Atom (Suc 0))))) [Some (l1, u1), Some (l2, u2), bs!n]) + else approx prec f bs)" + +lemma bounded_by_Cons: + assumes bnd: "bounded_by xs vs" + and x: "x \ { real l .. real u }" + shows "bounded_by (x#xs) ((Some (l, u))#vs)" +proof - + { fix i assume *: "i < length ((Some (l, u))#vs)" + have "case ((Some (l,u))#vs) ! i of Some (l, u) \ (x#xs)!i \ { real l .. real u } | None \ True" + proof (cases i) + case 0 with x show ?thesis by auto + next + case (Suc i) with * have "i < length vs" by auto + from bnd[THEN bounded_byE, OF this] + show ?thesis unfolding Suc nth_Cons_Suc . + qed } + thus ?thesis by (auto simp add: bounded_by_def) +qed + +lemma approx_tse_generic: + assumes "bounded_by xs vs" + and bnd_c: "bounded_by (xs[x := real c]) vs" and "x < length vs" and "x < length xs" + and bnd_x: "vs ! x = Some (lx, ux)" + and ate: "Some (l, u) = approx_tse prec x s c k f vs" + shows "\ n. (\ m < n. \ z \ {real lx .. real ux}. + DERIV (\ y. interpret_floatarith ((DERIV_floatarith x ^^ m) f) (xs[x := y])) z :> + (interpret_floatarith ((DERIV_floatarith x ^^ (Suc m)) f) (xs[x := z]))) + \ (\ t \ {real lx .. real ux}. (\ i = 0.. j \ {k.. j \ {k.. {real l .. real u})" (is "\ n. ?taylor f k l u n") +using ate proof (induct s arbitrary: k f l u) + case 0 + { fix t assume "t \ {real lx .. real ux}" + note bounded_by_update_var[OF `bounded_by xs vs` bnd_x this] + from approx[OF this 0[unfolded approx_tse.simps]] + have "(interpret_floatarith f (xs[x := t])) \ {real l .. real u}" + by (auto simp add: algebra_simps) + } thus ?case by (auto intro!: exI[of _ 0]) +next + case (Suc s) + show ?case + proof (cases "isDERIV_approx prec x f vs") + case False + note ap = Suc.prems[unfolded approx_tse.simps if_not_P[OF False]] + + { fix t assume "t \ {real lx .. real ux}" + note bounded_by_update_var[OF `bounded_by xs vs` bnd_x this] + from approx[OF this ap] + have "(interpret_floatarith f (xs[x := t])) \ {real l .. real u}" + by (auto simp add: algebra_simps) + } thus ?thesis by (auto intro!: exI[of _ 0]) + next + case True + with Suc.prems + obtain l1 u1 l2 u2 + where a: "Some (l1, u1) = approx prec f (vs[x := Some (c,c)])" + and ate: "Some (l2, u2) = approx_tse prec x s c (Suc k) (DERIV_floatarith x f) vs" + and final: "Some (l, u) = approx prec + (Add (Atom 0) + (Mult (Inverse (Num (Float (int k) 0))) + (Mult (Add (Atom (Suc (Suc 0))) (Minus (Num c))) + (Atom (Suc 0))))) [Some (l1, u1), Some (l2, u2), vs!x]" + by (auto elim!: lift_bin) blast + + from bnd_c `x < length xs` + have bnd: "bounded_by (xs[x:=real c]) (vs[x:= Some (c,c)])" + by (auto intro!: bounded_by_update) + + from approx[OF this a] + have f_c: "interpret_floatarith ((DERIV_floatarith x ^^ 0) f) (xs[x := real c]) \ { real l1 .. real u1 }" + (is "?f 0 (real c) \ _") + by auto + + { fix f :: "'a \ 'a" fix n :: nat fix x :: 'a + have "(f ^^ Suc n) x = (f ^^ n) (f x)" + by (induct n, auto) } + note funpow_Suc = this[symmetric] + from Suc.hyps[OF ate, unfolded this] + obtain n + where DERIV_hyp: "\ m z. \ m < n ; z \ { real lx .. real ux } \ \ DERIV (?f (Suc m)) z :> ?f (Suc (Suc m)) z" + and hyp: "\ t \ {real lx .. real ux}. (\ i = 0.. j \ {Suc k.. j \ {Suc k.. {real l2 .. real u2}" + (is "\ t \ _. ?X (Suc k) f n t \ _") + by blast + + { fix m z + assume "m < Suc n" and bnd_z: "z \ { real lx .. real ux }" + have "DERIV (?f m) z :> ?f (Suc m) z" + proof (cases m) + case 0 + with DERIV_floatarith[OF `x < length xs` isDERIV_approx'[OF `bounded_by xs vs` bnd_x bnd_z True]] + show ?thesis by simp + next + case (Suc m') + hence "m' < n" using `m < Suc n` by auto + from DERIV_hyp[OF this bnd_z] + show ?thesis using Suc by simp + qed } note DERIV = this + + have "\ k i. k < i \ {k ..< i} = insert k {Suc k ..< i}" by auto + hence setprod_head_Suc: "\ k i. \ {k ..< k + Suc i} = k * \ {Suc k ..< Suc k + i}" by auto + have setsum_move0: "\ k F. setsum F {0.. k. F (Suc k)) {0.. "xs!x - real c" + + { fix t assume t: "t \ {real lx .. real ux}" + hence "bounded_by [xs!x] [vs!x]" + using `bounded_by xs vs`[THEN bounded_byE, OF `x < length vs`] + by (cases "vs!x", auto simp add: bounded_by_def) + + with hyp[THEN bspec, OF t] f_c + have "bounded_by [?f 0 (real c), ?X (Suc k) f n t, xs!x] [Some (l1, u1), Some (l2, u2), vs!x]" + by (auto intro!: bounded_by_Cons) + from approx[OF this final, unfolded atLeastAtMost_iff[symmetric]] + have "?X (Suc k) f n t * (xs!x - real c) * inverse (real k) + ?f 0 (real c) \ {real l .. real u}" + by (auto simp add: algebra_simps) + also have "?X (Suc k) f n t * (xs!x - real c) * inverse (real k) + ?f 0 (real c) = + (\ i = 0.. j \ {k.. j \ {k.. {real l .. real u}" . } + thus ?thesis using DERIV by blast + qed +qed + +lemma setprod_fact: "\ {1..<1 + k} = fact (k :: nat)" +proof (induct k) + case (Suc k) + have "{ 1 ..< Suc (Suc k) } = insert (Suc k) { 1 ..< Suc k }" by auto + hence "\ { 1 ..< Suc (Suc k) } = (Suc k) * \ { 1 ..< Suc k }" by auto + thus ?case using Suc by auto +qed simp + +lemma approx_tse: + assumes "bounded_by xs vs" + and bnd_x: "vs ! x = Some (lx, ux)" and bnd_c: "real c \ {real lx .. real ux}" + and "x < length vs" and "x < length xs" + and ate: "Some (l, u) = approx_tse prec x s c 1 f vs" + shows "interpret_floatarith f xs \ { real l .. real u }" +proof - + def F \ "\ n z. interpret_floatarith ((DERIV_floatarith x ^^ n) f) (xs[x := z])" + hence F0: "F 0 = (\ z. interpret_floatarith f (xs[x := z]))" by auto + + hence "bounded_by (xs[x := real c]) vs" and "x < length vs" "x < length xs" + using `bounded_by xs vs` bnd_x bnd_c `x < length vs` `x < length xs` + by (auto intro!: bounded_by_update_var) + + from approx_tse_generic[OF `bounded_by xs vs` this bnd_x ate] + obtain n + where DERIV: "\ m z. m < n \ real lx \ z \ z \ real ux \ DERIV (F m) z :> F (Suc m) z" + and hyp: "\ t. t \ {real lx .. real ux} \ + (\ j = 0.. {real l .. real u}" (is "\ t. _ \ ?taylor t \ _") + unfolding F_def atLeastAtMost_iff[symmetric] setprod_fact by blast + + have bnd_xs: "xs ! x \ { real lx .. real ux }" + using `bounded_by xs vs`[THEN bounded_byE, OF `x < length vs`] bnd_x by auto + + show ?thesis + proof (cases n) + case 0 thus ?thesis using hyp[OF bnd_xs] unfolding F_def by auto + next + case (Suc n') + show ?thesis + proof (cases "xs ! x = real c") + case True + from True[symmetric] hyp[OF bnd_xs] Suc show ?thesis + unfolding F_def Suc setsum_head_upt_Suc[OF zero_less_Suc] setsum_shift_bounds_Suc_ivl by auto + next + case False + + have "real lx \ real c" "real c \ real ux" "real lx \ xs!x" "xs!x \ real ux" + using Suc bnd_c `bounded_by xs vs`[THEN bounded_byE, OF `x < length vs`] bnd_x by auto + from Taylor.taylor[OF zero_less_Suc, of F, OF F0 DERIV[unfolded Suc] this False] + obtain t where t_bnd: "if xs ! x < real c then xs ! x < t \ t < real c else real c < t \ t < xs ! x" + and fl_eq: "interpret_floatarith f (xs[x := xs ! x]) = + (\m = 0.. {real lx .. real ux}" + by (cases "xs ! x < real c", auto) + + have "interpret_floatarith f (xs[x := xs ! x]) = ?taylor t" + unfolding fl_eq Suc by (auto simp add: algebra_simps divide_inverse) + also have "\ \ {real l .. real u}" using * by (rule hyp) + finally show ?thesis by simp + qed + qed +qed + +fun approx_tse_form' where +"approx_tse_form' prec t f 0 l u cmp = + (case approx_tse prec 0 t ((l + u) * Float 1 -1) 1 f [Some (l, u)] + of Some (l, u) \ cmp l u | None \ False)" | +"approx_tse_form' prec t f (Suc s) l u cmp = + (let m = (l + u) * Float 1 -1 + in approx_tse_form' prec t f s l m cmp \ + approx_tse_form' prec t f s m u cmp)" + +lemma approx_tse_form': + assumes "approx_tse_form' prec t f s l u cmp" and "x \ {real l .. real u}" + shows "\ l' u' ly uy. x \ { real l' .. real u' } \ real l \ real l' \ real u' \ real u \ cmp ly uy \ + approx_tse prec 0 t ((l' + u') * Float 1 -1) 1 f [Some (l', u')] = Some (ly, uy)" +using assms proof (induct s arbitrary: l u) + case 0 + then obtain ly uy + where *: "approx_tse prec 0 t ((l + u) * Float 1 -1) 1 f [Some (l, u)] = Some (ly, uy)" + and **: "cmp ly uy" by (auto elim!: option_caseE) + with 0 show ?case by (auto intro!: exI) +next + case (Suc s) + let ?m = "(l + u) * Float 1 -1" + from Suc.prems + have l: "approx_tse_form' prec t f s l ?m cmp" + and u: "approx_tse_form' prec t f s ?m u cmp" + by (auto simp add: Let_def) + + have m_l: "real l \ real ?m" and m_u: "real ?m \ real u" + unfolding le_float_def using Suc.prems by auto + + with `x \ { real l .. real u }` + have "x \ { real l .. real ?m} \ x \ { real ?m .. real u }" by auto + thus ?case + proof (rule disjE) + assume "x \ { real l .. real ?m}" + from Suc.hyps[OF l this] + obtain l' u' ly uy + where "x \ { real l' .. real u' } \ real l \ real l' \ real u' \ real ?m \ cmp ly uy \ + approx_tse prec 0 t ((l' + u') * Float 1 -1) 1 f [Some (l', u')] = Some (ly, uy)" by blast + with m_u show ?thesis by (auto intro!: exI) + next + assume "x \ { real ?m .. real u }" + from Suc.hyps[OF u this] + obtain l' u' ly uy + where "x \ { real l' .. real u' } \ real ?m \ real l' \ real u' \ real u \ cmp ly uy \ + approx_tse prec 0 t ((l' + u') * Float 1 -1) 1 f [Some (l', u')] = Some (ly, uy)" by blast + with m_u show ?thesis by (auto intro!: exI) + qed +qed + +lemma approx_tse_form'_less: + assumes tse: "approx_tse_form' prec t (Add a (Minus b)) s l u (\ l u. 0 < l)" + and x: "x \ {real l .. real u}" + shows "interpret_floatarith b [x] < interpret_floatarith a [x]" +proof - + from approx_tse_form'[OF tse x] + obtain l' u' ly uy + where x': "x \ { real l' .. real u' }" and "real l \ real l'" + and "real u' \ real u" and "0 < ly" + and tse: "approx_tse prec 0 t ((l' + u') * Float 1 -1) 1 (Add a (Minus b)) [Some (l', u')] = Some (ly, uy)" + by blast + + hence "bounded_by [x] [Some (l', u')]" by (auto simp add: bounded_by_def) + + from approx_tse[OF this _ _ _ _ tse[symmetric], of l' u'] x' + have "real ly \ interpret_floatarith a [x] - interpret_floatarith b [x]" + by (auto simp add: diff_minus) + from order_less_le_trans[OF `0 < ly`[unfolded less_float_def] this] + show ?thesis by auto +qed + +lemma approx_tse_form'_le: + assumes tse: "approx_tse_form' prec t (Add a (Minus b)) s l u (\ l u. 0 \ l)" + and x: "x \ {real l .. real u}" + shows "interpret_floatarith b [x] \ interpret_floatarith a [x]" +proof - + from approx_tse_form'[OF tse x] + obtain l' u' ly uy + where x': "x \ { real l' .. real u' }" and "real l \ real l'" + and "real u' \ real u" and "0 \ ly" + and tse: "approx_tse prec 0 t ((l' + u') * Float 1 -1) 1 (Add a (Minus b)) [Some (l', u')] = Some (ly, uy)" + by blast + + hence "bounded_by [x] [Some (l', u')]" by (auto simp add: bounded_by_def) + + from approx_tse[OF this _ _ _ _ tse[symmetric], of l' u'] x' + have "real ly \ interpret_floatarith a [x] - interpret_floatarith b [x]" + by (auto simp add: diff_minus) + from order_trans[OF `0 \ ly`[unfolded le_float_def] this] + show ?thesis by auto +qed + +definition +"approx_tse_form prec t s f = + (case f + of (Bound x a b f) \ x = Atom 0 \ + (case (approx prec a [None], approx prec b [None]) + of (Some (l, u), Some (l', u')) \ + (case f + of Less lf rt \ approx_tse_form' prec t (Add rt (Minus lf)) s l u' (\ l u. 0 < l) + | LessEqual lf rt \ approx_tse_form' prec t (Add rt (Minus lf)) s l u' (\ l u. 0 \ l) + | AtLeastAtMost x lf rt \ + approx_tse_form' prec t (Add x (Minus lf)) s l u' (\ l u. 0 \ l) \ + approx_tse_form' prec t (Add rt (Minus x)) s l u' (\ l u. 0 \ l) + | _ \ False) + | _ \ False) + | _ \ False)" + +lemma approx_tse_form: + assumes "approx_tse_form prec t s f" + shows "interpret_form f [x]" +proof (cases f) + case (Bound i a b f') note f_def = this + with assms obtain l u l' u' + where a: "approx prec a [None] = Some (l, u)" + and b: "approx prec b [None] = Some (l', u')" + unfolding approx_tse_form_def by (auto elim!: option_caseE) + + from Bound assms have "i = Atom 0" unfolding approx_tse_form_def by auto + hence i: "interpret_floatarith i [x] = x" by auto + + { let "?f z" = "interpret_floatarith z [x]" + assume "?f i \ { ?f a .. ?f b }" + with approx[OF _ a[symmetric], of "[x]"] approx[OF _ b[symmetric], of "[x]"] + have bnd: "x \ { real l .. real u'}" unfolding bounded_by_def i by auto + + have "interpret_form f' [x]" + proof (cases f') + case (Less lf rt) + with Bound a b assms + have "approx_tse_form' prec t (Add rt (Minus lf)) s l u' (\ l u. 0 < l)" + unfolding approx_tse_form_def by auto + from approx_tse_form'_less[OF this bnd] + show ?thesis using Less by auto + next + case (LessEqual lf rt) + with Bound a b assms + have "approx_tse_form' prec t (Add rt (Minus lf)) s l u' (\ l u. 0 \ l)" + unfolding approx_tse_form_def by auto + from approx_tse_form'_le[OF this bnd] + show ?thesis using LessEqual by auto + next + case (AtLeastAtMost x lf rt) + with Bound a b assms + have "approx_tse_form' prec t (Add rt (Minus x)) s l u' (\ l u. 0 \ l)" + and "approx_tse_form' prec t (Add x (Minus lf)) s l u' (\ l u. 0 \ l)" + unfolding approx_tse_form_def by auto + from approx_tse_form'_le[OF this(1) bnd] approx_tse_form'_le[OF this(2) bnd] + show ?thesis using AtLeastAtMost by auto + next + case (Bound x a b f') with assms + show ?thesis by (auto elim!: option_caseE simp add: f_def approx_tse_form_def) + next + case (Assign x a f') with assms + show ?thesis by (auto elim!: option_caseE simp add: f_def approx_tse_form_def) + qed } thus ?thesis unfolding f_def by auto +next case Assign with assms show ?thesis by (auto simp add: approx_tse_form_def) +next case LessEqual with assms show ?thesis by (auto simp add: approx_tse_form_def) +next case Less with assms show ?thesis by (auto simp add: approx_tse_form_def) +next case AtLeastAtMost with assms show ?thesis by (auto simp add: approx_tse_form_def) +qed + subsection {* Implement proof method \texttt{approximation} *} lemmas interpret_form_equations = interpret_form.simps interpret_floatarith.simps interpret_floatarith_num @@ -2648,6 +3216,7 @@ @{code_datatype form = Bound | Assign | Less | LessEqual | AtLeastAtMost} val approx_form = @{code approx_form} +val approx_tse_form = @{code approx_tse_form} val approx' = @{code approx'} end @@ -2675,6 +3244,7 @@ "Float'_Arith.AtLeastAtMost/ (_,/ _,/ _)") code_const approx_form (Eval "Float'_Arith.approx'_form") +code_const approx_tse_form (Eval "Float'_Arith.approx'_tse'_form") code_const approx' (Eval "Float'_Arith.approx'") ML {* @@ -2712,30 +3282,49 @@ val form_equations = PureThy.get_thms @{theory} "interpret_form_equations"; - fun rewrite_interpret_form_tac ctxt prec splitting i st = let + fun rewrite_interpret_form_tac ctxt prec splitting taylor i st = let + fun lookup_splitting (Free (name, typ)) + = case AList.lookup (op =) splitting name + of SOME s => HOLogic.mk_number @{typ nat} s + | NONE => @{term "0 :: nat"} val vs = nth (prems_of st) (i - 1) |> Logic.strip_imp_concl |> HOLogic.dest_Trueprop |> Term.strip_comb |> snd |> List.last |> HOLogic.dest_list - val n = vs |> length - |> HOLogic.mk_number @{typ nat} - |> Thm.cterm_of (ProofContext.theory_of ctxt) val p = prec |> HOLogic.mk_number @{typ nat} |> Thm.cterm_of (ProofContext.theory_of ctxt) - val s = vs - |> map (fn Free (name, typ) => - case AList.lookup (op =) splitting name of - SOME s => HOLogic.mk_number @{typ nat} s - | NONE => @{term "0 :: nat"}) - |> HOLogic.mk_list @{typ nat} + in case taylor + of NONE => let + val n = vs |> length + |> HOLogic.mk_number @{typ nat} + |> Thm.cterm_of (ProofContext.theory_of ctxt) + val s = vs + |> map lookup_splitting + |> HOLogic.mk_list @{typ nat} + |> Thm.cterm_of (ProofContext.theory_of ctxt) + in + (rtac (Thm.instantiate ([], [(@{cpat "?n::nat"}, n), + (@{cpat "?prec::nat"}, p), + (@{cpat "?ss::nat list"}, s)]) + @{thm "approx_form"}) i + THEN simp_tac @{simpset} i) st + end + + | SOME t => if length vs <> 1 then raise (TERM ("More than one variable used for taylor series expansion", [prop_of st])) + else let + val t = t + |> HOLogic.mk_number @{typ nat} |> Thm.cterm_of (ProofContext.theory_of ctxt) - in - rtac (Thm.instantiate ([], [(@{cpat "?n::nat"}, n), - (@{cpat "?prec::nat"}, p), - (@{cpat "?ss::nat list"}, s)]) - @{thm "approx_form"}) i st + val s = vs |> map lookup_splitting |> hd + |> Thm.cterm_of (ProofContext.theory_of ctxt) + in + rtac (Thm.instantiate ([], [(@{cpat "?s::nat"}, s), + (@{cpat "?t::nat"}, t), + (@{cpat "?prec::nat"}, p)]) + @{thm "approx_tse_form"}) i st + end end (* copied from Tools/induct.ML should probably in args.ML *) @@ -2751,11 +3340,15 @@ by auto method_setup approximation = {* - Scan.lift (OuterParse.nat) -- + Scan.lift (OuterParse.nat) + -- Scan.optional (Scan.lift (Args.$$$ "splitting" |-- Args.colon) |-- OuterParse.and_list' (free --| Scan.lift (Args.$$$ "=") -- Scan.lift OuterParse.nat)) [] + -- + Scan.option (Scan.lift (Args.$$$ "taylor" |-- Args.colon) + |-- (free |-- Scan.lift (Args.$$$ "=") |-- Scan.lift OuterParse.nat)) >> - (fn (prec, splitting) => fn ctxt => + (fn ((prec, splitting), taylor) => fn ctxt => SIMPLE_METHOD' (fn i => REPEAT (FIRST' [etac @{thm intervalE}, etac @{thm meta_eqE}, @@ -2763,15 +3356,10 @@ THEN METAHYPS (reorder_bounds_tac i) i THEN TRY (filter_prems_tac (K false) i) THEN DETERM (Reflection.genreify_tac ctxt form_equations NONE i) - THEN print_tac "approximation" - THEN rewrite_interpret_form_tac ctxt prec splitting i - THEN simp_tac @{simpset} i + THEN rewrite_interpret_form_tac ctxt prec splitting taylor i THEN gen_eval_tac eval_oracle ctxt i)) *} "real number approximation" -lemma "\ \ {0..1 :: real} \ \ < \ + 0.7" - by (approximation 10 splitting: "\" = 1) - ML {* fun dest_interpret (@{const "interpret_floatarith"} $ b $ xs) = (b, xs) | dest_interpret t = raise TERM ("dest_interpret", [t]) diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Decision_Procs/ex/Approximation_Ex.thy --- a/src/HOL/Decision_Procs/ex/Approximation_Ex.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Decision_Procs/ex/Approximation_Ex.thy Tue Jun 30 14:55:06 2009 +0200 @@ -8,13 +8,28 @@ Here are some examples how to use the approximation method. -The parameter passed to the method specifies the precision used by the computations, it is specified -as number of bits to calculate. When a variable is used it needs to be bounded by an interval. This -interval is specified as a conjunction of the lower and upper bound. It must have the form -@{text "\ l\<^isub>1 \ x\<^isub>1 \ x\<^isub>1 \ u\<^isub>1 ; \ ; l\<^isub>n \ x\<^isub>n \ x\<^isub>n \ u\<^isub>n \ \ F"} where @{term F} is the formula, and -@{text "x\<^isub>1, \, x\<^isub>n"} are the variables. The lower bounds @{text "l\<^isub>1, \, l\<^isub>n"} and the upper bounds -@{text "u\<^isub>1, \, u\<^isub>n"} must either be integer numerals, floating point numbers or of the form -@{term "m * pow2 e"} to specify a exact floating point value. +The approximation method has the following syntax: + +approximate "prec" (splitting: "x" = "depth" and "y" = "depth" ...)? (taylor: "z" = "derivates")? + +Here "prec" specifies the precision used in all computations, it is specified as +number of bits to calculate. In the proposition to prove an arbitrary amount of +variables can be used, but each one need to be bounded by an upper and lower +bound. + +To specify the bounds either @{term "l\<^isub>1 \ x \ x \ u\<^isub>1"}, +@{term "x \ { l\<^isub>1 .. u\<^isub>1 }"} or @{term "x = bnd"} can be used. Where the +bound specification are again arithmetic formulas containing variables. They can +be connected using either meta level or HOL equivalence. + +To use interval splitting add for each variable whos interval should be splitted +to the "splitting:" parameter. The parameter specifies how often each interval +should be divided, e.g. when x = 16 is specified, there will be @{term "65536 = 2^16"} +intervals to be calculated. + +To use taylor series expansion specify the variable to derive. You need to +specify the amount of derivations to compute. When using taylor series expansion +only one variable can be used. *} @@ -57,4 +72,7 @@ shows "g / v * tan (35 * d) \ { 3 * d .. 3.1 * d }" using assms by (approximation 80) +lemma "\ \ { 0 .. 1 :: real } \ \ ^ 2 \ \" + by (approximation 30 splitting: \=1 taylor: \ = 3) + end diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Imperative_HOL/Array.thy --- a/src/HOL/Imperative_HOL/Array.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Imperative_HOL/Array.thy Tue Jun 30 14:55:06 2009 +0200 @@ -1,5 +1,4 @@ -(* Title: HOL/Library/Array.thy - ID: $Id$ +(* Title: HOL/Imperative_HOL/Array.thy Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen *) diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Imperative_HOL/Heap_Monad.thy --- a/src/HOL/Imperative_HOL/Heap_Monad.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Imperative_HOL/Heap_Monad.thy Tue Jun 30 14:55:06 2009 +0200 @@ -306,67 +306,75 @@ code_const "Heap_Monad.Fail" (OCaml "Failure") code_const "Heap_Monad.raise_exc" (OCaml "!(fun/ ()/ ->/ raise/ _)") -setup {* let - open Code_Thingol; +setup {* + +let - fun lookup naming = the o Code_Thingol.lookup_const naming; +open Code_Thingol; + +fun imp_program naming = - fun imp_monad_bind'' bind' return' unit' ts = - let - val dummy_name = ""; - val dummy_type = ITyVar dummy_name; - val dummy_case_term = IVar dummy_name; - (*assumption: dummy values are not relevant for serialization*) - val unitt = IConst (unit', (([], []), [])); - fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t) - | dest_abs (t, ty) = - let - val vs = Code_Thingol.fold_varnames cons t []; - val v = Name.variant vs "x"; - val ty' = (hd o fst o Code_Thingol.unfold_fun) ty; - in ((v, ty'), t `$ IVar v) end; - fun force (t as IConst (c, _) `$ t') = if c = return' - then t' else t `$ unitt - | force t = t `$ unitt; - fun tr_bind' [(t1, _), (t2, ty2)] = - let - val ((v, ty), t) = dest_abs (t2, ty2); - in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end - and tr_bind'' t = case Code_Thingol.unfold_app t - of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if c = bind' - then tr_bind' [(x1, ty1), (x2, ty2)] - else force t - | _ => force t; - in (dummy_name, dummy_type) `|=> ICase (((IVar dummy_name, dummy_type), - [(unitt, tr_bind' ts)]), dummy_case_term) end - and imp_monad_bind' bind' return' unit' (const as (c, (_, tys))) ts = if c = bind' then case (ts, tys) - of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' bind' return' unit' [(t1, ty1), (t2, ty2)] - | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' bind' return' unit' [(t1, ty1), (t2, ty2)] `$ t3 - | (ts, _) => imp_monad_bind bind' return' unit' (eta_expand 2 (const, ts)) - else IConst const `$$ map (imp_monad_bind bind' return' unit') ts - and imp_monad_bind bind' return' unit' (IConst const) = imp_monad_bind' bind' return' unit' const [] - | imp_monad_bind bind' return' unit' (t as IVar _) = t - | imp_monad_bind bind' return' unit' (t as _ `$ _) = (case unfold_app t - of (IConst const, ts) => imp_monad_bind' bind' return' unit' const ts - | (t, ts) => imp_monad_bind bind' return' unit' t `$$ map (imp_monad_bind bind' return' unit') ts) - | imp_monad_bind bind' return' unit' (v_ty `|=> t) = v_ty `|=> imp_monad_bind bind' return' unit' t - | imp_monad_bind bind' return' unit' (ICase (((t, ty), pats), t0)) = ICase - (((imp_monad_bind bind' return' unit' t, ty), (map o pairself) (imp_monad_bind bind' return' unit') pats), imp_monad_bind bind' return' unit' t0); + let + fun is_const c = case lookup_const naming c + of SOME c' => (fn c'' => c' = c'') + | NONE => K false; + val is_bindM = is_const @{const_name bindM}; + val is_return = is_const @{const_name return}; + val dummy_name = "X"; + val dummy_type = ITyVar dummy_name; + val dummy_case_term = IVar ""; + (*assumption: dummy values are not relevant for serialization*) + val unitt = case lookup_const naming @{const_name Unity} + of SOME unit' => IConst (unit', (([], []), [])) + | NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants."); + fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t) + | dest_abs (t, ty) = + let + val vs = fold_varnames cons t []; + val v = Name.variant vs "x"; + val ty' = (hd o fst o unfold_fun) ty; + in ((v, ty'), t `$ IVar v) end; + fun force (t as IConst (c, _) `$ t') = if is_return c + then t' else t `$ unitt + | force t = t `$ unitt; + fun tr_bind' [(t1, _), (t2, ty2)] = + let + val ((v, ty), t) = dest_abs (t2, ty2); + in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end + and tr_bind'' t = case unfold_app t + of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bindM c + then tr_bind' [(x1, ty1), (x2, ty2)] + else force t + | _ => force t; + fun imp_monad_bind'' ts = (dummy_name, dummy_type) `|=> ICase (((IVar dummy_name, dummy_type), + [(unitt, tr_bind' ts)]), dummy_case_term) + and imp_monad_bind' (const as (c, (_, tys))) ts = if is_bindM c then case (ts, tys) + of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] + | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3 + | (ts, _) => imp_monad_bind (eta_expand 2 (const, ts)) + else IConst const `$$ map imp_monad_bind ts + and imp_monad_bind (IConst const) = imp_monad_bind' const [] + | imp_monad_bind (t as IVar _) = t + | imp_monad_bind (t as _ `$ _) = (case unfold_app t + of (IConst const, ts) => imp_monad_bind' const ts + | (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts) + | imp_monad_bind (v_ty `|=> t) = v_ty `|=> imp_monad_bind t + | imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase + (((imp_monad_bind t, ty), + (map o pairself) imp_monad_bind pats), + imp_monad_bind t0); - fun imp_program naming = (Graph.map_nodes o map_terms_stmt) - (imp_monad_bind (lookup naming @{const_name bindM}) - (lookup naming @{const_name return}) - (lookup naming @{const_name Unity})); + in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end; in - Code_Target.extend_target ("SML_imp", ("SML", imp_program)) - #> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program)) +Code_Target.extend_target ("SML_imp", ("SML", imp_program)) +#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program)) end + *} - code_reserved OCaml Failure raise diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Imperative_HOL/Imperative_HOL_ex.thy --- a/src/HOL/Imperative_HOL/Imperative_HOL_ex.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Imperative_HOL/Imperative_HOL_ex.thy Tue Jun 30 14:55:06 2009 +0200 @@ -1,8 +1,9 @@ (* Title: HOL/Imperative_HOL/Imperative_HOL_ex.thy - Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen + Author: John Matthews, Galois Connections; + Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen *) -header {* Mmonadic imperative HOL with examples *} +header {* Monadic imperative HOL with examples *} theory Imperative_HOL_ex imports Imperative_HOL "ex/Imperative_Quicksort" diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy --- a/src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy Tue Jun 30 14:55:06 2009 +0200 @@ -631,9 +631,9 @@ ML {* @{code qsort} (Array.fromList [42, 2, 3, 5, 0, 1705, 8, 3, 15]) () *} -export_code qsort in SML_imp module_name QSort +(*export_code qsort in SML_imp module_name QSort*) export_code qsort in OCaml module_name QSort file - -export_code qsort in OCaml_imp module_name QSort file - +(*export_code qsort in OCaml_imp module_name QSort file -*) export_code qsort in Haskell module_name QSort file - end \ No newline at end of file diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/IsaMakefile Tue Jun 30 14:55:06 2009 +0200 @@ -319,7 +319,7 @@ Library/Abstract_Rat.thy \ Library/BigO.thy Library/ContNotDenum.thy Library/Efficient_Nat.thy \ Library/Euclidean_Space.thy Library/Sum_Of_Squares.thy Library/positivstellensatz.ML \ - Library/Code_Set.thy Library/Convex_Euclidean_Space.thy \ + Library/Fset.thy Library/Convex_Euclidean_Space.thy \ Library/sum_of_squares.ML Library/Glbs.thy Library/normarith.ML \ Library/Executable_Set.thy Library/Infinite_Set.thy \ Library/FuncSet.thy Library/Permutations.thy Library/Determinants.thy\ diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/Code_Set.thy --- a/src/HOL/Library/Code_Set.thy Tue Jun 30 14:54:30 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,169 +0,0 @@ - -(* Author: Florian Haftmann, TU Muenchen *) - -header {* Executable finite sets *} - -theory Code_Set -imports List_Set -begin - -lemma foldl_apply_inv: - assumes "\x. g (h x) = x" - shows "foldl f (g s) xs = g (foldl (\s x. h (f (g s) x)) s xs)" - by (rule sym, induct xs arbitrary: s) (simp_all add: assms) - -subsection {* Lifting *} - -datatype 'a fset = Fset "'a set" - -primrec member :: "'a fset \ 'a set" where - "member (Fset A) = A" - -lemma Fset_member [simp]: - "Fset (member A) = A" - by (cases A) simp - -definition Set :: "'a list \ 'a fset" where - "Set xs = Fset (set xs)" - -lemma member_Set [simp]: - "member (Set xs) = set xs" - by (simp add: Set_def) - -code_datatype Set - - -subsection {* Basic operations *} - -definition is_empty :: "'a fset \ bool" where - "is_empty A \ List_Set.is_empty (member A)" - -lemma is_empty_Set [code]: - "is_empty (Set xs) \ null xs" - by (simp add: is_empty_def is_empty_set) - -definition empty :: "'a fset" where - "empty = Fset {}" - -lemma empty_Set [code]: - "empty = Set []" - by (simp add: empty_def Set_def) - -definition insert :: "'a \ 'a fset \ 'a fset" where - "insert x A = Fset (Set.insert x (member A))" - -lemma insert_Set [code]: - "insert x (Set xs) = Set (List_Set.insert x xs)" - by (simp add: insert_def Set_def insert_set) - -definition remove :: "'a \ 'a fset \ 'a fset" where - "remove x A = Fset (List_Set.remove x (member A))" - -lemma remove_Set [code]: - "remove x (Set xs) = Set (remove_all x xs)" - by (simp add: remove_def Set_def remove_set) - -definition map :: "('a \ 'b) \ 'a fset \ 'b fset" where - "map f A = Fset (image f (member A))" - -lemma map_Set [code]: - "map f (Set xs) = Set (remdups (List.map f xs))" - by (simp add: map_def Set_def) - -definition project :: "('a \ bool) \ 'a fset \ 'a fset" where - "project P A = Fset (List_Set.project P (member A))" - -lemma project_Set [code]: - "project P (Set xs) = Set (filter P xs)" - by (simp add: project_def Set_def project_set) - -definition forall :: "('a \ bool) \ 'a fset \ bool" where - "forall P A \ Ball (member A) P" - -lemma forall_Set [code]: - "forall P (Set xs) \ list_all P xs" - by (simp add: forall_def Set_def ball_set) - -definition exists :: "('a \ bool) \ 'a fset \ bool" where - "exists P A \ Bex (member A) P" - -lemma exists_Set [code]: - "exists P (Set xs) \ list_ex P xs" - by (simp add: exists_def Set_def bex_set) - - -subsection {* Functorial operations *} - -definition union :: "'a fset \ 'a fset \ 'a fset" where - "union A B = Fset (member A \ member B)" - -lemma union_insert [code]: - "union (Set xs) A = foldl (\A x. insert x A) A xs" -proof - - have "foldl (\A x. Set.insert x A) (member A) xs = - member (foldl (\A x. Fset (Set.insert x (member A))) A xs)" - by (rule foldl_apply_inv) simp - then show ?thesis by (simp add: union_def union_set insert_def) -qed - -definition subtract :: "'a fset \ 'a fset \ 'a fset" where - "subtract A B = Fset (member B - member A)" - -lemma subtract_remove [code]: - "subtract (Set xs) A = foldl (\A x. remove x A) A xs" -proof - - have "foldl (\A x. List_Set.remove x A) (member A) xs = - member (foldl (\A x. Fset (List_Set.remove x (member A))) A xs)" - by (rule foldl_apply_inv) simp - then show ?thesis by (simp add: subtract_def minus_set remove_def) -qed - - -subsection {* Derived operations *} - -lemma member_exists [code]: - "member A y \ exists (\x. y = x) A" - by (simp add: exists_def mem_def) - -definition subfset_eq :: "'a fset \ 'a fset \ bool" where - "subfset_eq A B \ member A \ member B" - -lemma subfset_eq_forall [code]: - "subfset_eq A B \ forall (\x. member B x) A" - by (simp add: subfset_eq_def subset_eq forall_def mem_def) - -definition subfset :: "'a fset \ 'a fset \ bool" where - "subfset A B \ member A \ member B" - -lemma subfset_subfset_eq [code]: - "subfset A B \ subfset_eq A B \ \ subfset_eq B A" - by (simp add: subfset_def subfset_eq_def subset) - -lemma eq_fset_subfset_eq [code]: - "eq_class.eq A B \ subfset_eq A B \ subfset_eq B A" - by (cases A, cases B) (simp add: eq subfset_eq_def set_eq) - -definition inter :: "'a fset \ 'a fset \ 'a fset" where - "inter A B = Fset (List_Set.project (member A) (member B))" - -lemma inter_project [code]: - "inter A B = project (member A) B" - by (simp add: inter_def project_def inter) - - -subsection {* Misc operations *} - -lemma size_fset [code]: - "fset_size f A = 0" - "size A = 0" - by (cases A, simp) (cases A, simp) - -lemma fset_case_code [code]: - "fset_case f A = f (member A)" - by (cases A) simp - -lemma fset_rec_code [code]: - "fset_rec f A = f (member A)" - by (cases A) simp - -end diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/Executable_Set.thy --- a/src/HOL/Library/Executable_Set.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Library/Executable_Set.thy Tue Jun 30 14:55:06 2009 +0200 @@ -5,249 +5,43 @@ header {* Implementation of finite sets by lists *} theory Executable_Set -imports Main +imports Main Fset begin -subsection {* Definitional rewrites *} +subsection {* Derived set operations *} + +declare member [code] definition subset :: "'a set \ 'a set \ bool" where "subset = op \" declare subset_def [symmetric, code unfold] -lemma [code]: "subset A B \ (\x\A. x \ B)" - unfolding subset_def subset_eq .. - -definition is_empty :: "'a set \ bool" where - "is_empty A \ A = {}" +lemma [code]: + "subset A B \ (\x\A. x \ B)" + by (simp add: subset_def subset_eq) definition eq_set :: "'a set \ 'a set \ bool" where [code del]: "eq_set = op =" -lemma [code]: "eq_set A B \ A \ B \ B \ A" - unfolding eq_set_def by auto - (* FIXME allow for Stefan's code generator: declare set_eq_subset[code unfold] *) lemma [code]: - "a \ A \ (\x\A. x = a)" - unfolding bex_triv_one_point1 .. - -definition filter_set :: "('a \ bool) \ 'a set \ 'a set" where - "filter_set P xs = {x\xs. P x}" - -declare filter_set_def[symmetric, code unfold] - - -subsection {* Operations on lists *} - -subsubsection {* Basic definitions *} - -definition - flip :: "('a \ 'b \ 'c) \ 'b \ 'a \ 'c" where - "flip f a b = f b a" - -definition - member :: "'a list \ 'a \ bool" where - "member xs x \ x \ set xs" - -definition - insertl :: "'a \ 'a list \ 'a list" where - "insertl x xs = (if member xs x then xs else x#xs)" - -lemma [code target: List]: "member [] y \ False" - and [code target: List]: "member (x#xs) y \ y = x \ member xs y" - unfolding member_def by (induct xs) simp_all - -fun - drop_first :: "('a \ bool) \ 'a list \ 'a list" where - "drop_first f [] = []" -| "drop_first f (x#xs) = (if f x then xs else x # drop_first f xs)" -declare drop_first.simps [code del] -declare drop_first.simps [code target: List] + "eq_set A B \ A \ B \ B \ A" + by (simp add: eq_set_def set_eq) -declare remove1.simps [code del] -lemma [code target: List]: - "remove1 x xs = (if member xs x then drop_first (\y. y = x) xs else xs)" -proof (cases "member xs x") - case False thus ?thesis unfolding member_def by (induct xs) auto -next - case True - have "remove1 x xs = drop_first (\y. y = x) xs" by (induct xs) simp_all - with True show ?thesis by simp -qed - -lemma member_nil [simp]: - "member [] = (\x. False)" -proof (rule ext) - fix x - show "member [] x = False" unfolding member_def by simp -qed +declare inter [code] -lemma member_insertl [simp]: - "x \ set (insertl x xs)" - unfolding insertl_def member_def mem_iff by simp - -lemma insertl_member [simp]: - fixes xs x - assumes member: "member xs x" - shows "insertl x xs = xs" - using member unfolding insertl_def by simp - -lemma insertl_not_member [simp]: - fixes xs x - assumes member: "\ (member xs x)" - shows "insertl x xs = x # xs" - using member unfolding insertl_def by simp - -lemma foldr_remove1_empty [simp]: - "foldr remove1 xs [] = []" - by (induct xs) simp_all +declare Inter_image_eq [symmetric, code] +declare Union_image_eq [symmetric, code] -subsubsection {* Derived definitions *} - -function unionl :: "'a list \ 'a list \ 'a list" -where - "unionl [] ys = ys" -| "unionl xs ys = foldr insertl xs ys" -by pat_completeness auto -termination by lexicographic_order - -lemmas unionl_eq = unionl.simps(2) - -function intersect :: "'a list \ 'a list \ 'a list" -where - "intersect [] ys = []" -| "intersect xs [] = []" -| "intersect xs ys = filter (member xs) ys" -by pat_completeness auto -termination by lexicographic_order - -lemmas intersect_eq = intersect.simps(3) - -function subtract :: "'a list \ 'a list \ 'a list" -where - "subtract [] ys = ys" -| "subtract xs [] = []" -| "subtract xs ys = foldr remove1 xs ys" -by pat_completeness auto -termination by lexicographic_order - -lemmas subtract_eq = subtract.simps(3) - -function map_distinct :: "('a \ 'b) \ 'a list \ 'b list" -where - "map_distinct f [] = []" -| "map_distinct f xs = foldr (insertl o f) xs []" -by pat_completeness auto -termination by lexicographic_order - -lemmas map_distinct_eq = map_distinct.simps(2) - -function unions :: "'a list list \ 'a list" -where - "unions [] = []" -| "unions xs = foldr unionl xs []" -by pat_completeness auto -termination by lexicographic_order - -lemmas unions_eq = unions.simps(2) - -consts intersects :: "'a list list \ 'a list" -primrec - "intersects (x#xs) = foldr intersect xs x" - -definition - map_union :: "'a list \ ('a \ 'b list) \ 'b list" where - "map_union xs f = unions (map f xs)" - -definition - map_inter :: "'a list \ ('a \ 'b list) \ 'b list" where - "map_inter xs f = intersects (map f xs)" - - -subsection {* Isomorphism proofs *} - -lemma iso_member: - "member xs x \ x \ set xs" - unfolding member_def mem_iff .. +subsection {* Rewrites for primitive operations *} -lemma iso_insert: - "set (insertl x xs) = insert x (set xs)" - unfolding insertl_def iso_member by (simp add: insert_absorb) - -lemma iso_remove1: - assumes distnct: "distinct xs" - shows "set (remove1 x xs) = set xs - {x}" - using distnct set_remove1_eq by auto - -lemma iso_union: - "set (unionl xs ys) = set xs \ set ys" - unfolding unionl_eq - by (induct xs arbitrary: ys) (simp_all add: iso_insert) - -lemma iso_intersect: - "set (intersect xs ys) = set xs \ set ys" - unfolding intersect_eq Int_def by (simp add: Int_def iso_member) auto - -definition - subtract' :: "'a list \ 'a list \ 'a list" where - "subtract' = flip subtract" - -lemma iso_subtract: - fixes ys - assumes distnct: "distinct ys" - shows "set (subtract' ys xs) = set ys - set xs" - and "distinct (subtract' ys xs)" - unfolding subtract'_def flip_def subtract_eq - using distnct by (induct xs arbitrary: ys) auto - -lemma iso_map_distinct: - "set (map_distinct f xs) = image f (set xs)" - unfolding map_distinct_eq by (induct xs) (simp_all add: iso_insert) +declare List_Set.project_def [symmetric, code unfold] -lemma iso_unions: - "set (unions xss) = \ set (map set xss)" - unfolding unions_eq -proof (induct xss) - case Nil show ?case by simp -next - case (Cons xs xss) thus ?case by (induct xs) (simp_all add: iso_insert) -qed - -lemma iso_intersects: - "set (intersects (xs#xss)) = \ set (map set (xs#xss))" - by (induct xss) (simp_all add: Int_def iso_member, auto) - -lemma iso_UNION: - "set (map_union xs f) = UNION (set xs) (set o f)" - unfolding map_union_def iso_unions by simp - -lemma iso_INTER: - "set (map_inter (x#xs) f) = INTER (set (x#xs)) (set o f)" - unfolding map_inter_def iso_intersects by (induct xs) (simp_all add: iso_member, auto) - -definition - Blall :: "'a list \ ('a \ bool) \ bool" where - "Blall = flip list_all" -definition - Blex :: "'a list \ ('a \ bool) \ bool" where - "Blex = flip list_ex" - -lemma iso_Ball: - "Blall xs f = Ball (set xs) f" - unfolding Blall_def flip_def by (induct xs) simp_all - -lemma iso_Bex: - "Blex xs f = Bex (set xs) f" - unfolding Blex_def flip_def by (induct xs) simp_all - -lemma iso_filter: - "set (filter P xs) = filter_set P (set xs)" - unfolding filter_set_def by (induct xs) auto subsection {* code generator setup *} @@ -257,23 +51,33 @@ nonfix subset; *} -subsubsection {* const serializations *} +definition flip :: "('a \ 'b \ 'c) \ 'b \ 'a \ 'c" where + "flip f a b = f b a" + +types_code + fset ("(_/ \fset)") +attach {* +datatype 'a fset = Set of 'a list; +*} + +consts_code + Set ("\Set") consts_code - "Set.empty" ("{*[]*}") - insert ("{*insertl*}") - is_empty ("{*null*}") - "op \" ("{*unionl*}") - "op \" ("{*intersect*}") - "op - \ 'a set \ 'a set \ 'a set" ("{* flip subtract *}") - image ("{*map_distinct*}") - Union ("{*unions*}") - Inter ("{*intersects*}") - UNION ("{*map_union*}") - INTER ("{*map_inter*}") - Ball ("{*Blall*}") - Bex ("{*Blex*}") - filter_set ("{*filter*}") - fold ("{* foldl o flip *}") + "Set.empty" ("{*Fset.empty*}") + "List_Set.is_empty" ("{*Fset.is_empty*}") + "Set.insert" ("{*Fset.insert*}") + "List_Set.remove" ("{*Fset.remove*}") + "Set.image" ("{*Fset.map*}") + "List_Set.project" ("{*Fset.filter*}") + "Ball" ("{*flip Fset.forall*}") + "Bex" ("{*flip Fset.exists*}") + "op \" ("{*Fset.union*}") + "op \" ("{*Fset.inter*}") + "op - \ 'a set \ 'a set \ 'a set" ("{*flip Fset.subtract*}") + "Set.Union" ("{*Fset.Union*}") + "Set.Inter" ("{*Fset.Inter*}") + card ("{*Fset.card*}") + fold ("{*foldl o flip*}") -end +end \ No newline at end of file diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/Float.thy --- a/src/HOL/Library/Float.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Library/Float.thy Tue Jun 30 14:55:06 2009 +0200 @@ -59,6 +59,12 @@ "real (Float -1 0) = -1" and "real (Float (number_of n) 0) = number_of n" by auto +lemma float_number_of[simp]: "real (number_of x :: float) = number_of x" + by (simp only:number_of_float_def Float_num[unfolded number_of_is_id]) + +lemma float_number_of_int[simp]: "real (Float n 0) = real n" + by (simp add: Float_num[unfolded number_of_is_id] real_of_float_simp pow2_def) + lemma pow2_0[simp]: "pow2 0 = 1" by simp lemma pow2_1[simp]: "pow2 1 = 2" by simp lemma pow2_neg: "pow2 x = inverse (pow2 (-x))" by simp diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/Fset.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Library/Fset.thy Tue Jun 30 14:55:06 2009 +0200 @@ -0,0 +1,240 @@ + +(* Author: Florian Haftmann, TU Muenchen *) + +header {* Executable finite sets *} + +theory Fset +imports List_Set +begin + +lemma foldl_apply_inv: + assumes "\x. g (h x) = x" + shows "foldl f (g s) xs = g (foldl (\s x. h (f (g s) x)) s xs)" + by (rule sym, induct xs arbitrary: s) (simp_all add: assms) + +declare mem_def [simp] + + +subsection {* Lifting *} + +datatype 'a fset = Fset "'a set" + +primrec member :: "'a fset \ 'a set" where + "member (Fset A) = A" + +lemma Fset_member [simp]: + "Fset (member A) = A" + by (cases A) simp + +definition Set :: "'a list \ 'a fset" where + "Set xs = Fset (set xs)" + +lemma member_Set [simp]: + "member (Set xs) = set xs" + by (simp add: Set_def) + +code_datatype Set + + +subsection {* Basic operations *} + +definition is_empty :: "'a fset \ bool" where + [simp]: "is_empty A \ List_Set.is_empty (member A)" + +lemma is_empty_Set [code]: + "is_empty (Set xs) \ null xs" + by (simp add: is_empty_set) + +definition empty :: "'a fset" where + [simp]: "empty = Fset {}" + +lemma empty_Set [code]: + "empty = Set []" + by (simp add: Set_def) + +definition insert :: "'a \ 'a fset \ 'a fset" where + [simp]: "insert x A = Fset (Set.insert x (member A))" + +lemma insert_Set [code]: + "insert x (Set xs) = Set (List_Set.insert x xs)" + by (simp add: Set_def insert_set) + +definition remove :: "'a \ 'a fset \ 'a fset" where + [simp]: "remove x A = Fset (List_Set.remove x (member A))" + +lemma remove_Set [code]: + "remove x (Set xs) = Set (remove_all x xs)" + by (simp add: Set_def remove_set) + +definition map :: "('a \ 'b) \ 'a fset \ 'b fset" where + [simp]: "map f A = Fset (image f (member A))" + +lemma map_Set [code]: + "map f (Set xs) = Set (remdups (List.map f xs))" + by (simp add: Set_def) + +definition filter :: "('a \ bool) \ 'a fset \ 'a fset" where + [simp]: "filter P A = Fset (List_Set.project P (member A))" + +lemma filter_Set [code]: + "filter P (Set xs) = Set (List.filter P xs)" + by (simp add: Set_def project_set) + +definition forall :: "('a \ bool) \ 'a fset \ bool" where + [simp]: "forall P A \ Ball (member A) P" + +lemma forall_Set [code]: + "forall P (Set xs) \ list_all P xs" + by (simp add: Set_def ball_set) + +definition exists :: "('a \ bool) \ 'a fset \ bool" where + [simp]: "exists P A \ Bex (member A) P" + +lemma exists_Set [code]: + "exists P (Set xs) \ list_ex P xs" + by (simp add: Set_def bex_set) + +definition card :: "'a fset \ nat" where + [simp]: "card A = Finite_Set.card (member A)" + +lemma card_Set [code]: + "card (Set xs) = length (remdups xs)" +proof - + have "Finite_Set.card (set (remdups xs)) = length (remdups xs)" + by (rule distinct_card) simp + then show ?thesis by (simp add: Set_def card_def) +qed + + +subsection {* Derived operations *} + +lemma member_exists [code]: + "member A y \ exists (\x. y = x) A" + by simp + +definition subfset_eq :: "'a fset \ 'a fset \ bool" where + [simp]: "subfset_eq A B \ member A \ member B" + +lemma subfset_eq_forall [code]: + "subfset_eq A B \ forall (\x. member B x) A" + by (simp add: subset_eq) + +definition subfset :: "'a fset \ 'a fset \ bool" where + [simp]: "subfset A B \ member A \ member B" + +lemma subfset_subfset_eq [code]: + "subfset A B \ subfset_eq A B \ \ subfset_eq B A" + by (simp add: subset) + +lemma eq_fset_subfset_eq [code]: + "eq_class.eq A B \ subfset_eq A B \ subfset_eq B A" + by (cases A, cases B) (simp add: eq set_eq) + +definition inter :: "'a fset \ 'a fset \ 'a fset" where + [simp]: "inter A B = Fset (project (member A) (member B))" + +lemma inter_project [code]: + "inter A B = filter (member A) B" + by (simp add: inter) + + +subsection {* Functorial operations *} + +definition union :: "'a fset \ 'a fset \ 'a fset" where + [simp]: "union A B = Fset (member A \ member B)" + +lemma union_insert [code]: + "union (Set xs) A = foldl (\A x. insert x A) A xs" +proof - + have "foldl (\A x. Set.insert x A) (member A) xs = + member (foldl (\A x. Fset (Set.insert x (member A))) A xs)" + by (rule foldl_apply_inv) simp + then show ?thesis by (simp add: union_set) +qed + +definition subtract :: "'a fset \ 'a fset \ 'a fset" where + [simp]: "subtract A B = Fset (member B - member A)" + +lemma subtract_remove [code]: + "subtract (Set xs) A = foldl (\A x. remove x A) A xs" +proof - + have "foldl (\A x. List_Set.remove x A) (member A) xs = + member (foldl (\A x. Fset (List_Set.remove x (member A))) A xs)" + by (rule foldl_apply_inv) simp + then show ?thesis by (simp add: minus_set) +qed + +definition Inter :: "'a fset fset \ 'a fset" where + [simp]: "Inter A = Fset (Set.Inter (member ` member A))" + +lemma Inter_inter [code]: + "Inter (Set (A # As)) = foldl inter A As" +proof - + note Inter_image_eq [simp del] set_map [simp del] set.simps [simp del] + have "foldl (op \) (member A) (List.map member As) = + member (foldl (\B A. Fset (member B \ A)) A (List.map member As))" + by (rule foldl_apply_inv) simp + then show ?thesis + by (simp add: Inter_set image_set inter_def_raw inter foldl_map) +qed + +definition Union :: "'a fset fset \ 'a fset" where + [simp]: "Union A = Fset (Set.Union (member ` member A))" + +lemma Union_union [code]: + "Union (Set As) = foldl union empty As" +proof - + note Union_image_eq [simp del] set_map [simp del] + have "foldl (op \) (member empty) (List.map member As) = + member (foldl (\B A. Fset (member B \ A)) empty (List.map member As))" + by (rule foldl_apply_inv) simp + then show ?thesis + by (simp add: Union_set image_set union_def_raw foldl_map) +qed + + +subsection {* Misc operations *} + +lemma size_fset [code]: + "fset_size f A = 0" + "size A = 0" + by (cases A, simp) (cases A, simp) + +lemma fset_case_code [code]: + "fset_case f A = f (member A)" + by (cases A) simp + +lemma fset_rec_code [code]: + "fset_rec f A = f (member A)" + by (cases A) simp + + +subsection {* Simplified simprules *} + +lemma is_empty_simp [simp]: + "is_empty A \ member A = {}" + by (simp add: List_Set.is_empty_def) +declare is_empty_def [simp del] + +lemma remove_simp [simp]: + "remove x A = Fset (member A - {x})" + by (simp add: List_Set.remove_def) +declare remove_def [simp del] + +lemma filter_simp [simp]: + "filter P A = Fset {x \ member A. P x}" + by (simp add: List_Set.project_def) +declare filter_def [simp del] + +lemma inter_simp [simp]: + "inter A B = Fset (member A \ member B)" + by (simp add: inter) +declare inter_def [simp del] + +declare mem_def [simp del] + + +hide (open) const is_empty empty insert remove map filter forall exists card + subfset_eq subfset inter union subtract Inter Union + +end diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/Library.thy --- a/src/HOL/Library/Library.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Library/Library.thy Tue Jun 30 14:55:06 2009 +0200 @@ -10,7 +10,6 @@ Char_ord Code_Char_chr Code_Integer - Code_Set Coinductive_List Commutative_Ring Continuity @@ -28,6 +27,7 @@ Formal_Power_Series Fraction_Field FrechetDeriv + Fset FuncSet Fundamental_Theorem_Algebra Infinite_Set diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Library/List_Set.thy --- a/src/HOL/Library/List_Set.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Library/List_Set.thy Tue Jun 30 14:55:06 2009 +0200 @@ -70,7 +70,7 @@ by (auto simp add: remove_def remove_all_def) lemma image_set: - "image f (set xs) = set (remdups (map f xs))" + "image f (set xs) = set (map f xs)" by simp lemma project_set: @@ -160,4 +160,7 @@ "A \ B = project (\x. x \ A) B" by (auto simp add: project_def) + +hide (open) const insert + end \ No newline at end of file diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/MicroJava/BV/BVExample.thy --- a/src/HOL/MicroJava/BV/BVExample.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/MicroJava/BV/BVExample.thy Tue Jun 30 14:55:06 2009 +0200 @@ -1,5 +1,4 @@ (* Title: HOL/MicroJava/BV/BVExample.thy - ID: $Id$ Author: Gerwin Klein *) @@ -94,7 +93,7 @@ text {* Method and field lookup: *} lemma method_Object [simp]: - "method (E, Object) = empty" + "method (E, Object) = Map.empty" by (simp add: method_rec_lemma [OF class_Object wf_subcls1_E]) lemma method_append [simp]: @@ -436,7 +435,7 @@ "some_elem = (%S. SOME x. x : S)" consts_code - "some_elem" ("hd") + "some_elem" ("(case/ _ of/ {*Set*}/ xs/ =>/ hd/ xs)") text {* This code setup is just a demonstration and \emph{not} sound! *} @@ -451,11 +450,11 @@ qed lemma [code]: - "iter f step ss w = while (\(ss, w). \ (is_empty w)) + "iter f step ss w = while (\(ss, w). \ is_empty w) (\(ss, w). let p = some_elem w in propa f (step p (ss ! p)) ss (w - {p})) (ss, w)" - unfolding iter_def is_empty_def some_elem_def .. + unfolding iter_def List_Set.is_empty_def some_elem_def .. lemma JVM_sup_unfold [code]: "JVMType.sup S m n = lift2 (Opt.sup @@ -475,7 +474,6 @@ test1 = "test_kil E list_name [Class list_name] (PrimT Void) 3 0 [(Suc 0, 2, 8, Xcpt NullPointer)] append_ins" test2 = "test_kil E test_name [] (PrimT Void) 3 2 [] make_list_ins" - ML BV.test1 ML BV.test2 diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/Datatype/datatype.ML --- a/src/HOL/Tools/Datatype/datatype.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/Datatype/datatype.ML Tue Jun 30 14:55:06 2009 +0200 @@ -18,7 +18,7 @@ val the_info : theory -> string -> info val the_descr : theory -> string list -> descr * (string * sort) list * string list - * (string list * string list) * (typ list * typ list) + * string * (string list * string list) * (typ list * typ list) val the_spec : theory -> string -> (string * sort) list * (string * typ list) list val get_constrs : theory -> string -> (string * typ) list option val get_all : theory -> info Symtab.table @@ -125,9 +125,10 @@ val names = map Long_Name.base_name (the_default tycos (#alt_names info)); val (auxnames, _) = Name.make_context names - |> fold_map (yield_singleton Name.variants o name_of_typ) Us + |> fold_map (yield_singleton Name.variants o name_of_typ) Us; + val prefix = space_implode "_" names; - in (descr, vs, tycos, (names, auxnames), (Ts, Us)) end; + in (descr, vs, tycos, prefix, (names, auxnames), (Ts, Us)) end; fun get_constrs thy dtco = case try (the_spec thy) dtco diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/dseq.ML --- a/src/HOL/Tools/dseq.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/dseq.ML Tue Jun 30 14:55:06 2009 +0200 @@ -1,5 +1,4 @@ (* Title: HOL/Tools/dseq.ML - ID: $Id$ Author: Stefan Berghofer, TU Muenchen Sequences with recursion depth limit. diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/inductive_codegen.ML --- a/src/HOL/Tools/inductive_codegen.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/inductive_codegen.ML Tue Jun 30 14:55:06 2009 +0200 @@ -378,7 +378,7 @@ end | compile_prems out_ts vs names ps gr = let - val vs' = distinct (op =) (List.concat (vs :: map term_vs out_ts)); + val vs' = distinct (op =) (flat (vs :: map term_vs out_ts)); val SOME (p, mode as SOME (Mode (_, js, _))) = select_mode_prem thy modes' vs' ps; val ps' = filter_out (equal p) ps; @@ -404,7 +404,9 @@ (compile_expr thy defs dep module false modes (mode, t) gr2) else - apfst (fn p => [str "DSeq.of_list", Pretty.brk 1, p]) + apfst (fn p => Pretty.breaks [str "DSeq.of_list", str "(case", p, + str "of", str "Set", str "xs", str "=>", str "xs)"]) + (*this is a very strong assumption about the generated code!*) (invoke_codegen thy defs dep module true t gr2); val (rest, gr4) = compile_prems out_ts''' vs' (fst nvs) ps' gr3; in @@ -661,8 +663,10 @@ let val (call_p, gr') = mk_ind_call thy defs dep module true s T (ts1 @ ts2') names thyname k intrs gr in SOME ((if brack then parens else I) (Pretty.block - [str "DSeq.list_of", Pretty.brk 1, str "(", - conv_ntuple fs ots call_p, str ")"]), gr') + [str "Set", Pretty.brk 1, str "(DSeq.list_of", Pretty.brk 1, str "(", + conv_ntuple fs ots call_p, str "))"]), + (*this is a very strong assumption about the generated code!*) + gr') end else NONE end diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/quickcheck_generators.ML --- a/src/HOL/Tools/quickcheck_generators.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/quickcheck_generators.ML Tue Jun 30 14:55:06 2009 +0200 @@ -11,10 +11,10 @@ -> (seed -> ('b * (unit -> term)) * seed) -> (seed -> seed * seed) -> seed -> (('a -> 'b) * (unit -> Term.term)) * seed val ensure_random_typecopy: string -> theory -> theory - val random_aux_specification: string -> term list -> local_theory -> local_theory + val random_aux_specification: string -> string -> term list -> local_theory -> local_theory val mk_random_aux_eqs: theory -> Datatype.descr -> (string * sort) list -> string list -> string list * string list -> typ list * typ list - -> string * (term list * (term * term) list) + -> term list * (term * term) list val ensure_random_datatype: Datatype.config -> string list -> theory -> theory val eval_ref: (unit -> int -> seed -> term list option * seed) option ref val setup: theory -> theory @@ -184,18 +184,18 @@ end; -fun random_aux_primrec_multi prefix [eq] lthy = +fun random_aux_primrec_multi auxname [eq] lthy = lthy |> random_aux_primrec eq |>> (fn simp => [simp]) - | random_aux_primrec_multi prefix (eqs as _ :: _ :: _) lthy = + | random_aux_primrec_multi auxname (eqs as _ :: _ :: _) lthy = let val thy = ProofContext.theory_of lthy; val (lhss, rhss) = map_split (HOLogic.dest_eq o HOLogic.dest_Trueprop) eqs; val (vs, (arg as Free (v, _)) :: _) = map_split (fn (t1 $ t2) => (t1, t2)) lhss; val Ts = map fastype_of lhss; val tupleT = foldr1 HOLogic.mk_prodT Ts; - val aux_lhs = Free ("mutual_" ^ prefix, fastype_of arg --> tupleT) $ arg; + val aux_lhs = Free ("mutual_" ^ auxname, fastype_of arg --> tupleT) $ arg; val aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq) (aux_lhs, foldr1 HOLogic.mk_prod rhss); fun mk_proj t [T] = [t] @@ -223,7 +223,7 @@ |-> (fn (aux_simp, proj_defs) => prove_eqs aux_simp proj_defs) end; -fun random_aux_specification prefix eqs lthy = +fun random_aux_specification prfx name eqs lthy = let val vs = fold Term.add_free_names ((snd o strip_comb o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o hd) eqs) []; @@ -237,10 +237,10 @@ val ext_simps = map (fn thm => fun_cong OF [fun_cong OF [thm]]) proto_simps; val tac = ALLGOALS (ProofContext.fact_tac ext_simps); in (map (fn prop => SkipProof.prove lthy vs [] prop (K tac)) eqs, lthy) end; - val b = Binding.qualify true prefix (Binding.name "simps"); + val b = Binding.qualify true prfx (Binding.qualify true name (Binding.name "simps")); in lthy - |> random_aux_primrec_multi prefix proto_eqs + |> random_aux_primrec_multi (name ^ prfx) proto_eqs |-> (fn proto_simps => prove_simps proto_simps) |-> (fn simps => LocalTheory.note Thm.generatedK ((b, Code.add_default_eqn_attrib :: map (Attrib.internal o K) @@ -252,6 +252,8 @@ (* constructing random instances on datatypes *) +val random_auxN = "random_aux"; + fun mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us) = let val mk_const = curry (Sign.mk_const thy); @@ -259,7 +261,6 @@ val i1 = @{term "(i\code_numeral) - 1"}; val j = @{term "j\code_numeral"}; val seed = @{term "s\Random.seed"}; - val random_auxN = "random_aux"; val random_auxsN = map (prefix (random_auxN ^ "_")) (names @ auxnames); fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit \ term"}); val rTs = Ts @ Us; @@ -316,10 +317,9 @@ $ seed; val auxs_lhss = map (fn t => t $ i $ j $ seed) random_auxs; val auxs_rhss = map mk_select gen_exprss; - val prefix = space_implode "_" (random_auxN :: names); - in (prefix, (random_auxs, auxs_lhss ~~ auxs_rhss)) end; + in (random_auxs, auxs_lhss ~~ auxs_rhss) end; -fun mk_random_datatype config descr vs tycos (names, auxnames) (Ts, Us) thy = +fun mk_random_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy = let val _ = DatatypeAux.message config "Creating quickcheck generators ..."; val i = @{term "i\code_numeral"}; @@ -329,14 +329,14 @@ else @{term "max :: code_numeral \ code_numeral \ code_numeral"} $ HOLogic.mk_number @{typ code_numeral} l $ i | NONE => i; - val (prefix, (random_auxs, auxs_eqs)) = (apsnd o apsnd o map) mk_prop_eq + val (random_auxs, auxs_eqs) = (apsnd o map) mk_prop_eq (mk_random_aux_eqs thy descr vs tycos (names, auxnames) (Ts, Us)); val random_defs = map_index (fn (k, T) => mk_prop_eq (HOLogic.mk_random T i, nth random_auxs k $ mk_size_arg k $ i)) Ts; in thy |> TheoryTarget.instantiation (tycos, vs, @{sort random}) - |> random_aux_specification prefix auxs_eqs + |> random_aux_specification prfx random_auxN auxs_eqs |> `(fn lthy => map (Syntax.check_term lthy) random_defs) |-> (fn random_defs' => fold_map (fn random_def => Specification.definition (NONE, (Attrib.empty_binding, @@ -359,7 +359,7 @@ let val pp = Syntax.pp_global thy; val algebra = Sign.classes_of thy; - val (descr, raw_vs, tycos, (names, auxnames), raw_TUs) = + val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) = Datatype.the_descr thy raw_tycos; val typrep_vs = (map o apsnd) (curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs; @@ -374,7 +374,7 @@ in if has_inst then thy else case perhaps_constrain thy (random_insts @ term_of_insts) typrep_vs of SOME constrain => mk_random_datatype config descr - (map constrain typrep_vs) tycos (names, auxnames) + (map constrain typrep_vs) tycos prfx (names, auxnames) ((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy | NONE => thy end; diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/res_atp.ML --- a/src/HOL/Tools/res_atp.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/res_atp.ML Tue Jun 30 14:55:06 2009 +0200 @@ -11,8 +11,9 @@ val prepare_clauses : bool -> thm list -> thm list -> (thm * (ResHolClause.axiom_name * ResHolClause.clause_id)) list -> (thm * (ResHolClause.axiom_name * ResHolClause.clause_id)) list -> theory -> - ResHolClause.axiom_name vector * (ResHolClause.clause list * ResHolClause.clause list * - ResHolClause.clause list * ResClause.classrelClause list * ResClause.arityClause list) + ResHolClause.axiom_name vector * + (ResHolClause.clause list * ResHolClause.clause list * ResHolClause.clause list * + ResHolClause.clause list * ResClause.classrelClause list * ResClause.arityClause list) end; structure ResAtp: RES_ATP = @@ -550,13 +551,14 @@ and tycons = type_consts_of_terms thy (ccltms@axtms) (*TFrees in conjecture clauses; TVars in axiom clauses*) val conjectures = ResHolClause.make_conjecture_clauses dfg thy ccls + val (_, extra_clauses) = ListPair.unzip (ResHolClause.make_axiom_clauses dfg thy extra_cls) val (clnames,axiom_clauses) = ListPair.unzip (ResHolClause.make_axiom_clauses dfg thy axcls) val helper_clauses = ResHolClause.get_helper_clauses dfg thy isFO (conjectures, extra_cls, []) val (supers',arity_clauses) = ResClause.make_arity_clauses_dfg dfg thy tycons supers val classrel_clauses = ResClause.make_classrel_clauses thy subs supers' in (Vector.fromList clnames, - (conjectures, axiom_clauses, helper_clauses, classrel_clauses, arity_clauses)) + (conjectures, axiom_clauses, extra_clauses, helper_clauses, classrel_clauses, arity_clauses)) end end; diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/res_hol_clause.ML --- a/src/HOL/Tools/res_hol_clause.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/res_hol_clause.ML Tue Jun 30 14:55:06 2009 +0200 @@ -36,10 +36,12 @@ clause list * (thm * (axiom_name * clause_id)) list * string list -> clause list val tptp_write_file: bool -> Path.T -> - clause list * clause list * clause list * ResClause.classrelClause list * ResClause.arityClause list -> + clause list * clause list * clause list * clause list * + ResClause.classrelClause list * ResClause.arityClause list -> int * int val dfg_write_file: bool -> Path.T -> - clause list * clause list * clause list * ResClause.classrelClause list * ResClause.arityClause list -> + clause list * clause list * clause list * clause list * + ResClause.classrelClause list * ResClause.arityClause list -> int * int end @@ -459,11 +461,11 @@ Output.debug (fn () => "Constant: " ^ c ^ " arity:\t" ^ Int.toString n ^ (if needs_hBOOL const_needs_hBOOL c then " needs hBOOL" else "")); -fun count_constants (conjectures, axclauses, helper_clauses, _, _) = +fun count_constants (conjectures, _, extra_clauses, helper_clauses, _, _) = if minimize_applies then let val (const_min_arity, const_needs_hBOOL) = fold count_constants_clause conjectures (Symtab.empty, Symtab.empty) - |> fold count_constants_clause axclauses + |> fold count_constants_clause extra_clauses |> fold count_constants_clause helper_clauses val _ = List.app (display_arity const_needs_hBOOL) (Symtab.dest (const_min_arity)) in (const_min_arity, const_needs_hBOOL) end @@ -473,7 +475,8 @@ fun tptp_write_file t_full file clauses = let - val (conjectures, axclauses, helper_clauses, classrel_clauses, arity_clauses) = clauses + val (conjectures, axclauses, _, helper_clauses, + classrel_clauses, arity_clauses) = clauses val (cma, cnh) = count_constants clauses val params = (t_full, cma, cnh) val (tptp_clss,tfree_litss) = ListPair.unzip (map (clause2tptp params) conjectures) @@ -494,7 +497,8 @@ fun dfg_write_file t_full file clauses = let - val (conjectures, axclauses, helper_clauses, classrel_clauses, arity_clauses) = clauses + val (conjectures, axclauses, _, helper_clauses, + classrel_clauses, arity_clauses) = clauses val (cma, cnh) = count_constants clauses val params = (t_full, cma, cnh) val (dfg_clss, tfree_litss) = ListPair.unzip (map (clause2dfg params) conjectures) diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/Tools/res_reconstruct.ML --- a/src/HOL/Tools/res_reconstruct.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/Tools/res_reconstruct.ML Tue Jun 30 14:55:06 2009 +0200 @@ -457,9 +457,28 @@ in trace msg; msg end; - - (* ==== CHECK IF PROOF OF E OR VAMPIRE WAS SUCCESSFUL === *) - + (*=== EXTRACTING PROOF-TEXT === *) + + val begin_proof_strings = ["# SZS output start CNFRefutation.", + "=========== Refutation ==========", + "Here is a proof"]; + val end_proof_strings = ["# SZS output end CNFRefutation", + "======= End of refutation =======", + "Formulae used in the proof"]; + fun get_proof_extract proof = + let + (*splits to_split by the first possible of a list of splitters*) + val (begin_string, end_string) = + (find_first (fn s => String.isSubstring s proof) begin_proof_strings, + find_first (fn s => String.isSubstring s proof) end_proof_strings) + in + if is_none begin_string orelse is_none end_string + then error "Could not extract proof (no substring indicating a proof)" + else proof |> first_field (the begin_string) |> the |> snd + |> first_field (the end_string) |> the |> fst end; + +(* ==== CHECK IF PROOF OF E OR VAMPIRE WAS SUCCESSFUL === *) + val failure_strings_E = ["SZS status: Satisfiable","SZS status Satisfiable", "SZS status: ResourceOut","SZS status ResourceOut","# Cannot determine problem status"]; val failure_strings_vampire = ["Satisfiability detected", "Refutation not found", "CANNOT PROVE"]; @@ -469,31 +488,15 @@ fun find_failure proof = let val failures = map_filter (fn s => if String.isSubstring s proof then SOME s else NONE) - (failure_strings_E @ failure_strings_vampire @ failure_strings_SPASS @ failure_strings_remote) - in if null failures then NONE else SOME (hd failures) end; - - (*=== EXTRACTING PROOF-TEXT === *) - - val begin_proof_strings = ["# SZS output start CNFRefutation.", - "=========== Refutation ==========", - "Here is a proof"]; - val end_proof_strings = ["# SZS output end CNFRefutation", - "======= End of refutation =======", - "Formulae used in the proof"]; - fun get_proof_extract proof = - let - (*splits to_split by the first possible of a list of splitters*) - fun first_field_any [] to_split = NONE - | first_field_any (splitter::splitters) to_split = - let - val result = (first_field splitter to_split) - in - if isSome result then result else first_field_any splitters to_split - end - val (a:string, b:string) = valOf (first_field_any begin_proof_strings proof) - val (proofextract:string, c:string) = valOf (first_field_any end_proof_strings b) - in proofextract end; - + (failure_strings_E @ failure_strings_vampire @ failure_strings_SPASS @ failure_strings_remote) + val correct = null failures andalso + exists (fn s => String.isSubstring s proof) begin_proof_strings andalso + exists (fn s => String.isSubstring s proof) end_proof_strings + in + if correct then NONE + else if null failures then SOME "Output of ATP not in proper format" + else SOME (hd failures) end; + (* === EXTRACTING LEMMAS === *) (* lines have the form "cnf(108, axiom, ...", the number (108) has to be extracted)*) diff -r e3de75d3b898 -r 4e03a2cdf611 src/HOL/ex/Codegenerator_Candidates.thy --- a/src/HOL/ex/Codegenerator_Candidates.thy Tue Jun 30 14:54:30 2009 +0200 +++ b/src/HOL/ex/Codegenerator_Candidates.thy Tue Jun 30 14:55:06 2009 +0200 @@ -8,7 +8,7 @@ Complex_Main AssocList Binomial - Code_Set + Fset Commutative_Ring Enum List_Prefix diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/IsaMakefile diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/Isar/class_target.ML --- a/src/Pure/Isar/class_target.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Pure/Isar/class_target.ML Tue Jun 30 14:55:06 2009 +0200 @@ -32,6 +32,7 @@ (*instances*) val init_instantiation: string list * (string * sort) list * sort -> theory -> local_theory + val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state val instantiation_instance: (local_theory -> local_theory) -> local_theory -> Proof.state val prove_instantiation_instance: (Proof.context -> tactic) @@ -44,7 +45,8 @@ val instantiation_param: local_theory -> binding -> string option val confirm_declaration: binding -> local_theory -> local_theory val pretty_instantiation: local_theory -> Pretty.T - val instance_arity_cmd: xstring * xstring list * xstring -> theory -> Proof.state + val read_multi_arity: theory -> xstring list * xstring list * xstring + -> string list * (string * sort) list * sort val type_name: string -> string (*subclasses*) @@ -419,6 +421,15 @@ |> find_first (fn (_, (v, _)) => Binding.name_of b = v) |> Option.map (fst o fst); +fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) = + let + val all_arities = map (fn raw_tyco => Sign.read_arity thy + (raw_tyco, raw_sorts, raw_sort)) raw_tycos; + val tycos = map #1 all_arities; + val (_, sorts, sort) = hd all_arities; + val vs = Name.names Name.context Name.aT sorts; + in (tycos, vs, sort) end; + (* syntax *) @@ -578,15 +589,17 @@ (* simplified instantiation interface with no class parameter *) -fun instance_arity_cmd arities thy = +fun instance_arity_cmd raw_arities thy = let + val (tycos, vs, sort) = read_multi_arity thy raw_arities; + val sorts = map snd vs; + val arities = maps (fn tyco => Logic.mk_arities (tyco, sorts, sort)) tycos; fun after_qed results = ProofContext.theory ((fold o fold) AxClass.add_arity results); in thy |> ProofContext.init - |> Proof.theorem_i NONE after_qed ((map (fn t => [(t, [])]) - o Logic.mk_arities o Sign.read_arity thy) arities) + |> Proof.theorem_i NONE after_qed (map (fn t => [(t, [])]) arities) end; diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/Isar/isar_syn.ML --- a/src/Pure/Isar/isar_syn.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Pure/Isar/isar_syn.ML Tue Jun 30 14:55:06 2009 +0200 @@ -465,7 +465,7 @@ val _ = OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal ((P.xname -- ((P.$$$ "\\" || P.$$$ "<") |-- P.!!! P.xname) >> Class.classrel_cmd || - P.arity >> Class.instance_arity_cmd) + P.multi_arity >> Class.instance_arity_cmd) >> (Toplevel.print oo Toplevel.theory_to_proof) || Scan.succeed (Toplevel.print o Toplevel.local_theory_to_proof NONE (Class.instantiation_instance I))); diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/Isar/theory_target.ML --- a/src/Pure/Isar/theory_target.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Pure/Isar/theory_target.ML Tue Jun 30 14:55:06 2009 +0200 @@ -330,15 +330,6 @@ else I)} and init_lthy_ctxt ta = init_lthy ta o init_ctxt ta; -fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) = - let - val all_arities = map (fn raw_tyco => Sign.read_arity thy - (raw_tyco, raw_sorts, raw_sort)) raw_tycos; - val tycos = map #1 all_arities; - val (_, sorts, sort) = hd all_arities; - val vs = Name.names Name.context Name.aT sorts; - in (tycos, vs, sort) end; - fun gen_overloading prep_const raw_ops thy = let val ctxt = ProofContext.init thy; @@ -356,7 +347,7 @@ fun instantiation arities = init_lthy_ctxt (make_target "" false false arities []); fun instantiation_cmd raw_arities thy = - instantiation (read_multi_arity thy raw_arities) thy; + instantiation (Class_Target.read_multi_arity thy raw_arities) thy; val overloading = gen_overloading (fn ctxt => Syntax.check_term ctxt o Const); val overloading_cmd = gen_overloading Syntax.read_term; diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/System/cygwin.scala diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/System/gui_setup.scala --- a/src/Pure/System/gui_setup.scala Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Pure/System/gui_setup.scala Tue Jun 30 14:55:06 2009 +0200 @@ -29,8 +29,8 @@ // components val text = new TextArea { editable = false - columns = 40 - rows = 15 + columns = 80 + rows = 20 xLayoutAlignment = 0.5 } val ok = new Button { @@ -53,6 +53,7 @@ text.append("Main platform: " + name1 + "\n") text.append("Alternative platform: " + name2 + "\n") } + text.append("Isabelle home: " + java.lang.System.getProperty("isabelle.home")) // reactions listenTo(ok) diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/System/isabelle_system.scala diff -r e3de75d3b898 -r 4e03a2cdf611 src/Pure/System/platform.scala diff -r e3de75d3b898 -r 4e03a2cdf611 src/Tools/Code/code_haskell.ML --- a/src/Tools/Code/code_haskell.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Tools/Code/code_haskell.ML Tue Jun 30 14:55:06 2009 +0200 @@ -25,10 +25,8 @@ fun pr_haskell_bind pr_term = let - fun pr_bind ((NONE, NONE), _) = str "_" - | pr_bind ((SOME v, NONE), _) = str v - | pr_bind ((NONE, SOME p), _) = p - | pr_bind ((SOME v, SOME p), _) = brackets [str v, str "@", p]; + fun pr_bind (NONE, _) = str "_" + | pr_bind (SOME p, _) = p; in gen_pr_bind pr_bind pr_term end; fun pr_haskell_stmt labelled_name syntax_class syntax_tyco syntax_const @@ -72,9 +70,8 @@ (str o Code_Printer.lookup_var vars) v | pr_term tyvars thm vars fxy (t as _ `|=> _) = let - val (binds, t') = Code_Thingol.unfold_abs t; - fun pr ((v, pat), ty) = pr_bind tyvars thm BR ((SOME v, pat), ty); - val (ps, vars') = fold_map pr binds vars; + val (binds, t') = Code_Thingol.unfold_pat_abs t; + val (ps, vars') = fold_map (pr_bind tyvars thm BR) binds vars; in brackets (str "\\" :: ps @ str "->" @@ pr_term tyvars thm vars' NOBR t') end | pr_term tyvars thm vars fxy (ICase (cases as (_, t0))) = (case Code_Thingol.unfold_const_app t0 @@ -103,7 +100,7 @@ val (binds, body) = Code_Thingol.unfold_let (ICase cases); fun pr ((pat, ty), t) vars = vars - |> pr_bind tyvars thm BR ((NONE, SOME pat), ty) + |> pr_bind tyvars thm BR (SOME pat, ty) |>> (fn p => semicolon [p, str "=", pr_term tyvars thm vars NOBR t]) val (ps, vars') = fold_map pr binds vars; in brackify_block fxy (str "let {") @@ -114,7 +111,7 @@ let fun pr (pat, body) = let - val (p, vars') = pr_bind tyvars thm NOBR ((NONE, SOME pat), ty) vars; + val (p, vars') = pr_bind tyvars thm NOBR (SOME pat, ty) vars; in semicolon [p, str "->", pr_term tyvars thm vars' NOBR body] end; in brackify_block fxy (concat [str "case", pr_term tyvars thm vars NOBR t, str "of", str "{"]) @@ -240,8 +237,6 @@ end | pr_stmt (_, Code_Thingol.Classinst ((class, (tyco, vs)), (_, classparam_insts))) = let - val split_abs_pure = (fn (v, _) `|=> t => SOME (v, t) | _ => NONE); - val unfold_abs_pure = Code_Thingol.unfoldr split_abs_pure; val tyvars = Code_Printer.intro_vars (map fst vs) init_syms; fun pr_instdef ((classparam, c_inst), (thm, _)) = case syntax_const classparam of NONE => semicolon [ @@ -255,7 +250,7 @@ val const = if (is_some o syntax_const) c_inst_name then NONE else (SOME o Long_Name.base_name o deresolve) c_inst_name; val proto_rhs = Code_Thingol.eta_expand k (c_inst, []); - val (vs, rhs) = unfold_abs_pure proto_rhs; + val (vs, rhs) = (apfst o map) fst (Code_Thingol.unfold_abs proto_rhs); val vars = init_syms |> Code_Printer.intro_vars (the_list const) |> Code_Printer.intro_vars vs; @@ -447,16 +442,16 @@ fun pretty_haskell_monad c_bind = let - fun dest_bind t1 t2 = case Code_Thingol.split_abs t2 - of SOME (((v, pat), ty), t') => - SOME ((SOME (((SOME v, pat), ty), true), t1), t') + fun dest_bind t1 t2 = case Code_Thingol.split_pat_abs t2 + of SOME ((some_pat, ty), t') => + SOME ((SOME ((some_pat, ty), true), t1), t') | NONE => NONE; fun dest_monad c_bind_name (IConst (c, _) `$ t1 `$ t2) = if c = c_bind_name then dest_bind t1 t2 else NONE | dest_monad _ t = case Code_Thingol.split_let t of SOME (((pat, ty), tbind), t') => - SOME ((SOME (((NONE, SOME pat), ty), false), tbind), t') + SOME ((SOME ((SOME pat, ty), false), tbind), t') | NONE => NONE; fun implode_monad c_bind_name = Code_Thingol.unfoldr (dest_monad c_bind_name); fun pr_monad pr_bind pr (NONE, t) vars = diff -r e3de75d3b898 -r 4e03a2cdf611 src/Tools/Code/code_ml.ML --- a/src/Tools/Code/code_ml.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Tools/Code/code_ml.ML Tue Jun 30 14:55:06 2009 +0200 @@ -94,9 +94,9 @@ [pr_term is_closure thm vars NOBR t1, pr_term is_closure thm vars BR t2]) | pr_term is_closure thm vars fxy (t as _ `|=> _) = let - val (binds, t') = Code_Thingol.unfold_abs t; - fun pr ((v, pat), ty) = - pr_bind is_closure thm NOBR ((SOME v, pat), ty) + val (binds, t') = Code_Thingol.unfold_pat_abs t; + fun pr (some_pat, ty) = + pr_bind is_closure thm NOBR (some_pat, ty) #>> (fn p => concat [str "fn", p, str "=>"]); val (ps, vars') = fold_map pr binds vars; in brackets (ps @ [pr_term is_closure thm vars' NOBR t']) end @@ -122,17 +122,15 @@ :: (map (pr_dicts BR) o filter_out null) iss @ map (pr_term is_closure thm vars BR) ts and pr_app is_closure thm vars = gen_pr_app (pr_app' is_closure) (pr_term is_closure) syntax_const thm vars - and pr_bind' ((NONE, NONE), _) = str "_" - | pr_bind' ((SOME v, NONE), _) = str v - | pr_bind' ((NONE, SOME p), _) = p - | pr_bind' ((SOME v, SOME p), _) = concat [str v, str "as", p] + and pr_bind' (NONE, _) = str "_" + | pr_bind' (SOME p, _) = p and pr_bind is_closure = gen_pr_bind pr_bind' (pr_term is_closure) and pr_case is_closure thm vars fxy (cases as ((_, [_]), _)) = let val (binds, body) = Code_Thingol.unfold_let (ICase cases); fun pr ((pat, ty), t) vars = vars - |> pr_bind is_closure thm NOBR ((NONE, SOME pat), ty) + |> pr_bind is_closure thm NOBR (SOME pat, ty) |>> (fn p => semicolon [str "val", p, str "=", pr_term is_closure thm vars NOBR t]) val (ps, vars') = fold_map pr binds vars; in @@ -146,7 +144,7 @@ let fun pr delim (pat, body) = let - val (p, vars') = pr_bind is_closure thm NOBR ((NONE, SOME pat), ty) vars; + val (p, vars') = pr_bind is_closure thm NOBR (SOME pat, ty) vars; in concat [str delim, p, str "=>", pr_term is_closure thm vars' NOBR body] end; @@ -403,9 +401,8 @@ brackify fxy [pr_term is_closure thm vars NOBR t1, pr_term is_closure thm vars BR t2]) | pr_term is_closure thm vars fxy (t as _ `|=> _) = let - val (binds, t') = Code_Thingol.unfold_abs t; - fun pr ((v, pat), ty) = pr_bind is_closure thm BR ((SOME v, pat), ty); - val (ps, vars') = fold_map pr binds vars; + val (binds, t') = Code_Thingol.unfold_pat_abs t; + val (ps, vars') = fold_map (pr_bind is_closure thm BR) binds vars; in brackets (str "fun" :: ps @ str "->" @@ pr_term is_closure thm vars' NOBR t') end | pr_term is_closure thm vars fxy (ICase (cases as (_, t0))) = (case Code_Thingol.unfold_const_app t0 of SOME (c_ts as ((c, _), _)) => if is_none (syntax_const c) @@ -427,17 +424,15 @@ :: ((map (pr_dicts BR) o filter_out null) iss @ map (pr_term is_closure thm vars BR) ts) and pr_app is_closure = gen_pr_app (pr_app' is_closure) (pr_term is_closure) syntax_const - and pr_bind' ((NONE, NONE), _) = str "_" - | pr_bind' ((SOME v, NONE), _) = str v - | pr_bind' ((NONE, SOME p), _) = p - | pr_bind' ((SOME v, SOME p), _) = brackets [p, str "as", str v] + and pr_bind' (NONE, _) = str "_" + | pr_bind' (SOME p, _) = p and pr_bind is_closure = gen_pr_bind pr_bind' (pr_term is_closure) and pr_case is_closure thm vars fxy (cases as ((_, [_]), _)) = let val (binds, body) = Code_Thingol.unfold_let (ICase cases); fun pr ((pat, ty), t) vars = vars - |> pr_bind is_closure thm NOBR ((NONE, SOME pat), ty) + |> pr_bind is_closure thm NOBR (SOME pat, ty) |>> (fn p => concat [str "let", p, str "=", pr_term is_closure thm vars NOBR t, str "in"]) val (ps, vars') = fold_map pr binds vars; @@ -449,7 +444,7 @@ let fun pr delim (pat, body) = let - val (p, vars') = pr_bind is_closure thm NOBR ((NONE, SOME pat), ty) vars; + val (p, vars') = pr_bind is_closure thm NOBR (SOME pat, ty) vars; in concat [str delim, p, str "->", pr_term is_closure thm vars' NOBR body] end; in brackets ( diff -r e3de75d3b898 -r 4e03a2cdf611 src/Tools/Code/code_printer.ML --- a/src/Tools/Code/code_printer.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Tools/Code/code_printer.ML Tue Jun 30 14:55:06 2009 +0200 @@ -68,10 +68,10 @@ -> (thm -> var_ctxt -> fixity -> iterm -> Pretty.T) -> (string -> const_syntax option) -> thm -> var_ctxt -> fixity -> const * iterm list -> Pretty.T - val gen_pr_bind: ((string option * Pretty.T option) * itype -> Pretty.T) + val gen_pr_bind: (Pretty.T option * itype -> Pretty.T) -> (thm -> var_ctxt -> fixity -> iterm -> Pretty.T) -> thm -> fixity - -> (string option * iterm option) * itype -> var_ctxt -> Pretty.T * var_ctxt + -> iterm option * itype -> var_ctxt -> Pretty.T * var_ctxt val mk_name_module: Name.context -> string option -> (string -> string option) -> 'a Graph.T -> string -> string @@ -216,16 +216,14 @@ else pr_term thm vars fxy (Code_Thingol.eta_expand k app) end; -fun gen_pr_bind pr_bind pr_term thm (fxy : fixity) ((v, pat), ty : itype) vars = +fun gen_pr_bind pr_bind pr_term thm (fxy : fixity) (some_pat, ty : itype) vars = let - val vs = case pat + val vs = case some_pat of SOME pat => Code_Thingol.fold_varnames (insert (op =)) pat [] | NONE => []; - val vars' = intro_vars (the_list v) vars; - val vars'' = intro_vars vs vars'; - val v' = Option.map (lookup_var vars') v; - val pat' = Option.map (pr_term thm vars'' fxy) pat; - in (pr_bind ((v', pat'), ty), vars'') end; + val vars' = intro_vars vs vars; + val some_pat' = Option.map (pr_term thm vars' fxy) some_pat; + in (pr_bind (some_pat', ty), vars') end; (* mixfix syntax *) diff -r e3de75d3b898 -r 4e03a2cdf611 src/Tools/Code/code_thingol.ML --- a/src/Tools/Code/code_thingol.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Tools/Code/code_thingol.ML Tue Jun 30 14:55:06 2009 +0200 @@ -40,13 +40,12 @@ val unfoldr: ('a -> ('b * 'a) option) -> 'a -> 'b list * 'a val unfold_fun: itype -> itype list * itype val unfold_app: iterm -> iterm * iterm list - val split_abs: iterm -> (((vname * iterm option) * itype) * iterm) option - val unfold_abs: iterm -> ((vname * iterm option) * itype) list * iterm + val unfold_abs: iterm -> (vname * itype) list * iterm val split_let: iterm -> (((iterm * itype) * iterm) * iterm) option val unfold_let: iterm -> ((iterm * itype) * iterm) list * iterm + val split_pat_abs: iterm -> ((iterm option * itype) * iterm) option + val unfold_pat_abs: iterm -> (iterm option * itype) list * iterm val unfold_const_app: iterm -> (const * iterm list) option - val collapse_let: ((vname * itype) * iterm) * iterm - -> (iterm * itype) * (iterm * iterm) list val eta_expand: int -> const * iterm list -> iterm val contains_dictvar: iterm -> bool val locally_monomorphic: iterm -> bool @@ -139,14 +138,10 @@ (fn op `$ t => SOME t | _ => NONE); -val split_abs = - (fn (v, ty) `|=> (t as ICase (((IVar w, _), [(p, t')]), _)) => - if v = w then SOME (((v, SOME p), ty), t') else SOME (((v, NONE), ty), t) - | (v, ty) `|=> t => SOME (((v, NONE), ty), t) +val unfold_abs = unfoldr + (fn op `|=> t => SOME t | _ => NONE); -val unfold_abs = unfoldr split_abs; - val split_let = (fn ICase (((td, ty), [(p, t)]), _) => SOME (((p, ty), td), t) | _ => NONE); @@ -186,17 +181,17 @@ | add vs (ICase (_, t)) = add vs t; in add [] end; -fun collapse_let (((v, ty), se), be as ICase (((IVar w, _), ds), _)) = - let - fun exists_v t = fold_unbound_varnames (fn w => fn b => - b orelse v = w) t false; - in if v = w andalso forall (fn (t1, t2) => - exists_v t1 orelse not (exists_v t2)) ds - then ((se, ty), ds) - else ((se, ty), [(IVar v, be)]) - end - | collapse_let (((v, ty), se), be) = - ((se, ty), [(IVar v, be)]) +fun exists_var t v = fold_unbound_varnames (fn w => fn b => v = w orelse b) t false; + +val split_pat_abs = (fn (v, ty) `|=> t => (case t + of ICase (((IVar w, _), [(p, t')]), _) => + if v = w andalso (exists_var p v orelse not (exists_var t' v)) + then SOME ((SOME p, ty), t') + else SOME ((SOME (IVar v), ty), t) + | _ => SOME ((if exists_var t v then SOME (IVar v) else NONE, ty), t)) + | _ => NONE); + +val unfold_pat_abs = unfoldr split_pat_abs; fun eta_expand k (c as (_, (_, tys)), ts) = let diff -r e3de75d3b898 -r 4e03a2cdf611 src/Tools/coherent.ML --- a/src/Tools/coherent.ML Tue Jun 30 14:54:30 2009 +0200 +++ b/src/Tools/coherent.ML Tue Jun 30 14:55:06 2009 +0200 @@ -110,9 +110,9 @@ (* Check whether disjunction is valid in given state *) fun is_valid_disj ctxt facts [] = false | is_valid_disj ctxt facts ((Ts, ts) :: ds) = - let val vs = rev (map_index (fn (i, T) => Var (("x", i), T)) Ts) + let val vs = map_index (fn (i, T) => Var (("x", i), T)) Ts in case Seq.pull (valid_conj ctxt facts empty_env - (map (fn t => subst_bounds (vs, t)) ts)) of + (map (fn t => subst_bounds (rev vs, t)) ts)) of SOME _ => true | NONE => is_valid_disj ctxt facts ds end; @@ -153,10 +153,10 @@ | valid_cases ctxt rules goal dom facts nfacts nparams ((Ts, ts) :: ds) = let val _ = message (fn () => "case " ^ commas (map (Syntax.string_of_term ctxt) ts)); - val params = rev (map_index (fn (i, T) => - Free ("par" ^ string_of_int (nparams + i), T)) Ts); + val params = map_index (fn (i, T) => + Free ("par" ^ string_of_int (nparams + i), T)) Ts; val ts' = map_index (fn (i, t) => - (subst_bounds (params, t), nfacts + i)) ts; + (subst_bounds (rev params, t), nfacts + i)) ts; val dom' = fold (fn (T, p) => Typtab.map_default (T, []) (fn ps => ps @ [p])) (Ts ~~ params) dom;