# HG changeset patch # User wenzelm # Date 1256836646 -3600 # Node ID 78faaec3209f60affd866e218a8f2b980b9fa5af # Parent 9b5286c0fb14fee7491f755e2f29aaf4c9474d8e# Parent b4534348b8fd3176d92cf087c18b4ca54704cc27 merged diff -r b4534348b8fd -r 78faaec3209f src/HOL/Code_Numeral.thy --- a/src/HOL/Code_Numeral.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Code_Numeral.thy Thu Oct 29 18:17:26 2009 +0100 @@ -3,7 +3,7 @@ header {* Type of target language numerals *} theory Code_Numeral -imports Nat_Numeral Divides +imports Nat_Numeral Nat_Transfer Divides begin text {* diff -r b4534348b8fd -r 78faaec3209f src/HOL/Divides.thy --- a/src/HOL/Divides.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Divides.thy Thu Oct 29 18:17:26 2009 +0100 @@ -6,7 +6,7 @@ header {* The division operators div and mod *} theory Divides -imports Nat_Numeral +imports Nat_Numeral Nat_Transfer uses "~~/src/Provers/Arith/assoc_fold.ML" "~~/src/Provers/Arith/cancel_numerals.ML" diff -r b4534348b8fd -r 78faaec3209f src/HOL/Fact.thy --- a/src/HOL/Fact.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Fact.thy Thu Oct 29 18:17:26 2009 +0100 @@ -8,7 +8,7 @@ header{*Factorial Function*} theory Fact -imports Nat_Transfer +imports Main begin class fact = @@ -266,9 +266,6 @@ lemma of_nat_fact_not_zero [simp]: "of_nat (fact n) \ (0::'a::semiring_char_0)" by auto -class ordered_semiring_1 = ordered_semiring + semiring_1 -class ordered_semiring_1_strict = ordered_semiring_strict + semiring_1 - lemma of_nat_fact_gt_zero [simp]: "(0::'a::{ordered_semidom}) < of_nat(fact n)" by auto lemma of_nat_fact_ge_zero [simp]: "(0::'a::ordered_semidom) \ of_nat(fact n)" diff -r b4534348b8fd -r 78faaec3209f src/HOL/Fun.thy --- a/src/HOL/Fun.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Fun.thy Thu Oct 29 18:17:26 2009 +0100 @@ -7,7 +7,6 @@ theory Fun imports Complete_Lattice -uses ("Tools/transfer.ML") begin text{*As a simplification rule, it replaces all function equalities by @@ -604,16 +603,6 @@ *} -subsection {* Generic transfer procedure *} - -definition TransferMorphism:: "('b \ 'a) \ 'b set \ bool" - where "TransferMorphism a B \ True" - -use "Tools/transfer.ML" - -setup Transfer.setup - - subsection {* Code generator setup *} types_code diff -r b4534348b8fd -r 78faaec3209f src/HOL/GCD.thy --- a/src/HOL/GCD.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/GCD.thy Thu Oct 29 18:17:26 2009 +0100 @@ -28,7 +28,7 @@ header {* GCD *} theory GCD -imports Fact +imports Fact Parity begin declare One_nat_def [simp del] diff -r b4534348b8fd -r 78faaec3209f src/HOL/Int.thy --- a/src/HOL/Int.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Int.thy Thu Oct 29 18:17:26 2009 +0100 @@ -1984,6 +1984,135 @@ lemmas half_gt_zero [simp] = half_gt_zero_iff [THEN iffD2, standard] +subsection {* The divides relation *} + +lemma zdvd_anti_sym: + "0 < m ==> 0 < n ==> m dvd n ==> n dvd m ==> m = (n::int)" + apply (simp add: dvd_def, auto) + apply (simp add: mult_assoc zero_less_mult_iff zmult_eq_1_iff) + done + +lemma zdvd_dvd_eq: assumes "a \ 0" and "(a::int) dvd b" and "b dvd a" + shows "\a\ = \b\" +proof- + from `a dvd b` obtain k where k:"b = a*k" unfolding dvd_def by blast + from `b dvd a` obtain k' where k':"a = b*k'" unfolding dvd_def by blast + from k k' have "a = a*k*k'" by simp + with mult_cancel_left1[where c="a" and b="k*k'"] + have kk':"k*k' = 1" using `a\0` by (simp add: mult_assoc) + hence "k = 1 \ k' = 1 \ k = -1 \ k' = -1" by (simp add: zmult_eq_1_iff) + thus ?thesis using k k' by auto +qed + +lemma zdvd_zdiffD: "k dvd m - n ==> k dvd n ==> k dvd (m::int)" + apply (subgoal_tac "m = n + (m - n)") + apply (erule ssubst) + apply (blast intro: dvd_add, simp) + done + +lemma zdvd_reduce: "(k dvd n + k * m) = (k dvd (n::int))" +apply (rule iffI) + apply (erule_tac [2] dvd_add) + apply (subgoal_tac "n = (n + k * m) - k * m") + apply (erule ssubst) + apply (erule dvd_diff) + apply(simp_all) +done + +lemma dvd_imp_le_int: + fixes d i :: int + assumes "i \ 0" and "d dvd i" + shows "\d\ \ \i\" +proof - + from `d dvd i` obtain k where "i = d * k" .. + with `i \ 0` have "k \ 0" by auto + then have "1 \ \k\" and "0 \ \d\" by auto + then have "\d\ * 1 \ \d\ * \k\" by (rule mult_left_mono) + with `i = d * k` show ?thesis by (simp add: abs_mult) +qed + +lemma zdvd_not_zless: + fixes m n :: int + assumes "0 < m" and "m < n" + shows "\ n dvd m" +proof + from assms have "0 < n" by auto + assume "n dvd m" then obtain k where k: "m = n * k" .. + with `0 < m` have "0 < n * k" by auto + with `0 < n` have "0 < k" by (simp add: zero_less_mult_iff) + with k `0 < n` `m < n` have "n * k < n * 1" by simp + with `0 < n` `0 < k` show False unfolding mult_less_cancel_left by auto +qed + +lemma zdvd_mult_cancel: assumes d:"k * m dvd k * n" and kz:"k \ (0::int)" + shows "m dvd n" +proof- + from d obtain h where h: "k*n = k*m * h" unfolding dvd_def by blast + {assume "n \ m*h" hence "k* n \ k* (m*h)" using kz by simp + with h have False by (simp add: mult_assoc)} + hence "n = m * h" by blast + thus ?thesis by simp +qed + +theorem zdvd_int: "(x dvd y) = (int x dvd int y)" +proof - + have "\k. int y = int x * k \ x dvd y" + proof - + fix k + assume A: "int y = int x * k" + then show "x dvd y" proof (cases k) + case (1 n) with A have "y = x * n" by (simp add: of_nat_mult [symmetric]) + then show ?thesis .. + next + case (2 n) with A have "int y = int x * (- int (Suc n))" by simp + also have "\ = - (int x * int (Suc n))" by (simp only: mult_minus_right) + also have "\ = - int (x * Suc n)" by (simp only: of_nat_mult [symmetric]) + finally have "- int (x * Suc n) = int y" .. + then show ?thesis by (simp only: negative_eq_positive) auto + qed + qed + then show ?thesis by (auto elim!: dvdE simp only: dvd_triv_left of_nat_mult) +qed + +lemma zdvd1_eq[simp]: "(x::int) dvd 1 = ( \x\ = 1)" +proof + assume d: "x dvd 1" hence "int (nat \x\) dvd int (nat 1)" by simp + hence "nat \x\ dvd 1" by (simp add: zdvd_int) + hence "nat \x\ = 1" by simp + thus "\x\ = 1" by (cases "x < 0", auto) +next + assume "\x\=1" + then have "x = 1 \ x = -1" by auto + then show "x dvd 1" by (auto intro: dvdI) +qed + +lemma zdvd_mult_cancel1: + assumes mp:"m \(0::int)" shows "(m * n dvd m) = (\n\ = 1)" +proof + assume n1: "\n\ = 1" thus "m * n dvd m" + by (cases "n >0", auto simp add: minus_dvd_iff minus_equation_iff) +next + assume H: "m * n dvd m" hence H2: "m * n dvd m * 1" by simp + from zdvd_mult_cancel[OF H2 mp] show "\n\ = 1" by (simp only: zdvd1_eq) +qed + +lemma int_dvd_iff: "(int m dvd z) = (m dvd nat (abs z))" + unfolding zdvd_int by (cases "z \ 0") simp_all + +lemma dvd_int_iff: "(z dvd int m) = (nat (abs z) dvd m)" + unfolding zdvd_int by (cases "z \ 0") simp_all + +lemma nat_dvd_iff: "(nat z dvd m) = (if 0 \ z then (z dvd int m) else m = 0)" + by (auto simp add: dvd_int_iff) + +lemma zdvd_imp_le: "[| z dvd n; 0 < n |] ==> z \ (n::int)" + apply (rule_tac z=n in int_cases) + apply (auto simp add: dvd_int_iff) + apply (rule_tac z=z in int_cases) + apply (auto simp add: dvd_imp_le) + done + + subsection {* Configuration of the code generator *} code_datatype Pls Min Bit0 Bit1 "number_of \ int \ int" diff -r b4534348b8fd -r 78faaec3209f src/HOL/IntDiv.thy --- a/src/HOL/IntDiv.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/IntDiv.thy Thu Oct 29 18:17:26 2009 +0100 @@ -1024,139 +1024,16 @@ lemmas zdvd_iff_zmod_eq_0_number_of [simp] = dvd_eq_mod_eq_0 [of "number_of x::int" "number_of y::int", standard] -lemma zdvd_anti_sym: - "0 < m ==> 0 < n ==> m dvd n ==> n dvd m ==> m = (n::int)" - apply (simp add: dvd_def, auto) - apply (simp add: mult_assoc zero_less_mult_iff zmult_eq_1_iff) - done - -lemma zdvd_dvd_eq: assumes "a \ 0" and "(a::int) dvd b" and "b dvd a" - shows "\a\ = \b\" -proof- - from `a dvd b` obtain k where k:"b = a*k" unfolding dvd_def by blast - from `b dvd a` obtain k' where k':"a = b*k'" unfolding dvd_def by blast - from k k' have "a = a*k*k'" by simp - with mult_cancel_left1[where c="a" and b="k*k'"] - have kk':"k*k' = 1" using `a\0` by (simp add: mult_assoc) - hence "k = 1 \ k' = 1 \ k = -1 \ k' = -1" by (simp add: zmult_eq_1_iff) - thus ?thesis using k k' by auto -qed - -lemma zdvd_zdiffD: "k dvd m - n ==> k dvd n ==> k dvd (m::int)" - apply (subgoal_tac "m = n + (m - n)") - apply (erule ssubst) - apply (blast intro: dvd_add, simp) - done - -lemma zdvd_reduce: "(k dvd n + k * m) = (k dvd (n::int))" -apply (rule iffI) - apply (erule_tac [2] dvd_add) - apply (subgoal_tac "n = (n + k * m) - k * m") - apply (erule ssubst) - apply (erule dvd_diff) - apply(simp_all) -done - lemma zdvd_zmod: "f dvd m ==> f dvd (n::int) ==> f dvd m mod n" by (rule dvd_mod) (* TODO: remove *) lemma zdvd_zmod_imp_zdvd: "k dvd m mod n ==> k dvd n ==> k dvd (m::int)" by (rule dvd_mod_imp_dvd) (* TODO: remove *) -lemma dvd_imp_le_int: "(i::int) ~= 0 ==> d dvd i ==> abs d <= abs i" -apply(auto simp:abs_if) - apply(clarsimp simp:dvd_def mult_less_0_iff) - using mult_le_cancel_left_neg[of _ "-1::int"] - apply(clarsimp simp:dvd_def mult_less_0_iff) - apply(clarsimp simp:dvd_def mult_less_0_iff - minus_mult_right simp del: mult_minus_right) -apply(clarsimp simp:dvd_def mult_less_0_iff) -done - -lemma zdvd_not_zless: "0 < m ==> m < n ==> \ n dvd (m::int)" - apply (auto elim!: dvdE) - apply (subgoal_tac "0 < n") - prefer 2 - apply (blast intro: order_less_trans) - apply (simp add: zero_less_mult_iff) - done - lemma zmult_div_cancel: "(n::int) * (m div n) = m - (m mod n)" using zmod_zdiv_equality[where a="m" and b="n"] by (simp add: algebra_simps) -lemma zdvd_mult_div_cancel:"(n::int) dvd m \ n * (m div n) = m" -apply (subgoal_tac "m mod n = 0") - apply (simp add: zmult_div_cancel) -apply (simp only: dvd_eq_mod_eq_0) -done - -lemma zdvd_mult_cancel: assumes d:"k * m dvd k * n" and kz:"k \ (0::int)" - shows "m dvd n" -proof- - from d obtain h where h: "k*n = k*m * h" unfolding dvd_def by blast - {assume "n \ m*h" hence "k* n \ k* (m*h)" using kz by simp - with h have False by (simp add: mult_assoc)} - hence "n = m * h" by blast - thus ?thesis by simp -qed - -theorem zdvd_int: "(x dvd y) = (int x dvd int y)" -proof - - have "\k. int y = int x * k \ x dvd y" - proof - - fix k - assume A: "int y = int x * k" - then show "x dvd y" proof (cases k) - case (1 n) with A have "y = x * n" by (simp add: zmult_int) - then show ?thesis .. - next - case (2 n) with A have "int y = int x * (- int (Suc n))" by simp - also have "\ = - (int x * int (Suc n))" by (simp only: mult_minus_right) - also have "\ = - int (x * Suc n)" by (simp only: zmult_int) - finally have "- int (x * Suc n) = int y" .. - then show ?thesis by (simp only: negative_eq_positive) auto - qed - qed - then show ?thesis by (auto elim!: dvdE simp only: dvd_triv_left int_mult) -qed - -lemma zdvd1_eq[simp]: "(x::int) dvd 1 = ( \x\ = 1)" -proof - assume d: "x dvd 1" hence "int (nat \x\) dvd int (nat 1)" by simp - hence "nat \x\ dvd 1" by (simp add: zdvd_int) - hence "nat \x\ = 1" by simp - thus "\x\ = 1" by (cases "x < 0", auto) -next - assume "\x\=1" thus "x dvd 1" - by(cases "x < 0",simp_all add: minus_equation_iff dvd_eq_mod_eq_0) -qed -lemma zdvd_mult_cancel1: - assumes mp:"m \(0::int)" shows "(m * n dvd m) = (\n\ = 1)" -proof - assume n1: "\n\ = 1" thus "m * n dvd m" - by (cases "n >0", auto simp add: minus_dvd_iff minus_equation_iff) -next - assume H: "m * n dvd m" hence H2: "m * n dvd m * 1" by simp - from zdvd_mult_cancel[OF H2 mp] show "\n\ = 1" by (simp only: zdvd1_eq) -qed - -lemma int_dvd_iff: "(int m dvd z) = (m dvd nat (abs z))" - unfolding zdvd_int by (cases "z \ 0") simp_all - -lemma dvd_int_iff: "(z dvd int m) = (nat (abs z) dvd m)" - unfolding zdvd_int by (cases "z \ 0") simp_all - -lemma nat_dvd_iff: "(nat z dvd m) = (if 0 \ z then (z dvd int m) else m = 0)" - by (auto simp add: dvd_int_iff) - -lemma zdvd_imp_le: "[| z dvd n; 0 < n |] ==> z \ (n::int)" - apply (rule_tac z=n in int_cases) - apply (auto simp add: dvd_int_iff) - apply (rule_tac z=z in int_cases) - apply (auto simp add: dvd_imp_le) - done - lemma zpower_zmod: "((x::int) mod m)^y mod m = x^y mod m" apply (induct "y", auto) apply (rule zmod_zmult1_eq [THEN trans]) @@ -1182,6 +1059,12 @@ lemma abs_div: "(y::int) dvd x \ abs (x div y) = abs x div abs y" by (unfold dvd_def, cases "y=0", auto simp add: abs_mult) +lemma zdvd_mult_div_cancel:"(n::int) dvd m \ n * (m div n) = m" +apply (subgoal_tac "m mod n = 0") + apply (simp add: zmult_div_cancel) +apply (simp only: dvd_eq_mod_eq_0) +done + text{*Suggested by Matthias Daum*} lemma int_power_div_base: "\0 < m; 0 < k\ \ k ^ m div k = (k::int) ^ (m - Suc 0)" @@ -1349,6 +1232,43 @@ declare dvd_eq_mod_eq_0_number_of [simp] +subsection {* Transfer setup *} + +lemma transfer_nat_int_functions: + "(x::int) >= 0 \ y >= 0 \ (nat x) div (nat y) = nat (x div y)" + "(x::int) >= 0 \ y >= 0 \ (nat x) mod (nat y) = nat (x mod y)" + by (auto simp add: nat_div_distrib nat_mod_distrib) + +lemma transfer_nat_int_function_closures: + "(x::int) >= 0 \ y >= 0 \ x div y >= 0" + "(x::int) >= 0 \ y >= 0 \ x mod y >= 0" + apply (cases "y = 0") + apply (auto simp add: pos_imp_zdiv_nonneg_iff) + apply (cases "y = 0") + apply auto +done + +declare TransferMorphism_nat_int[transfer add return: + transfer_nat_int_functions + transfer_nat_int_function_closures +] + +lemma transfer_int_nat_functions: + "(int x) div (int y) = int (x div y)" + "(int x) mod (int y) = int (x mod y)" + by (auto simp add: zdiv_int zmod_int) + +lemma transfer_int_nat_function_closures: + "is_nat x \ is_nat y \ is_nat (x div y)" + "is_nat x \ is_nat y \ is_nat (x mod y)" + by (simp_all only: is_nat_def transfer_nat_int_function_closures) + +declare TransferMorphism_int_nat[transfer add return: + transfer_int_nat_functions + transfer_int_nat_function_closures +] + + subsection {* Code generation *} definition pdivmod :: "int \ int \ int \ int" where diff -r b4534348b8fd -r 78faaec3209f src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/IsaMakefile Thu Oct 29 18:17:26 2009 +0100 @@ -223,7 +223,6 @@ Tools/sat_funcs.ML \ Tools/sat_solver.ML \ Tools/split_rule.ML \ - Tools/transfer.ML \ Tools/typecopy.ML \ Tools/typedef_codegen.ML \ Tools/typedef.ML \ @@ -255,6 +254,7 @@ Main.thy \ Map.thy \ Nat_Numeral.thy \ + Nat_Transfer.thy \ Presburger.thy \ Predicate_Compile.thy \ Quickcheck.thy \ @@ -276,6 +276,7 @@ Tools/Groebner_Basis/misc.ML \ Tools/Groebner_Basis/normalizer.ML \ Tools/Groebner_Basis/normalizer_data.ML \ + Tools/choice_specification.ML \ Tools/int_arith.ML \ Tools/list_code.ML \ Tools/meson.ML \ @@ -299,7 +300,6 @@ Tools/Qelim/presburger.ML \ Tools/Qelim/qelim.ML \ Tools/recdef.ML \ - Tools/choice_specification.ML \ Tools/res_atp.ML \ Tools/res_axioms.ML \ Tools/res_blacklist.ML \ @@ -308,6 +308,7 @@ Tools/res_reconstruct.ML \ Tools/string_code.ML \ Tools/string_syntax.ML \ + Tools/transfer.ML \ Tools/TFL/casesplit.ML \ Tools/TFL/dcterm.ML \ Tools/TFL/post.ML \ @@ -335,7 +336,6 @@ Log.thy \ Lubs.thy \ MacLaurin.thy \ - Nat_Transfer.thy \ NthRoot.thy \ PReal.thy \ Parity.thy \ diff -r b4534348b8fd -r 78faaec3209f src/HOL/List.thy --- a/src/HOL/List.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/List.thy Thu Oct 29 18:17:26 2009 +0100 @@ -3587,8 +3587,8 @@ by (blast intro: listrel.intros) lemma listrel_Cons: - "listrel r `` {x#xs} = set_Cons (r``{x}) (listrel r `` {xs})"; -by (auto simp add: set_Cons_def intro: listrel.intros) + "listrel r `` {x#xs} = set_Cons (r``{x}) (listrel r `` {xs})" +by (auto simp add: set_Cons_def intro: listrel.intros) subsection {* Size function *} @@ -3615,6 +3615,45 @@ by (induct xs) force+ +subsection {* Transfer *} + +definition + embed_list :: "nat list \ int list" +where + "embed_list l = map int l" + +definition + nat_list :: "int list \ bool" +where + "nat_list l = nat_set (set l)" + +definition + return_list :: "int list \ nat list" +where + "return_list l = map nat l" + +lemma transfer_nat_int_list_return_embed: "nat_list l \ + embed_list (return_list l) = l" + unfolding embed_list_def return_list_def nat_list_def nat_set_def + apply (induct l) + apply auto +done + +lemma transfer_nat_int_list_functions: + "l @ m = return_list (embed_list l @ embed_list m)" + "[] = return_list []" + unfolding return_list_def embed_list_def + apply auto + apply (induct l, auto) + apply (induct m, auto) +done + +(* +lemma transfer_nat_int_fold1: "fold f l x = + fold (%x. f (nat x)) (embed_list l) x"; +*) + + subsection {* Code generator *} subsubsection {* Setup *} @@ -4017,5 +4056,4 @@ "list_ex P [i..j] = (~ all_from_to_int (%x. ~P x) i j)" by(simp add: all_from_to_int_iff_ball list_ex_iff) - end diff -r b4534348b8fd -r 78faaec3209f src/HOL/Nat_Transfer.thy --- a/src/HOL/Nat_Transfer.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Nat_Transfer.thy Thu Oct 29 18:17:26 2009 +0100 @@ -1,15 +1,26 @@ (* Authors: Jeremy Avigad and Amine Chaieb *) -header {* Sets up transfer from nats to ints and back. *} +header {* Generic transfer machinery; specific transfer from nats to ints and back. *} theory Nat_Transfer -imports Main Parity +imports Nat_Numeral +uses ("Tools/transfer.ML") begin +subsection {* Generic transfer machinery *} + +definition TransferMorphism:: "('b \ 'a) \ 'b set \ bool" + where "TransferMorphism a B \ True" + +use "Tools/transfer.ML" + +setup Transfer.setup + + subsection {* Set up transfer from nat to int *} -(* set up transfer direction *) +text {* set up transfer direction *} lemma TransferMorphism_nat_int: "TransferMorphism nat (op <= (0::int))" by (simp add: TransferMorphism_def) @@ -20,7 +31,7 @@ labels: natint ] -(* basic functions and relations *) +text {* basic functions and relations *} lemma transfer_nat_int_numerals: "(0::nat) = nat 0" @@ -43,31 +54,20 @@ "(x::int) >= 0 \ y >= 0 \ (nat x) * (nat y) = nat (x * y)" "(x::int) >= 0 \ y >= 0 \ (nat x) - (nat y) = nat (tsub x y)" "(x::int) >= 0 \ (nat x)^n = nat (x^n)" - "(x::int) >= 0 \ y >= 0 \ (nat x) div (nat y) = nat (x div y)" - "(x::int) >= 0 \ y >= 0 \ (nat x) mod (nat y) = nat (x mod y)" by (auto simp add: eq_nat_nat_iff nat_mult_distrib - nat_power_eq nat_div_distrib nat_mod_distrib tsub_def) + nat_power_eq tsub_def) lemma transfer_nat_int_function_closures: "(x::int) >= 0 \ y >= 0 \ x + y >= 0" "(x::int) >= 0 \ y >= 0 \ x * y >= 0" "(x::int) >= 0 \ y >= 0 \ tsub x y >= 0" "(x::int) >= 0 \ x^n >= 0" - "(x::int) >= 0 \ y >= 0 \ x div y >= 0" - "(x::int) >= 0 \ y >= 0 \ x mod y >= 0" "(0::int) >= 0" "(1::int) >= 0" "(2::int) >= 0" "(3::int) >= 0" "int z >= 0" apply (auto simp add: zero_le_mult_iff tsub_def) - apply (case_tac "y = 0") - apply auto - apply (subst pos_imp_zdiv_nonneg_iff, auto) - apply (case_tac "y = 0") - apply force - apply (rule pos_mod_sign) - apply arith done lemma transfer_nat_int_relations: @@ -89,7 +89,21 @@ ] -(* first-order quantifiers *) +text {* first-order quantifiers *} + +lemma all_nat: "(\x. P x) \ (\x\0. P (nat x))" + by (simp split add: split_nat) + +lemma ex_nat: "(\x. P x) \ (\x. 0 \ x \ P (nat x))" +proof + assume "\x. P x" + then obtain x where "P x" .. + then have "int x \ 0 \ P (nat (int x))" by simp + then show "\x\0. P (nat x)" .. +next + assume "\x\0. P (nat x)" + then show "\x. P x" by auto +qed lemma transfer_nat_int_quantifiers: "(ALL (x::nat). P x) = (ALL (x::int). x >= 0 \ P (nat x))" @@ -110,7 +124,7 @@ cong: all_cong ex_cong] -(* if *) +text {* if *} lemma nat_if_cong: "(if P then (nat x) else (nat y)) = nat (if P then x else y)" @@ -119,7 +133,7 @@ declare TransferMorphism_nat_int [transfer add return: nat_if_cong] -(* operations with sets *) +text {* operations with sets *} definition nat_set :: "int set \ bool" @@ -132,8 +146,6 @@ "A Un B = nat ` (int ` A Un int ` B)" "A Int B = nat ` (int ` A Int int ` B)" "{x. P x} = nat ` {x. x >= 0 & P(nat x)}" - "{..n} = nat ` {0..int n}" - "{m..n} = nat ` {int m..int n}" (* need all variants of these! *) apply (rule card_image [symmetric]) apply (auto simp add: inj_on_def image_def) apply (rule_tac x = "int x" in bexI) @@ -144,17 +156,12 @@ apply auto apply (rule_tac x = "int x" in exI) apply auto - apply (rule_tac x = "int x" in bexI) - apply auto - apply (rule_tac x = "int x" in bexI) - apply auto done lemma transfer_nat_int_set_function_closures: "nat_set {}" "nat_set A \ nat_set B \ nat_set (A Un B)" "nat_set A \ nat_set B \ nat_set (A Int B)" - "x >= 0 \ nat_set {x..y}" "nat_set {x. x >= 0 & P x}" "nat_set (int ` C)" "nat_set A \ x : A \ x >= 0" (* does it hurt to turn this on? *) @@ -167,7 +174,6 @@ "(A = B) = (int ` A = int ` B)" "(A < B) = (int ` A < int ` B)" "(A <= B) = (int ` A <= int ` B)" - apply (rule iffI) apply (erule finite_imageI) apply (erule finite_imageD) @@ -194,7 +200,7 @@ ] -(* setsum and setprod *) +text {* setsum and setprod *} (* this handles the case where the *domain* of f is nat *) lemma transfer_nat_int_sum_prod: @@ -262,52 +268,10 @@ transfer_nat_int_sum_prod_closure cong: transfer_nat_int_sum_prod_cong] -(* lists *) - -definition - embed_list :: "nat list \ int list" -where - "embed_list l = map int l"; - -definition - nat_list :: "int list \ bool" -where - "nat_list l = nat_set (set l)"; - -definition - return_list :: "int list \ nat list" -where - "return_list l = map nat l"; - -thm nat_0_le; - -lemma transfer_nat_int_list_return_embed: "nat_list l \ - embed_list (return_list l) = l"; - unfolding embed_list_def return_list_def nat_list_def nat_set_def - apply (induct l); - apply auto; -done; - -lemma transfer_nat_int_list_functions: - "l @ m = return_list (embed_list l @ embed_list m)" - "[] = return_list []"; - unfolding return_list_def embed_list_def; - apply auto; - apply (induct l, auto); - apply (induct m, auto); -done; - -(* -lemma transfer_nat_int_fold1: "fold f l x = - fold (%x. f (nat x)) (embed_list l) x"; -*) - - - subsection {* Set up transfer from int to nat *} -(* set up transfer direction *) +text {* set up transfer direction *} lemma TransferMorphism_int_nat: "TransferMorphism int (UNIV :: nat set)" by (simp add: TransferMorphism_def) @@ -319,7 +283,11 @@ ] -(* basic functions and relations *) +text {* basic functions and relations *} + +lemma UNIV_apply: + "UNIV x = True" + by (simp add: top_fun_eq top_bool_eq) definition is_nat :: "int \ bool" @@ -338,17 +306,13 @@ "(int x) * (int y) = int (x * y)" "tsub (int x) (int y) = int (x - y)" "(int x)^n = int (x^n)" - "(int x) div (int y) = int (x div y)" - "(int x) mod (int y) = int (x mod y)" - by (auto simp add: int_mult tsub_def int_power zdiv_int zmod_int) + by (auto simp add: int_mult tsub_def int_power) lemma transfer_int_nat_function_closures: "is_nat x \ is_nat y \ is_nat (x + y)" "is_nat x \ is_nat y \ is_nat (x * y)" "is_nat x \ is_nat y \ is_nat (tsub x y)" "is_nat x \ is_nat (x^n)" - "is_nat x \ is_nat y \ is_nat (x div y)" - "is_nat x \ is_nat y \ is_nat (x mod y)" "is_nat 0" "is_nat 1" "is_nat 2" @@ -361,12 +325,7 @@ "(int x < int y) = (x < y)" "(int x <= int y) = (x <= y)" "(int x dvd int y) = (x dvd y)" - "(even (int x)) = (even x)" - by (auto simp add: zdvd_int even_nat_def) - -lemma UNIV_apply: - "UNIV x = True" - by (simp add: top_fun_eq top_bool_eq) + by (auto simp add: zdvd_int) declare TransferMorphism_int_nat[transfer add return: transfer_int_nat_numerals @@ -377,7 +336,7 @@ ] -(* first-order quantifiers *) +text {* first-order quantifiers *} lemma transfer_int_nat_quantifiers: "(ALL (x::int) >= 0. P x) = (ALL (x::nat). P (int x))" @@ -392,7 +351,7 @@ return: transfer_int_nat_quantifiers] -(* if *) +text {* if *} lemma int_if_cong: "(if P then (int x) else (int y)) = int (if P then x else y)" @@ -402,7 +361,7 @@ -(* operations with sets *) +text {* operations with sets *} lemma transfer_int_nat_set_functions: "nat_set A \ card A = card (nat ` A)" @@ -410,7 +369,6 @@ "nat_set A \ nat_set B \ A Un B = int ` (nat ` A Un nat ` B)" "nat_set A \ nat_set B \ A Int B = int ` (nat ` A Int nat ` B)" "{x. x >= 0 & P x} = int ` {x. P(int x)}" - "is_nat m \ is_nat n \ {m..n} = int ` {nat m..nat n}" (* need all variants of these! *) by (simp_all only: is_nat_def transfer_nat_int_set_functions transfer_nat_int_set_function_closures @@ -421,7 +379,6 @@ "nat_set {}" "nat_set A \ nat_set B \ nat_set (A Un B)" "nat_set A \ nat_set B \ nat_set (A Int B)" - "is_nat x \ nat_set {x..y}" "nat_set {x. x >= 0 & P x}" "nat_set (int ` C)" "nat_set A \ x : A \ is_nat x" @@ -454,7 +411,7 @@ ] -(* setsum and setprod *) +text {* setsum and setprod *} (* this handles the case where the *domain* of f is int *) lemma transfer_int_nat_sum_prod: diff -r b4534348b8fd -r 78faaec3209f src/HOL/Parity.thy --- a/src/HOL/Parity.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Parity.thy Thu Oct 29 18:17:26 2009 +0100 @@ -28,6 +28,13 @@ end +lemma transfer_int_nat_relations: + "even (int x) \ even x" + by (simp add: even_nat_def) + +declare TransferMorphism_int_nat[transfer add return: + transfer_int_nat_relations +] lemma even_zero_int[simp]: "even (0::int)" by presburger @@ -310,6 +317,8 @@ subsection {* General Lemmas About Division *} +(*FIXME move to Divides.thy*) + lemma Suc_times_mod_eq: "1 Suc (k * m) mod k = 1" apply (induct "m") apply (simp_all add: mod_Suc) diff -r b4534348b8fd -r 78faaec3209f src/HOL/Presburger.thy --- a/src/HOL/Presburger.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Presburger.thy Thu Oct 29 18:17:26 2009 +0100 @@ -385,20 +385,6 @@ text {* \bigskip Theorems for transforming predicates on nat to predicates on @{text int}*} -lemma all_nat: "(\x. P x) \ (\x\0. P (nat x))" - by (simp split add: split_nat) - -lemma ex_nat: "(\x. P x) \ (\x. 0 \ x \ P (nat x))" -proof - assume "\x. P x" - then obtain x where "P x" .. - then have "int x \ 0 \ P (nat (int x))" by simp - then show "\x\0. P (nat x)" .. -next - assume "\x\0. P (nat x)" - then show "\x. P x" by auto -qed - lemma zdiff_int_split: "P (int (x - y)) = ((y \ x \ P (int x - int y)) \ (x < y \ P 0))" by (case_tac "y \ x", simp_all add: zdiff_int) diff -r b4534348b8fd -r 78faaec3209f src/HOL/Ring_and_Field.thy --- a/src/HOL/Ring_and_Field.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Ring_and_Field.thy Thu Oct 29 18:17:26 2009 +0100 @@ -767,6 +767,8 @@ end +class ordered_semiring_1 = ordered_semiring + semiring_1 + class ordered_semiring_strict = semiring + comm_monoid_add + ordered_cancel_ab_semigroup_add + assumes mult_strict_left_mono: "a < b \ 0 < c \ c * a < c * b" assumes mult_strict_right_mono: "a < b \ 0 < c \ a * c < b * c" @@ -884,6 +886,8 @@ end +class ordered_semiring_1_strict = ordered_semiring_strict + semiring_1 + class mult_mono1 = times + zero + ord + assumes mult_mono1: "a \ b \ 0 \ c \ c * a \ c * b" @@ -2025,15 +2029,15 @@ lemma mult_right_le_one_le: "0 <= (x::'a::ordered_idom) ==> 0 <= y ==> y <= 1 ==> x * y <= x" -by (auto simp add: mult_compare_simps); +by (auto simp add: mult_compare_simps) lemma mult_left_le_one_le: "0 <= (x::'a::ordered_idom) ==> 0 <= y ==> y <= 1 ==> y * x <= x" -by (auto simp add: mult_compare_simps); +by (auto simp add: mult_compare_simps) lemma mult_imp_div_pos_le: "0 < (y::'a::ordered_field) ==> x <= z * y ==> - x / y <= z"; -by (subst pos_divide_le_eq, assumption+); + x / y <= z" +by (subst pos_divide_le_eq, assumption+) lemma mult_imp_le_div_pos: "0 < (y::'a::ordered_field) ==> z * y <= x ==> z <= x / y" @@ -2060,8 +2064,8 @@ lemma frac_less: "(0::'a::ordered_field) <= x ==> x < y ==> 0 < w ==> w <= z ==> x / z < y / w" apply (rule mult_imp_div_pos_less) - apply simp; - apply (subst times_divide_eq_left); + apply simp + apply (subst times_divide_eq_left) apply (rule mult_imp_less_div_pos, assumption) apply (erule mult_less_le_imp_less) apply simp_all @@ -2071,7 +2075,7 @@ x <= y ==> 0 < w ==> w < z ==> x / z < y / w" apply (rule mult_imp_div_pos_less) apply simp_all - apply (subst times_divide_eq_left); + apply (subst times_divide_eq_left) apply (rule mult_imp_less_div_pos, assumption) apply (erule mult_le_less_imp_less) apply simp_all diff -r b4534348b8fd -r 78faaec3209f src/HOL/SetInterval.thy --- a/src/HOL/SetInterval.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/SetInterval.thy Thu Oct 29 18:17:26 2009 +0100 @@ -9,7 +9,7 @@ header {* Set intervals *} theory SetInterval -imports Int +imports Int Nat_Transfer begin context ord @@ -1150,4 +1150,41 @@ "\i\n. t" == "CONST setprod (\i. t) {..n}" "\ii. t) {..= 0 \ nat_set {x..y}" + by (simp add: nat_set_def) + +declare TransferMorphism_nat_int[transfer add + return: transfer_nat_int_set_functions + transfer_nat_int_set_function_closures +] + +lemma transfer_int_nat_set_functions: + "is_nat m \ is_nat n \ {m..n} = int ` {nat m..nat n}" + by (simp only: is_nat_def transfer_nat_int_set_functions + transfer_nat_int_set_function_closures + transfer_nat_int_set_return_embed nat_0_le + cong: transfer_nat_int_set_cong) + +lemma transfer_int_nat_set_function_closures: + "is_nat x \ nat_set {x..y}" + by (simp only: transfer_nat_int_set_function_closures is_nat_def) + +declare TransferMorphism_int_nat[transfer add + return: transfer_int_nat_set_functions + transfer_int_nat_set_function_closures +] + end diff -r b4534348b8fd -r 78faaec3209f src/HOL/Tools/Predicate_Compile/predicate_compile.ML --- a/src/HOL/Tools/Predicate_Compile/predicate_compile.ML Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Tools/Predicate_Compile/predicate_compile.ML Thu Oct 29 18:17:26 2009 +0100 @@ -156,10 +156,35 @@ local structure P = OuterParse in +(*val parse_argmode' = P.nat >> rpair NONE || P.$$$ "(" |-- P.enum1 "," --| P.$$$ ")"*) +datatype raw_argmode = Argmode of string | Argmode_Tuple of string list + +val parse_argmode' = + ((Args.$$$ "i" || Args.$$$ "o") >> Argmode) || + (Args.$$$ "(" |-- P.enum1 "," (Args.$$$ "i" || Args.$$$ "o") --| Args.$$$ ")" >> Argmode_Tuple) + +fun mk_numeral_mode ss = flat (map_index (fn (i, s) => if s = "i" then [i + 1] else []) ss) + +val parse_smode' = P.$$$ "[" |-- P.enum1 "," parse_argmode' --| P.$$$ "]" + >> (fn m => flat (map_index + (fn (i, Argmode s) => if s = "i" then [(i + 1, NONE)] else [] + | (i, Argmode_Tuple ss) => [(i + 1, SOME (mk_numeral_mode ss))]) m)) + +val parse_smode = (P.$$$ "[" |-- P.enum "," P.nat --| P.$$$ "]") + >> map (rpair (NONE : int list option)) + +fun gen_parse_mode smode_parser = + (Scan.optional + ((P.enum "=>" ((Args.$$$ "X" >> K NONE) || (smode_parser >> SOME))) --| Args.$$$ "==>") []) + -- smode_parser + +val parse_mode = gen_parse_mode parse_smode + +val parse_mode' = gen_parse_mode parse_smode' + val opt_modes = Scan.optional (P.$$$ "(" |-- Args.$$$ "mode" |-- P.$$$ ":" |-- - P.enum1 "," (P.$$$ "[" |-- P.enum "," P.nat --| P.$$$ "]") - --| P.$$$ ")" >> SOME) NONE + P.enum1 "," (parse_mode || parse_mode') --| P.$$$ ")" >> SOME) NONE val scan_params = let @@ -170,8 +195,7 @@ val _ = OuterSyntax.local_theory_to_proof "code_pred" "prove equations for predicate specified by intro/elim rules" - OuterKeyword.thy_goal (opt_modes -- scan_params -- P.term_group >> - code_pred_cmd) + OuterKeyword.thy_goal (opt_modes -- scan_params -- P.term_group >> code_pred_cmd) end diff -r b4534348b8fd -r 78faaec3209f src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML --- a/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML Thu Oct 29 18:17:26 2009 +0100 @@ -9,6 +9,29 @@ structure Predicate_Compile_Aux = struct + +(* mode *) + +type smode = (int * int list option) list +type mode = smode option list * smode +datatype tmode = Mode of mode * smode * tmode option list; + +fun string_of_smode js = + commas (map + (fn (i, is) => + string_of_int i ^ (case is of NONE => "" + | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js) + +fun string_of_mode (iss, is) = space_implode " -> " (map + (fn NONE => "X" + | SOME js => enclose "[" "]" (string_of_smode js)) + (iss @ [SOME is])); + +fun string_of_tmode (Mode (predmode, termmode, param_modes)) = + "predmode: " ^ (string_of_mode predmode) ^ + (if null param_modes then "" else + "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes)) + (* general syntactic functions *) (*Like dest_conj, but flattens conjunctions however nested*) @@ -136,7 +159,7 @@ (* Different options for compiler *) datatype options = Options of { - expected_modes : (string * int list list) option, + expected_modes : (string * mode list) option, show_steps : bool, show_proof_trace : bool, show_intermediate_results : bool, diff -r b4534348b8fd -r 78faaec3209f src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML --- a/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML Thu Oct 29 18:17:26 2009 +0100 @@ -9,24 +9,20 @@ val setup: theory -> theory val code_pred: Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state val code_pred_cmd: Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state - type smode = (int * int list option) list - type mode = smode option list * smode - datatype tmode = Mode of mode * smode * tmode option list; val register_predicate : (string * thm list * thm * int) -> theory -> theory val register_intros : string * thm list -> theory -> theory val is_registered : theory -> string -> bool - val predfun_intro_of: theory -> string -> mode -> thm - val predfun_elim_of: theory -> string -> mode -> thm - val predfun_name_of: theory -> string -> mode -> string + val predfun_intro_of: theory -> string -> Predicate_Compile_Aux.mode -> thm + val predfun_elim_of: theory -> string -> Predicate_Compile_Aux.mode -> thm + val predfun_name_of: theory -> string -> Predicate_Compile_Aux.mode -> string val all_preds_of : theory -> string list - val modes_of: theory -> string -> mode list - val depth_limited_modes_of: theory -> string -> mode list - val depth_limited_function_name_of : theory -> string -> mode -> string - val generator_modes_of: theory -> string -> mode list - val generator_name_of : theory -> string -> mode -> string - val all_modes_of : theory -> (string * mode list) list - val all_generator_modes_of : theory -> (string * mode list) list - val string_of_mode : mode -> string + val modes_of: theory -> string -> Predicate_Compile_Aux.mode list + val depth_limited_modes_of: theory -> string -> Predicate_Compile_Aux.mode list + val depth_limited_function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string + val generator_modes_of: theory -> string -> Predicate_Compile_Aux.mode list + val generator_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string + val all_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list + val all_generator_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list val intros_of: theory -> string -> thm list val nparams_of: theory -> string -> int val add_intro: thm -> theory -> theory @@ -67,8 +63,6 @@ (* debug stuff *) -fun tracing s = (if ! Toplevel.debug then Output.tracing s else ()); - fun print_tac s = Seq.single; fun print_tac' options s = @@ -140,9 +134,6 @@ type mode = arg_mode list type tmode = Mode of mode * *) -type smode = (int * int list option) list -type mode = smode option list * smode; -datatype tmode = Mode of mode * smode * tmode option list; fun gen_split_smode (mk_tuple, strip_tuple) smode ts = let @@ -165,32 +156,16 @@ (split_smode' smode (i+1) ts) in split_smode' smode 1 ts end -val split_smode = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) -val split_smodeT = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) +fun split_smode smode ts = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) smode ts +fun split_smodeT smode ts = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) smode ts fun gen_split_mode split_smode (iss, is) ts = let val (t1, t2) = chop (length iss) ts in (t1, split_smode is t2) end -val split_mode = gen_split_mode split_smode -val split_modeT = gen_split_mode split_smodeT - -fun string_of_smode js = - commas (map - (fn (i, is) => - string_of_int i ^ (case is of NONE => "" - | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js) - -fun string_of_mode (iss, is) = space_implode " -> " (map - (fn NONE => "X" - | SOME js => enclose "[" "]" (string_of_smode js)) - (iss @ [SOME is])); - -fun string_of_tmode (Mode (predmode, termmode, param_modes)) = - "predmode: " ^ (string_of_mode predmode) ^ - (if null param_modes then "" else - "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes)) +fun split_mode (iss, is) ts = gen_split_mode split_smode (iss, is) ts +fun split_modeT (iss, is) ts = gen_split_mode split_smodeT (iss, is) ts datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | Generator of (string * typ); @@ -333,7 +308,7 @@ fun print_modes options modes = if show_modes options then - Output.tracing ("Inferred modes:\n" ^ + tracing ("Inferred modes:\n" ^ cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map string_of_mode ms)) modes)) else () @@ -344,7 +319,7 @@ ^ (string_of_entry pred mode entry) fun print_pred (pred, modes) = "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes) - val _ = Output.tracing (cat_lines (map print_pred pred_mode_table)) + val _ = tracing (cat_lines (map print_pred pred_mode_table)) in () end; fun string_of_prem thy (Prem (ts, p)) = @@ -423,10 +398,10 @@ case expected_modes options of SOME (s, ms) => (case AList.lookup (op =) modes s of SOME modes => - if not (eq_set (op =) (map (map (rpair NONE)) ms, map snd modes)) then + if not (eq_set (op =) (ms, modes)) then error ("expected modes were not inferred:\n" - ^ "inferred modes for " ^ s ^ ": " - ^ commas (map ((enclose "[" "]") o string_of_smode o snd) modes)) + ^ "inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes) + ^ "\n expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms)) else () | NONE => ()) | NONE => () @@ -661,7 +636,7 @@ fun cons_intro gr = case try (Graph.get_node gr) name of SOME pred_data => Graph.map_node name (map_pred_data - (apfst (fn (intros, elim, nparams) => (thm::intros, elim, nparams)))) gr + (apfst (fn (intros, elim, nparams) => (intros @ [thm], elim, nparams)))) gr | NONE => let val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name) @@ -1052,9 +1027,9 @@ fun print_failed_mode options thy modes p m rs i = if show_mode_inference options then let - val _ = Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^ + val _ = tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^ p ^ " violates mode " ^ string_of_mode m) - val _ = Output.tracing (string_of_clause thy p (nth rs i)) + val _ = tracing (string_of_clause thy p (nth rs i)) in () end else () @@ -1191,6 +1166,28 @@ (t, names) end; +structure Comp_Mod = +struct + +datatype comp_modifiers = Comp_Modifiers of +{ + const_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string, + funT_of : compilation_funs -> mode -> typ -> typ, + additional_arguments : string list -> term list, + wrap_compilation : compilation_funs -> string -> typ -> mode -> term list -> term -> term, + transform_additional_arguments : indprem -> term list -> term list +} + +fun dest_comp_modifiers (Comp_Modifiers c) = c + +val const_name_of = #const_name_of o dest_comp_modifiers +val funT_of = #funT_of o dest_comp_modifiers +val additional_arguments = #additional_arguments o dest_comp_modifiers +val wrap_compilation = #wrap_compilation o dest_comp_modifiers +val transform_additional_arguments = #transform_additional_arguments o dest_comp_modifiers + +end; + fun compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss arg = let fun map_params (t as Free (f, T)) = @@ -1198,7 +1195,7 @@ case (the (AList.lookup (op =) (param_vs ~~ iss) f)) of SOME is => let - val T' = #funT_of compilation_modifiers compfuns ([], is) T + val T' = Comp_Mod.funT_of compilation_modifiers compfuns ([], is) T in fst (mk_Eval_of additional_arguments ((Free (f, T'), T), SOME is) []) end | NONE => t else t @@ -1248,9 +1245,9 @@ val params' = map (compile_param compilation_modifiers compfuns thy) (ms ~~ params) val f' = case f of - Const (name, T) => Const (#const_name_of compilation_modifiers thy name mode, - #funT_of compilation_modifiers compfuns mode T) - | Free (name, T) => Free (name, #funT_of compilation_modifiers compfuns mode T) + Const (name, T) => Const (Comp_Mod.const_name_of compilation_modifiers thy name mode, + Comp_Mod.funT_of compilation_modifiers compfuns mode T) + | Free (name, T) => Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T) | _ => error ("PredicateCompiler: illegal parameter term") in list_comb (f', params' @ args') @@ -1262,13 +1259,13 @@ let val params' = map (compile_param compilation_modifiers compfuns thy) (ms ~~ params) (*val mk_fun_of = if depth_limited then mk_depth_limited_fun_of else mk_fun_of*) - val name' = #const_name_of compilation_modifiers thy name mode - val T' = #funT_of compilation_modifiers compfuns mode T + val name' = Comp_Mod.const_name_of compilation_modifiers thy name mode + val T' = Comp_Mod.funT_of compilation_modifiers compfuns mode T in (list_comb (Const (name', T'), params' @ inargs @ additional_arguments)) end | (Free (name, T), params) => - list_comb (Free (name, #funT_of compilation_modifiers compfuns mode T), params @ inargs @ additional_arguments) + list_comb (Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T), params @ inargs @ additional_arguments) fun compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments (iss, is) inp (ts, moded_ps) = let @@ -1302,7 +1299,7 @@ val (out_ts'', (names'', constr_vs')) = fold_map distinct_v out_ts' ((names', map (rpair []) vs)) val additional_arguments' = - #transform_additional_arguments compilation_modifiers p additional_arguments + Comp_Mod.transform_additional_arguments compilation_modifiers p additional_arguments val (compiled_clause, rest) = case p of Prem (us, t) => let @@ -1356,7 +1353,7 @@ val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T) val (Us1, Us2) = split_smodeT (snd mode) Ts2 val Ts1' = - map2 (fn NONE => I | SOME is => #funT_of compilation_modifiers compfuns ([], is)) (fst mode) Ts1 + map2 (fn NONE => I | SOME is => Comp_Mod.funT_of compilation_modifiers compfuns ([], is)) (fst mode) Ts1 fun mk_input_term (i, NONE) = [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))] | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of @@ -1370,17 +1367,17 @@ else [HOLogic.mk_tuple (map Free (vnames ~~ map (fn j => nth Ts (j - 1)) pis))] end val in_ts = maps mk_input_term (snd mode) val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1' - val additional_arguments = #additional_arguments compilation_modifiers (all_vs @ param_vs) + val additional_arguments = Comp_Mod.additional_arguments compilation_modifiers (all_vs @ param_vs) val cl_ts = map (compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments mode (HOLogic.mk_tuple in_ts)) moded_cls; - val compilation = #wrap_compilation compilation_modifiers compfuns s T mode additional_arguments + val compilation = Comp_Mod.wrap_compilation compilation_modifiers compfuns s T mode additional_arguments (if null cl_ts then mk_bot compfuns (HOLogic.mk_tupleT Us2) else foldr1 (mk_sup compfuns) cl_ts) val fun_const = - Const (#const_name_of compilation_modifiers thy s mode, - #funT_of compilation_modifiers compfuns mode T) + Const (Comp_Mod.const_name_of compilation_modifiers thy s mode, + Comp_Mod.funT_of compilation_modifiers compfuns mode T) in HOLogic.mk_Trueprop (HOLogic.mk_eq (list_comb (fun_const, params @ in_ts @ additional_arguments), compilation)) @@ -2139,31 +2136,47 @@ (** main function of predicate compiler **) +datatype steps = Steps of + { + compile_preds : theory -> string list -> string list -> (string * typ) list + -> (moded_clause list) pred_mode_table -> term pred_mode_table, + create_definitions: (string * typ) list -> string * mode list -> theory -> theory, + infer_modes : options -> theory -> (string * mode list) list -> (string * mode list) list + -> string list -> (string * (term list * indprem list) list) list + -> moded_clause list pred_mode_table, + prove : options -> theory -> (string * (term list * indprem list) list) list + -> (string * typ) list -> (string * mode list) list + -> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table, + are_not_defined : theory -> string list -> bool, + qname : bstring + } + + fun add_equations_of steps options prednames thy = let + fun dest_steps (Steps s) = s val _ = print_step options ("Starting predicate compiler for predicates " ^ commas prednames ^ "...") - val _ = tracing (commas (map (Display.string_of_thm_global thy) (maps (intros_of thy) prednames))) (*val _ = check_intros_elim_match thy prednames*) (*val _ = map (check_format_of_intro_rule thy) (maps (intros_of thy) prednames)*) val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) = prepare_intrs thy prednames (maps (intros_of thy) prednames) val _ = print_step options "Infering modes..." - val moded_clauses = #infer_modes steps options thy extra_modes all_modes param_vs clauses + val moded_clauses = #infer_modes (dest_steps steps) options thy extra_modes all_modes param_vs clauses val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses val _ = check_expected_modes options modes val _ = print_modes options modes (*val _ = print_moded_clauses thy moded_clauses*) val _ = print_step options "Defining executable functions..." - val thy' = fold (#create_definitions steps preds) modes thy + val thy' = fold (#create_definitions (dest_steps steps) preds) modes thy |> Theory.checkpoint val _ = print_step options "Compiling equations..." val compiled_terms = - (#compile_preds steps) thy' all_vs param_vs preds moded_clauses + #compile_preds (dest_steps steps) thy' all_vs param_vs preds moded_clauses val _ = print_compiled_terms options thy' compiled_terms val _ = print_step options "Proving equations..." - val result_thms = #prove steps options thy' clauses preds (extra_modes @ modes) + val result_thms = #prove (dest_steps steps) options thy' clauses preds (extra_modes @ modes) moded_clauses compiled_terms - val qname = #qname steps + val qname = #qname (dest_steps steps) val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute (fn thm => Context.mapping (Code.add_eqn thm) I)))) val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss @@ -2181,7 +2194,7 @@ SOME v => (G, v) | NONE => (Graph.new_node (key, value_of key) G, value_of key) val (G'', visited') = fold (extend' value_of edges_of) (subtract (op =) visited (edges_of (key, v))) - (G', key :: visited) + (G', key :: visited) in (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited') end; @@ -2190,6 +2203,7 @@ fun gen_add_equations steps options names thy = let + fun dest_steps (Steps s) = s val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy |> Theory.checkpoint; fun strong_conn_of gr keys = @@ -2197,24 +2211,25 @@ val scc = strong_conn_of (PredData.get thy') names val thy'' = fold_rev (fn preds => fn thy => - if #are_not_defined steps thy preds then + if #are_not_defined (dest_steps steps) thy preds then add_equations_of steps options preds thy else thy) scc thy' |> Theory.checkpoint in thy'' end (* different instantiantions of the predicate compiler *) -val predicate_comp_modifiers = - {const_name_of = predfun_name_of, - funT_of = funT_of, +val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers + {const_name_of = predfun_name_of : (theory -> string -> mode -> string), + funT_of = funT_of : (compilation_funs -> mode -> typ -> typ), additional_arguments = K [], - wrap_compilation = K (K (K (K (K I)))), - transform_additional_arguments = K I + wrap_compilation = K (K (K (K (K I)))) + : (compilation_funs -> string -> typ -> mode -> term list -> term -> term), + transform_additional_arguments = K I : (indprem -> term list -> term list) } -val depth_limited_comp_modifiers = +val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers {const_name_of = depth_limited_function_name_of, - funT_of = depth_limited_funT_of, + funT_of = depth_limited_funT_of : (compilation_funs -> mode -> typ -> typ), additional_arguments = fn names => let val [depth_name, polarity_name] = Name.variant_list names ["depth", "polarity"] @@ -2245,38 +2260,38 @@ in [polarity', depth'] end } -val rpred_comp_modifiers = +val rpred_comp_modifiers = Comp_Mod.Comp_Modifiers {const_name_of = generator_name_of, - funT_of = K generator_funT_of, + funT_of = K generator_funT_of : (compilation_funs -> mode -> typ -> typ), additional_arguments = fn names => [Free (Name.variant names "size", @{typ code_numeral})], - wrap_compilation = K (K (K (K (K I)))), - transform_additional_arguments = K I + wrap_compilation = K (K (K (K (K I)))) + : (compilation_funs -> string -> typ -> mode -> term list -> term -> term), + transform_additional_arguments = K I : (indprem -> term list -> term list) } - val add_equations = gen_add_equations - {infer_modes = infer_modes, + (Steps {infer_modes = infer_modes, create_definitions = create_definitions, compile_preds = compile_preds predicate_comp_modifiers PredicateCompFuns.compfuns, prove = prove, are_not_defined = fn thy => forall (null o modes_of thy), - qname = "equation"} + qname = "equation"}) val add_depth_limited_equations = gen_add_equations - {infer_modes = infer_modes, + (Steps {infer_modes = infer_modes, create_definitions = create_definitions_of_depth_limited_functions, compile_preds = compile_preds depth_limited_comp_modifiers PredicateCompFuns.compfuns, prove = prove_by_skip, are_not_defined = fn thy => forall (null o depth_limited_modes_of thy), - qname = "depth_limited_equation"} + qname = "depth_limited_equation"}) val add_quickcheck_equations = gen_add_equations - {infer_modes = infer_modes_with_generator, + (Steps {infer_modes = infer_modes_with_generator, create_definitions = rpred_create_definitions, compile_preds = compile_preds rpred_comp_modifiers RandomPredCompFuns.compfuns, prove = prove_by_skip, are_not_defined = fn thy => forall (null o rpred_modes_of thy), - qname = "rpred_equation"} + qname = "rpred_equation"}) (** user interface **) @@ -2307,7 +2322,7 @@ (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy |> LocalTheory.checkpoint val thy' = ProofContext.theory_of lthy' - val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy') + val preds = Graph.all_succs (PredData.get thy') [const] |> filter_out (has_elim thy') fun mk_cases const = let val T = Sign.the_const_type thy const diff -r b4534348b8fd -r 78faaec3209f src/HOL/Tools/transfer.ML --- a/src/HOL/Tools/transfer.ML Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/Tools/transfer.ML Thu Oct 29 18:17:26 2009 +0100 @@ -14,8 +14,15 @@ structure Transfer : TRANSFER = struct -type entry = {inj : thm list, emb : thm list, ret : thm list, cong : thm list, - guess : bool, hints : string list}; +type entry = { inj : thm list, emb : thm list, ret : thm list, cong : thm list, + guess : bool, hints : string list }; + +fun merge_entry ({ inj = inj1, emb = emb1, ret = ret1, cong = cong1, guess = guess1, hints = hints1 } : entry, + { inj = inj2, emb = emb2, ret = ret2, cong = cong2, guess = guess2, hints = hints2 } : entry) = + { inj = merge Thm.eq_thm (inj1, inj2), emb = merge Thm.eq_thm (emb1, emb2), + ret = merge Thm.eq_thm (ret1, ret2), cong = merge Thm.eq_thm (cong1, cong2), + guess = guess1 andalso guess2, hints = merge (op =) (hints1, hints2) }; + type data = simpset * (thm * entry) list; structure Data = GenericDataFun @@ -24,7 +31,7 @@ val empty = (HOL_ss, []); val extend = I; fun merge _ ((ss1, e1), (ss2, e2)) = - (merge_ss (ss1, ss2), AList.merge Thm.eq_thm (K true) (e1, e2)); + (merge_ss (ss1, ss2), AList.join Thm.eq_thm (K merge_entry) (e1, e2)); ); val get = Data.get o Context.Proof; diff -r b4534348b8fd -r 78faaec3209f src/HOL/ex/Predicate_Compile_Alternative_Defs.thy --- a/src/HOL/ex/Predicate_Compile_Alternative_Defs.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/ex/Predicate_Compile_Alternative_Defs.thy Thu Oct 29 18:17:26 2009 +0100 @@ -45,7 +45,7 @@ unfolding mem_def[symmetric, of _ a2] apply auto unfolding mem_def - apply auto + apply fastsimp done qed diff -r b4534348b8fd -r 78faaec3209f src/HOL/ex/Predicate_Compile_ex.thy --- a/src/HOL/ex/Predicate_Compile_ex.thy Thu Oct 29 17:58:26 2009 +0100 +++ b/src/HOL/ex/Predicate_Compile_ex.thy Thu Oct 29 18:17:26 2009 +0100 @@ -1,12 +1,12 @@ theory Predicate_Compile_ex -imports Main Predicate_Compile_Alternative_Defs +imports "../Main" Predicate_Compile_Alternative_Defs begin subsection {* Basic predicates *} inductive False' :: "bool" -code_pred (mode: []) False' . +code_pred (mode : []) False' . code_pred [depth_limited] False' . code_pred [rpred] False' . @@ -17,7 +17,7 @@ definition EmptySet' :: "'a \ bool" where "EmptySet' = {}" -code_pred (mode: [], [1]) [inductify, show_intermediate_results] EmptySet' . +code_pred (mode: [], [1]) [inductify] EmptySet' . inductive EmptyRel :: "'a \ 'b \ bool" @@ -26,7 +26,13 @@ inductive EmptyClosure :: "('a \ 'a \ bool) \ 'a \ 'a \ bool" for r :: "'a \ 'a \ bool" -code_pred (mode: [], [1], [2], [1, 2])EmptyClosure . +code_pred + (mode: [] ==> [], [] ==> [1], [] ==> [2], [] ==> [1, 2], + [1] ==> [], [1] ==> [1], [1] ==> [2], [1] ==> [1, 2], + [2] ==> [], [2] ==> [1], [2] ==> [2], [2] ==> [1, 2], + [1, 2] ==> [], [1, 2] ==> [1], [1, 2] ==> [2], [1, 2] ==> [1, 2]) + EmptyClosure . + thm EmptyClosure.equation (* TODO: inductive package is broken! inductive False'' :: "bool" @@ -60,8 +66,88 @@ where "zerozero (0, 0)" -code_pred zerozero . -code_pred [rpred, show_compilation] zerozero . +code_pred (mode: [i], [(i, o)], [(o, i)], [o]) zerozero . +code_pred [rpred] zerozero . + +subsection {* Alternative Rules *} + +datatype char = C | D | E | F | G | H + +inductive is_C_or_D +where + "(x = C) \ (x = D) ==> is_C_or_D x" + +code_pred (mode: [1]) is_C_or_D . +thm is_C_or_D.equation + +inductive is_D_or_E +where + "(x = D) \ (x = E) ==> is_D_or_E x" + +lemma [code_pred_intros]: + "is_D_or_E D" +by (auto intro: is_D_or_E.intros) + +lemma [code_pred_intros]: + "is_D_or_E E" +by (auto intro: is_D_or_E.intros) + +code_pred (mode: [], [1]) is_D_or_E +proof - + case is_D_or_E + from this(1) show thesis + proof + fix x + assume x: "a1 = x" + assume "x = D \ x = E" + from this show thesis + proof + assume "x = D" from this x is_D_or_E(2) show thesis by simp + next + assume "x = E" from this x is_D_or_E(3) show thesis by simp + qed + qed +qed + +thm is_D_or_E.equation + +inductive is_F_or_G +where + "x = F \ x = G ==> is_F_or_G x" + +lemma [code_pred_intros]: + "is_F_or_G F" +by (auto intro: is_F_or_G.intros) + +lemma [code_pred_intros]: + "is_F_or_G G" +by (auto intro: is_F_or_G.intros) + +inductive is_FGH +where + "is_F_or_G x ==> is_FGH x" +| "is_FGH H" + +text {* Compilation of is_FGH requires elimination rule for is_F_or_G *} + +code_pred (mode: [], [1]) is_FGH +proof - + case is_F_or_G + from this(1) show thesis + proof + fix x + assume x: "a1 = x" + assume "x = F \ x = G" + from this show thesis + proof + assume "x = F" + from this x is_F_or_G(2) show thesis by simp + next + assume "x = G" + from this x is_F_or_G(3) show thesis by simp + qed + qed +qed subsection {* Preprocessor Inlining *} @@ -123,7 +209,7 @@ definition odd' where "odd' x == \ even x" -code_pred [inductify] odd' . +code_pred (mode: [1]) [inductify] odd' . code_pred [inductify, depth_limited] odd' . code_pred [inductify, rpred] odd' . @@ -135,7 +221,7 @@ where "n mod 2 = 0 \ is_even n" -code_pred is_even . +code_pred (mode: [1]) is_even . subsection {* append predicate *} @@ -172,10 +258,19 @@ lemmas [code_pred_intros] = append2_Nil append2.intros(2) -code_pred append2 +code_pred (mode: [1, 2], [3], [2, 3], [1, 3], [1, 2, 3]) append2 proof - case append2 - from append2.cases[OF append2(1)] append2(2-3) show thesis by blast + from append2(1) show thesis + proof + fix xs + assume "a1 = []" "a2 = xs" "a3 = xs" + from this append2(2) show thesis by simp + next + fix xs ys zs x + assume "a1 = x # xs" "a2 = ys" "a3 = x # zs" "append2 xs ys zs" + from this append2(3) show thesis by fastsimp + qed qed inductive tupled_append :: "'a list \ 'a list \ 'a list \ bool" @@ -183,7 +278,7 @@ "tupled_append ([], xs, xs)" | "tupled_append (xs, ys, zs) \ tupled_append (x # xs, ys, x # zs)" -code_pred tupled_append . +code_pred (mode: [(i,i,o)], [(i,o,i)], [(o,i,i)], [(o,o,i)], [i]) tupled_append . code_pred [rpred] tupled_append . thm tupled_append.equation (* @@ -197,7 +292,7 @@ | "[| ys = fst (xa, y); x # zs = snd (xa, y); tupled_append' (xs, ys, zs) |] ==> tupled_append' (x # xs, xa, y)" -code_pred tupled_append' . +code_pred (mode: [(i,i,o)], [(i,o,i)], [(o,i,i)], [(o,o,i)], [i]) tupled_append' . thm tupled_append'.equation inductive tupled_append'' :: "'a list \ 'a list \ 'a list \ bool" @@ -205,9 +300,7 @@ "tupled_append'' ([], xs, xs)" | "ys = fst yszs ==> x # zs = snd yszs ==> tupled_append'' (xs, ys, zs) \ tupled_append'' (x # xs, yszs)" -thm tupled_append''.cases - -code_pred [inductify] tupled_append'' . +code_pred (mode: [(i,i,o)], [(i,o,i)], [(o,i,i)], [(o,o,i)], [i]) [inductify] tupled_append'' . thm tupled_append''.equation inductive tupled_append''' :: "'a list \ 'a list \ 'a list \ bool" @@ -215,7 +308,7 @@ "tupled_append''' ([], xs, xs)" | "yszs = (ys, zs) ==> tupled_append''' (xs, yszs) \ tupled_append''' (x # xs, ys, x # zs)" -code_pred [inductify] tupled_append''' . +code_pred (mode: [(i,i,o)], [(i,o,i)], [(o,i,i)], [(o,o,i)], [i]) [inductify] tupled_append''' . thm tupled_append'''.equation subsection {* map_ofP predicate *} @@ -237,7 +330,7 @@ | "P x ==> filter1 P xs ys ==> filter1 P (x#xs) (x#ys)" | "\ P x ==> filter1 P xs ys ==> filter1 P (x#xs) ys" -code_pred (mode: [1], [1, 2]) filter1 . +code_pred (mode: [1] ==> [1], [1] ==> [1, 2]) filter1 . code_pred [depth_limited] filter1 . code_pred [rpred] filter1 . @@ -260,7 +353,7 @@ where "List.filter P xs = ys ==> filter3 P xs ys" -code_pred filter3 . +code_pred (mode: [] ==> [1], [] ==> [1, 2], [1] ==> [1], [1] ==> [1, 2]) filter3 . code_pred [depth_limited] filter3 . thm filter3.depth_limited_equation @@ -268,7 +361,7 @@ where "List.filter P xs = ys ==> filter4 P xs ys" -code_pred filter4 . +code_pred (mode: [1, 2], [1, 2, 3]) filter4 . code_pred [depth_limited] filter4 . code_pred [rpred] filter4 . @@ -288,7 +381,7 @@ "tupled_rev ([], [])" | "tupled_rev (xs, xs') \ tupled_append (xs', [x], ys) \ tupled_rev (x#xs, ys)" -code_pred tupled_rev . +code_pred (mode: [(i, o)], [(o, i)], [i]) tupled_rev . thm tupled_rev.equation subsection {* partition predicate *} @@ -299,7 +392,7 @@ | "f x \ partition f xs ys zs \ partition f (x # xs) (x # ys) zs" | "\ f x \ partition f xs ys zs \ partition f (x # xs) ys (x # zs)" -code_pred (mode: [1], [2, 3], [1, 2], [1, 3], [1, 2, 3]) partition . +code_pred (mode: [1] ==> [1], [1] ==> [2, 3], [1] ==> [1, 2], [1] ==> [1, 3], [1] ==> [1, 2, 3]) partition . code_pred [depth_limited] partition . code_pred [rpred] partition . @@ -314,7 +407,7 @@ | "f x \ tupled_partition f (xs, ys, zs) \ tupled_partition f (x # xs, x # ys, zs)" | "\ f x \ tupled_partition f (xs, ys, zs) \ tupled_partition f (x # xs, ys, x # zs)" -code_pred tupled_partition . +code_pred (mode: [i] ==> [i], [i] ==> [(i, i, o)], [i] ==> [(i, o, i)], [i] ==> [(o, i, i)], [i] ==> [(i, o, o)]) tupled_partition . thm tupled_partition.equation @@ -325,7 +418,7 @@ subsection {* transitive predicate *} -code_pred tranclp +code_pred (mode: [1] ==> [1, 2], [1] ==> [1], [2] ==> [1, 2], [2] ==> [2], [] ==> [1, 2], [] ==> [1], [] ==> [2], [] ==> []) tranclp proof - case tranclp from this converse_tranclpE[OF this(1)] show thesis by metis @@ -658,6 +751,8 @@ | "w \ S\<^isub>4 \ b # w \ B\<^isub>4" | "\v \ B\<^isub>4; w \ B\<^isub>4\ \ a # v @ w \ B\<^isub>4" +code_pred (mode: [], [1]) S\<^isub>4p . + subsection {* Lambda *} datatype type = @@ -708,4 +803,10 @@ | appR [simp, intro!]: "s \\<^sub>\ t ==> u \ s \\<^sub>\ u \ t" | abs [simp, intro!]: "s \\<^sub>\ t ==> Abs T s \\<^sub>\ Abs T t" +code_pred (mode: [1, 2], [1, 2, 3]) typing . +thm typing.equation + +code_pred (mode: [1], [1, 2]) beta . +thm beta.equation + end \ No newline at end of file diff -r b4534348b8fd -r 78faaec3209f src/HOL/ex/predicate_compile.ML --- a/src/HOL/ex/predicate_compile.ML Thu Oct 29 17:58:26 2009 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,2182 +0,0 @@ -(* Author: Lukas Bulwahn, TU Muenchen - -(Prototype of) A compiler from predicates specified by intro/elim rules -to equations. -*) - -signature PREDICATE_COMPILE = -sig - type mode = int list option list * int list - (*val add_equations_of: bool -> string list -> theory -> theory *) - val register_predicate : (thm list * thm * int) -> theory -> theory - val is_registered : theory -> string -> bool - (* val fetch_pred_data : theory -> string -> (thm list * thm * int) *) - val predfun_intro_of: theory -> string -> mode -> thm - val predfun_elim_of: theory -> string -> mode -> thm - val strip_intro_concl: int -> term -> term * (term list * term list) - val predfun_name_of: theory -> string -> mode -> string - val all_preds_of : theory -> string list - val modes_of: theory -> string -> mode list - val string_of_mode : mode -> string - val intros_of: theory -> string -> thm list - val nparams_of: theory -> string -> int - val add_intro: thm -> theory -> theory - val set_elim: thm -> theory -> theory - val setup: theory -> theory - val code_pred: string -> Proof.context -> Proof.state - val code_pred_cmd: string -> Proof.context -> Proof.state - val print_stored_rules: theory -> unit - val print_all_modes: theory -> unit - val do_proofs: bool Unsynchronized.ref - val mk_casesrule : Proof.context -> int -> thm list -> term - val analyze_compr: theory -> term -> term - val eval_ref: (unit -> term Predicate.pred) option Unsynchronized.ref - val add_equations : string list -> theory -> theory - val code_pred_intros_attrib : attribute - (* used by Quickcheck_Generator *) - (*val funT_of : mode -> typ -> typ - val mk_if_pred : term -> term - val mk_Eval : term * term -> term*) - val mk_tupleT : typ list -> typ -(* val mk_predT : typ -> typ *) - (* temporary for testing of the compilation *) - datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | - GeneratorPrem of term list * term | Generator of (string * typ); - val prepare_intrs: theory -> string list -> - (string * typ) list * int * string list * string list * (string * mode list) list * - (string * (term list * indprem list) list) list * (string * (int option list * int)) list - datatype compilation_funs = CompilationFuns of { - mk_predT : typ -> typ, - dest_predT : typ -> typ, - mk_bot : typ -> term, - mk_single : term -> term, - mk_bind : term * term -> term, - mk_sup : term * term -> term, - mk_if : term -> term, - mk_not : term -> term, - mk_map : typ -> typ -> term -> term -> term, - lift_pred : term -> term - }; - datatype tmode = Mode of mode * int list * tmode option list; - type moded_clause = term list * (indprem * tmode) list - type 'a pred_mode_table = (string * (mode * 'a) list) list - val infer_modes : bool -> theory -> (string * (int list option list * int list) list) list - -> (string * (int option list * int)) list -> string list - -> (string * (term list * indprem list) list) list - -> (moded_clause list) pred_mode_table - val infer_modes_with_generator : theory -> (string * (int list option list * int list) list) list - -> (string * (int option list * int)) list -> string list - -> (string * (term list * indprem list) list) list - -> (moded_clause list) pred_mode_table - (*val compile_preds : theory -> compilation_funs -> string list -> string list - -> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table - val rpred_create_definitions :(string * typ) list -> string * mode list - -> theory -> theory - val split_smode : int list -> term list -> (term list * term list) *) - val print_moded_clauses : - theory -> (moded_clause list) pred_mode_table -> unit - val print_compiled_terms : theory -> term pred_mode_table -> unit - (*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*) - val rpred_compfuns : compilation_funs - val dest_funT : typ -> typ * typ - (* val depending_preds_of : theory -> thm list -> string list *) - val add_quickcheck_equations : string list -> theory -> theory - val add_sizelim_equations : string list -> theory -> theory - val is_inductive_predicate : theory -> string -> bool - val terms_vs : term list -> string list - val subsets : int -> int -> int list list - val check_mode_clause : bool -> theory -> string list -> - (string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list) - -> (term list * (indprem * tmode) list) option - val string_of_moded_prem : theory -> (indprem * tmode) -> string - val all_modes_of : theory -> (string * mode list) list - val all_generator_modes_of : theory -> (string * mode list) list - val compile_clause : compilation_funs -> term option -> (term list -> term) -> - theory -> string list -> string list -> mode -> term -> moded_clause -> term - val preprocess_intro : theory -> thm -> thm - val is_constrt : theory -> term -> bool - val is_predT : typ -> bool - val guess_nparams : typ -> int -end; - -structure Predicate_Compile : PREDICATE_COMPILE = -struct - -(** auxiliary **) - -(* debug stuff *) - -fun tracing s = (if ! Toplevel.debug then tracing s else ()); - -fun print_tac s = Seq.single; (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *) -fun debug_tac msg = Seq.single; (* (fn st => (tracing msg; Seq.single st)); *) - -val do_proofs = Unsynchronized.ref true; - -fun mycheat_tac thy i st = - (Tactic.rtac (Skip_Proof.make_thm thy (Var (("A", 0), propT))) i) st - -fun remove_last_goal thy st = - (Tactic.rtac (Skip_Proof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st - -(* reference to preprocessing of InductiveSet package *) - -val ind_set_codegen_preproc = Inductive_Set.codegen_preproc; - -(** fundamentals **) - -(* syntactic operations *) - -fun mk_eq (x, xs) = - let fun mk_eqs _ [] = [] - | mk_eqs a (b::cs) = - HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs - in mk_eqs x xs end; - -fun mk_tupleT [] = HOLogic.unitT - | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts; - -fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = [] - | dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2) - | dest_tupleT t = [t] - -fun mk_tuple [] = HOLogic.unit - | mk_tuple ts = foldr1 HOLogic.mk_prod ts; - -fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = [] - | dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2) - | dest_tuple t = [t] - -fun mk_scomp (t, u) = - let - val T = fastype_of t - val U = fastype_of u - val [A] = binder_types T - val D = body_type U - in - Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u - end; - -fun dest_funT (Type ("fun",[S, T])) = (S, T) - | dest_funT T = raise TYPE ("dest_funT", [T], []) - -fun mk_fun_comp (t, u) = - let - val (_, B) = dest_funT (fastype_of t) - val (C, A) = dest_funT (fastype_of u) - in - Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u - end; - -fun dest_randomT (Type ("fun", [@{typ Random.seed}, - Type ("*", [Type ("*", [T, @{typ "unit => Code_Evaluation.term"}]) ,@{typ Random.seed}])])) = T - | dest_randomT T = raise TYPE ("dest_randomT", [T], []) - -(* destruction of intro rules *) - -(* FIXME: look for other place where this functionality was used before *) -fun strip_intro_concl nparams intro = let - val _ $ u = Logic.strip_imp_concl intro - val (pred, all_args) = strip_comb u - val (params, args) = chop nparams all_args -in (pred, (params, args)) end - -(** data structures **) - -type smode = int list; -type mode = smode option list * smode; -datatype tmode = Mode of mode * int list * tmode option list; - -fun split_smode is ts = - let - fun split_smode' _ _ [] = ([], []) - | split_smode' is i (t::ts) = (if i mem is then apfst else apsnd) (cons t) - (split_smode' is (i+1) ts) - in split_smode' is 1 ts end - -fun split_mode (iss, is) ts = - let - val (t1, t2) = chop (length iss) ts - in (t1, split_smode is t2) end - -fun string_of_mode (iss, is) = space_implode " -> " (map - (fn NONE => "X" - | SOME js => enclose "[" "]" (commas (map string_of_int js))) - (iss @ [SOME is])); - -fun string_of_tmode (Mode (predmode, termmode, param_modes)) = - "predmode: " ^ (string_of_mode predmode) ^ - (if null param_modes then "" else - "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes)) - -datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | - GeneratorPrem of term list * term | Generator of (string * typ); - -type moded_clause = term list * (indprem * tmode) list -type 'a pred_mode_table = (string * (mode * 'a) list) list - -datatype predfun_data = PredfunData of { - name : string, - definition : thm, - intro : thm, - elim : thm -}; - -fun rep_predfun_data (PredfunData data) = data; -fun mk_predfun_data (name, definition, intro, elim) = - PredfunData {name = name, definition = definition, intro = intro, elim = elim} - -datatype function_data = FunctionData of { - name : string, - equation : thm option (* is not used at all? *) -}; - -fun rep_function_data (FunctionData data) = data; -fun mk_function_data (name, equation) = - FunctionData {name = name, equation = equation} - -datatype pred_data = PredData of { - intros : thm list, - elim : thm option, - nparams : int, - functions : (mode * predfun_data) list, - generators : (mode * function_data) list, - sizelim_functions : (mode * function_data) list -}; - -fun rep_pred_data (PredData data) = data; -fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) = - PredData {intros = intros, elim = elim, nparams = nparams, - functions = functions, generators = generators, sizelim_functions = sizelim_functions} -fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) = - mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions))) - -fun eq_option eq (NONE, NONE) = true - | eq_option eq (SOME x, SOME y) = eq (x, y) - | eq_option eq _ = false - -fun eq_pred_data (PredData d1, PredData d2) = - eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso - eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso - #nparams d1 = #nparams d2 - -structure PredData = TheoryDataFun -( - type T = pred_data Graph.T; - val empty = Graph.empty; - val copy = I; - val extend = I; - fun merge _ = Graph.merge eq_pred_data; -); - -(* queries *) - -fun lookup_pred_data thy name = - Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name) - -fun the_pred_data thy name = case lookup_pred_data thy name - of NONE => error ("No such predicate " ^ quote name) - | SOME data => data; - -val is_registered = is_some oo lookup_pred_data - -val all_preds_of = Graph.keys o PredData.get - -val intros_of = #intros oo the_pred_data - -fun the_elim_of thy name = case #elim (the_pred_data thy name) - of NONE => error ("No elimination rule for predicate " ^ quote name) - | SOME thm => thm - -val has_elim = is_some o #elim oo the_pred_data; - -val nparams_of = #nparams oo the_pred_data - -val modes_of = (map fst) o #functions oo the_pred_data - -fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy) - -val is_compiled = not o null o #functions oo the_pred_data - -fun lookup_predfun_data thy name mode = - Option.map rep_predfun_data (AList.lookup (op =) - (#functions (the_pred_data thy name)) mode) - -fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode - of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) - | SOME data => data; - -val predfun_name_of = #name ooo the_predfun_data - -val predfun_definition_of = #definition ooo the_predfun_data - -val predfun_intro_of = #intro ooo the_predfun_data - -val predfun_elim_of = #elim ooo the_predfun_data - -fun lookup_generator_data thy name mode = - Option.map rep_function_data (AList.lookup (op =) - (#generators (the_pred_data thy name)) mode) - -fun the_generator_data thy name mode = case lookup_generator_data thy name mode - of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) - | SOME data => data - -val generator_name_of = #name ooo the_generator_data - -val generator_modes_of = (map fst) o #generators oo the_pred_data - -fun all_generator_modes_of thy = - map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy) - -fun lookup_sizelim_function_data thy name mode = - Option.map rep_function_data (AList.lookup (op =) - (#sizelim_functions (the_pred_data thy name)) mode) - -fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode - of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode - ^ " of predicate " ^ name) - | SOME data => data - -val sizelim_function_name_of = #name ooo the_sizelim_function_data - -(*val generator_modes_of = (map fst) o #generators oo the_pred_data*) - -(* diagnostic display functions *) - -fun print_modes modes = tracing ("Inferred modes:\n" ^ - cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map - string_of_mode ms)) modes)); - -fun print_pred_mode_table string_of_entry thy pred_mode_table = - let - fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode) - ^ (string_of_entry pred mode entry) - fun print_pred (pred, modes) = - "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes) - val _ = tracing (cat_lines (map print_pred pred_mode_table)) - in () end; - -fun string_of_moded_prem thy (Prem (ts, p), tmode) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(" ^ (string_of_tmode tmode) ^ ")" - | string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(generator_mode: " ^ (string_of_mode predmode) ^ ")" - | string_of_moded_prem thy (Generator (v, T), _) = - "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T) - | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(negative mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")" - | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) = - (Syntax.string_of_term_global thy t) ^ - "(sidecond mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")" - | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented" - -fun print_moded_clauses thy = - let - fun string_of_clause pred mode clauses = - cat_lines (map (fn (ts, prems) => (space_implode " --> " - (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " " - ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses) - in print_pred_mode_table string_of_clause thy end; - -fun print_compiled_terms thy = - print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy - -fun print_stored_rules thy = - let - val preds = (Graph.keys o PredData.get) thy - fun print pred () = let - val _ = writeln ("predicate: " ^ pred) - val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred)) - val _ = writeln ("introrules: ") - val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm)) - (rev (intros_of thy pred)) () - in - if (has_elim thy pred) then - writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred)) - else - writeln ("no elimrule defined") - end - in - fold print preds () - end; - -fun print_all_modes thy = - let - val _ = writeln ("Inferred modes:") - fun print (pred, modes) u = - let - val _ = writeln ("predicate: " ^ pred) - val _ = writeln ("modes: " ^ (commas (map string_of_mode modes))) - in u end - in - fold print (all_modes_of thy) () - end - -(** preprocessing rules **) - -fun imp_prems_conv cv ct = - case Thm.term_of ct of - Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct - | _ => Conv.all_conv ct - -fun Trueprop_conv cv ct = - case Thm.term_of ct of - Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct - | _ => error "Trueprop_conv" - -fun preprocess_intro thy rule = - Conv.fconv_rule - (imp_prems_conv - (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq}))))) - (Thm.transfer thy rule) - -fun preprocess_elim thy nparams elimrule = - let - fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) = - HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs) - | replace_eqs t = t - val prems = Thm.prems_of elimrule - val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams - fun preprocess_case t = - let - val params = Logic.strip_params t - val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t) - val assums_hyp' = assums1 @ (map replace_eqs assums2) - in - list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t)) - end - val cases' = map preprocess_case (tl prems) - val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule) - in - Thm.equal_elim - (Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@{thm eq_is_eq}]) - (cterm_of thy elimrule'))) - elimrule - end; - -(* special case: predicate with no introduction rule *) -fun noclause thy predname elim = let - val T = (Logic.unvarifyT o Sign.the_const_type thy) predname - val Ts = binder_types T - val names = Name.variant_list [] - (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts))) - val vs = map2 (curry Free) names Ts - val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs)) - val intro_t = Logic.mk_implies (@{prop False}, clausehd) - val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)) - val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P) - val intro = Goal.prove (ProofContext.init thy) names [] intro_t - (fn {...} => etac @{thm FalseE} 1) - val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t - (fn {...} => etac elim 1) -in - ([intro], elim) -end - -fun fetch_pred_data thy name = - case try (Inductive.the_inductive (ProofContext.init thy)) name of - SOME (info as (_, result)) => - let - fun is_intro_of intro = - let - val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro)) - in (fst (dest_Const const) = name) end; - val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy)) - (filter is_intro_of (#intrs result))) - val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info))) - val nparams = length (Inductive.params_of (#raw_induct result)) - val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) - val (intros, elim) = if null intros then noclause thy name elim else (intros, elim) - in - mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) - end - | NONE => error ("No such predicate: " ^ quote name) - -(* updaters *) - -fun apfst3 f (x, y, z) = (f x, y, z) -fun apsnd3 f (x, y, z) = (x, f y, z) -fun aptrd3 f (x, y, z) = (x, y, f z) - -fun add_predfun name mode data = - let - val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data) - in PredData.map (Graph.map_node name (map_pred_data add)) end - -fun is_inductive_predicate thy name = - is_some (try (Inductive.the_inductive (ProofContext.init thy)) name) - -fun depending_preds_of thy (key, value) = - let - val intros = (#intros o rep_pred_data) value - in - fold Term.add_const_names (map Thm.prop_of intros) [] - |> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c)) - end; - - -(* code dependency graph *) -(* -fun dependencies_of thy name = - let - val (intros, elim, nparams) = fetch_pred_data thy name - val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) - val keys = depending_preds_of thy intros - in - (data, keys) - end; -*) -(* guessing number of parameters *) -fun find_indexes pred xs = - let - fun find is n [] = is - | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs; - in rev (find [] 0 xs) end; - -fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT) - | is_predT _ = false - -fun guess_nparams T = - let - val argTs = binder_types T - val nparams = fold Integer.max - (map (fn x => x + 1) (find_indexes is_predT argTs)) 0 - in nparams end; - -fun add_intro thm thy = let - val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm))) - fun cons_intro gr = - case try (Graph.get_node gr) name of - SOME pred_data => Graph.map_node name (map_pred_data - (apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr - | NONE => - let - val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name) - in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end; - in PredData.map cons_intro thy end - -fun set_elim thm = let - val (name, _) = dest_Const (fst - (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm))))) - fun set (intros, _, nparams) = (intros, SOME thm, nparams) - in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end - -fun set_nparams name nparams = let - fun set (intros, elim, _ ) = (intros, elim, nparams) - in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end - -fun register_predicate (pre_intros, pre_elim, nparams) thy = let - val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros)))) - (* preprocessing *) - val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros) - val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) - in - PredData.map - (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy - end - -fun set_generator_name pred mode name = - let - val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE)) - in - PredData.map (Graph.map_node pred (map_pred_data set)) - end - -fun set_sizelim_function_name pred mode name = - let - val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE)) - in - PredData.map (Graph.map_node pred (map_pred_data set)) - end - -(** data structures for generic compilation for different monads **) - -(* maybe rename functions more generic: - mk_predT -> mk_monadT; dest_predT -> dest_monadT - mk_single -> mk_return (?) -*) -datatype compilation_funs = CompilationFuns of { - mk_predT : typ -> typ, - dest_predT : typ -> typ, - mk_bot : typ -> term, - mk_single : term -> term, - mk_bind : term * term -> term, - mk_sup : term * term -> term, - mk_if : term -> term, - mk_not : term -> term, -(* funT_of : mode -> typ -> typ, *) -(* mk_fun_of : theory -> (string * typ) -> mode -> term, *) - mk_map : typ -> typ -> term -> term -> term, - lift_pred : term -> term -}; - -fun mk_predT (CompilationFuns funs) = #mk_predT funs -fun dest_predT (CompilationFuns funs) = #dest_predT funs -fun mk_bot (CompilationFuns funs) = #mk_bot funs -fun mk_single (CompilationFuns funs) = #mk_single funs -fun mk_bind (CompilationFuns funs) = #mk_bind funs -fun mk_sup (CompilationFuns funs) = #mk_sup funs -fun mk_if (CompilationFuns funs) = #mk_if funs -fun mk_not (CompilationFuns funs) = #mk_not funs -(*fun funT_of (CompilationFuns funs) = #funT_of funs*) -(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*) -fun mk_map (CompilationFuns funs) = #mk_map funs -fun lift_pred (CompilationFuns funs) = #lift_pred funs - -fun funT_of compfuns (iss, is) T = - let - val Ts = binder_types T - val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts - val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs - in - (paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs)) - end; - -fun sizelim_funT_of compfuns (iss, is) T = - let - val Ts = binder_types T - val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts - val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs - in - (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs)) - end; - -fun mk_fun_of compfuns thy (name, T) mode = - Const (predfun_name_of thy name mode, funT_of compfuns mode T) - -fun mk_sizelim_fun_of compfuns thy (name, T) mode = - Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T) - -fun mk_generator_of compfuns thy (name, T) mode = - Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T) - - -structure PredicateCompFuns = -struct - -fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T]) - -fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T - | dest_predT T = raise TYPE ("dest_predT", [T], []); - -fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T); - -fun mk_single t = - let val T = fastype_of t - in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end; - -fun mk_bind (x, f) = - let val T as Type ("fun", [_, U]) = fastype_of f - in - Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f - end; - -val mk_sup = HOLogic.mk_binop @{const_name sup}; - -fun mk_if cond = Const (@{const_name Predicate.if_pred}, - HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond; - -fun mk_not t = let val T = mk_predT HOLogic.unitT - in Const (@{const_name Predicate.not_pred}, T --> T) $ t end - -fun mk_Enum f = - let val T as Type ("fun", [T', _]) = fastype_of f - in - Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f - end; - -fun mk_Eval (f, x) = - let - val T = fastype_of x - in - Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x - end; - -fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map}, - (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp; - -val lift_pred = I - -val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot, - mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, - mk_map = mk_map, lift_pred = lift_pred}; - -end; - -(* termify_code: -val termT = Type ("Code_Evaluation.term", []); -fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT) -*) -(* -fun lift_random random = - let - val T = dest_randomT (fastype_of random) - in - mk_scomp (random, - mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed}, - mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)), - Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T)))) - end; -*) - -structure RPredCompFuns = -struct - -fun mk_rpredT T = - @{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"}) - -fun dest_rpredT (Type ("fun", [_, - Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T - | dest_rpredT T = raise TYPE ("dest_rpredT", [T], []); - -fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T) - -fun mk_single t = - let - val T = fastype_of t - in - Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t - end; - -fun mk_bind (x, f) = - let - val T as (Type ("fun", [_, U])) = fastype_of f - in - Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f - end - -val mk_sup = HOLogic.mk_binop @{const_name RPred.supp} - -fun mk_if cond = Const (@{const_name RPred.if_rpred}, - HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond; - -fun mk_not t = error "Negation is not defined for RPred" - -fun mk_map t = error "FIXME" (*FIXME*) - -fun lift_pred t = - let - val T = PredicateCompFuns.dest_predT (fastype_of t) - val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T - in - Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t - end; - -val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot, - mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, - mk_map = mk_map, lift_pred = lift_pred}; - -end; -(* for external use with interactive mode *) -val rpred_compfuns = RPredCompFuns.compfuns; - -fun lift_random random = - let - val T = dest_randomT (fastype_of random) - in - Const (@{const_name lift_random}, (@{typ Random.seed} --> - HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) --> - RPredCompFuns.mk_rpredT T) $ random - end; - -(* Mode analysis *) - -(*** check if a term contains only constructor functions ***) -fun is_constrt thy = - let - val cnstrs = flat (maps - (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd) - (Symtab.dest (Datatype.get_all thy))); - fun check t = (case strip_comb t of - (Free _, []) => true - | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of - (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts - | _ => false) - | _ => false) - in check end; - -(*** check if a type is an equality type (i.e. doesn't contain fun) - FIXME this is only an approximation ***) -fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts - | is_eqT _ = true; - -fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm []; -val terms_vs = distinct (op =) o maps term_vs; - -(** collect all Frees in a term (with duplicates!) **) -fun term_vTs tm = - fold_aterms (fn Free xT => cons xT | _ => I) tm []; - -(*FIXME this function should not be named merge... make it local instead*) -fun merge xs [] = xs - | merge [] ys = ys - | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys) - else y::merge (x::xs) ys; - -fun subsets i j = if i <= j then - let val is = subsets (i+1) j - in merge (map (fn ks => i::ks) is) is end - else [[]]; - -(* FIXME: should be in library - map_prod *) -fun cprod ([], ys) = [] - | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys); - -fun cprods xss = List.foldr (map op :: o cprod) [[]] xss; - - - -(*TODO: cleanup function and put together with modes_of_term *) -(* -fun modes_of_param default modes t = let - val (vs, t') = strip_abs t - val b = length vs - fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => - let - val (args1, args2) = - if length args < length iss then - error ("Too few arguments for inductive predicate " ^ name) - else chop (length iss) args; - val k = length args2; - val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1) - (1 upto b) - val partial_mode = (1 upto k) \\ perm - in - if not (partial_mode subset is) then [] else - let - val is' = - (fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm []) - |> fold (fn i => if i > k then cons (i - k + b) else I) is - - val res = map (fn x => Mode (m, is', x)) (cprods (map - (fn (NONE, _) => [NONE] - | (SOME js, arg) => map SOME (filter - (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) - (iss ~~ args1))) - in res end - end)) (AList.lookup op = modes name) - in case strip_comb t' of - (Const (name, _), args) => the_default default (mk_modes name args) - | (Var ((name, _), _), args) => the (mk_modes name args) - | (Free (name, _), args) => the (mk_modes name args) - | _ => default end - -and -*) -fun modes_of_term modes t = - let - val ks = 1 upto length (binder_types (fastype_of t)); - val default = [Mode (([], ks), ks, [])]; - fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => - let - val (args1, args2) = - if length args < length iss then - error ("Too few arguments for inductive predicate " ^ name) - else chop (length iss) args; - val k = length args2; - val prfx = 1 upto k - in - if not (is_prefix op = prfx is) then [] else - let val is' = map (fn i => i - k) (List.drop (is, k)) - in map (fn x => Mode (m, is', x)) (cprods (map - (fn (NONE, _) => [NONE] - | (SOME js, arg) => map SOME (filter - (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) - (iss ~~ args1))) - end - end)) (AList.lookup op = modes name) - - in - case strip_comb (Envir.eta_contract t) of - (Const (name, _), args) => the_default default (mk_modes name args) - | (Var ((name, _), _), args) => the (mk_modes name args) - | (Free (name, _), args) => the (mk_modes name args) - | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *) - | _ => default - end - -fun select_mode_prem thy modes vs ps = - find_first (is_some o snd) (ps ~~ map - (fn Prem (us, t) => find_first (fn Mode (_, is, _) => - let - val (in_ts, out_ts) = split_smode is us; - val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts; - val vTs = maps term_vTs out_ts'; - val dupTs = map snd (duplicates (op =) vTs) @ - map_filter (AList.lookup (op =) vTs) vs; - in - subset (op =) (terms_vs (in_ts @ in_ts'), vs) andalso - forall (is_eqT o fastype_of) in_ts' andalso - subset (op =) (term_vs t, vs) andalso - forall is_eqT dupTs - end) - (modes_of_term modes t handle Option => - error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) - | Negprem (us, t) => find_first (fn Mode (_, is, _) => - length us = length is andalso - subset (op =) (terms_vs us, vs) andalso - subset (op =) (term_vs t, vs) - (modes_of_term modes t handle Option => - error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) - | Sidecond t => if subset (op =) (term_vs t, vs) then SOME (Mode (([], []), [], [])) - else NONE - ) ps); - -fun fold_prem f (Prem (args, _)) = fold f args - | fold_prem f (Negprem (args, _)) = fold f args - | fold_prem f (Sidecond t) = f t - -fun all_subsets [] = [[]] - | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end - -fun generator vTs v = - let - val T = the (AList.lookup (op =) vTs v) - in - (Generator (v, T), Mode (([], []), [], [])) - end; - -fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t) - | gen_prem _ = error "gen_prem : invalid input for gen_prem" - -fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) = - if member (op =) param_vs v then - GeneratorPrem (us, t) - else p - | param_gen_prem param_vs p = p - -fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) = - let - val modes' = modes @ map_filter - (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) - (param_vs ~~ iss); - val gen_modes' = gen_modes @ map_filter - (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) - (param_vs ~~ iss); - val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts [])) - val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps []) - fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs) - | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of - NONE => - (if with_generator then - (case select_mode_prem thy gen_modes' vs ps of - SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps) - (case p of Prem (us, _) => union (op =) vs (terms_vs us) | _ => vs) - (filter_out (equal p) ps) - | NONE => - let - val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length)) - in - case (find_first (fn generator_vs => is_some - (select_mode_prem thy modes' (union (op =) vs generator_vs) ps)) all_generator_vs) of - SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps) - (union (op =) vs generator_vs) ps - | NONE => NONE - end) - else - NONE) - | SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps) - (case p of Prem (us, _) => union (op =) vs (terms_vs us) | _ => vs) - (filter_out (equal p) ps)) - val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts)); - val in_vs = terms_vs in_ts; - val concl_vs = terms_vs ts - in - if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso - forall (is_eqT o fastype_of) in_ts' then - case check_mode_prems [] (union (op =) param_vs in_vs) ps of - NONE => NONE - | SOME (acc_ps, vs) => - if with_generator then - SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs))) - else - if subset (op =) (concl_vs, vs) then SOME (ts, rev acc_ps) else NONE - else NONE - end; - -fun check_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) = - let val SOME rs = AList.lookup (op =) preds p - in (p, filter (fn m => case find_index - (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of - ~1 => true - | i => (tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^ - p ^ " violates mode " ^ string_of_mode m); false)) ms) - end; - -fun get_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) = - let - val SOME rs = AList.lookup (op =) preds p - in - (p, map (fn m => - (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms) - end; - -fun fixp f (x : (string * mode list) list) = - let val y = f x - in if x = y then x else fixp f y end; - -fun modes_of_arities arities = - (map (fn (s, (ks, k)) => (s, cprod (cprods (map - (fn NONE => [NONE] - | SOME k' => map SOME (subsets 1 k')) ks), - subsets 1 k))) arities) - -fun infer_modes with_generator thy extra_modes arities param_vs preds = - let - val modes = - fixp (fn modes => - map (check_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes) - (modes_of_arities arities) - in - map (get_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes - end; - -fun remove_from rem [] = [] - | remove_from rem ((k, vs) :: xs) = - (case AList.lookup (op =) rem k of - NONE => (k, vs) - | SOME vs' => (k, vs \\ vs')) - :: remove_from rem xs - -fun infer_modes_with_generator thy extra_modes arities param_vs preds = - let - val prednames = map fst preds - val extra_modes = all_modes_of thy - val gen_modes = all_generator_modes_of thy - |> filter_out (fn (name, _) => member (op =) prednames name) - val starting_modes = remove_from extra_modes (modes_of_arities arities) - val modes = - fixp (fn modes => - map (check_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes) - starting_modes - in - map (get_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes - end; - -(* term construction *) - -fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of - NONE => (Free (s, T), (names, (s, [])::vs)) - | SOME xs => - let - val s' = Name.variant names s; - val v = Free (s', T) - in - (v, (s'::names, AList.update (op =) (s, v::xs) vs)) - end); - -fun distinct_v (Free (s, T)) nvs = mk_v nvs s T - | distinct_v (t $ u) nvs = - let - val (t', nvs') = distinct_v t nvs; - val (u', nvs'') = distinct_v u nvs'; - in (t' $ u', nvs'') end - | distinct_v x nvs = (x, nvs); - -fun compile_match thy compfuns eqs eqs' out_ts success_t = - let - val eqs'' = maps mk_eq eqs @ eqs' - val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) []; - val name = Name.variant names "x"; - val name' = Name.variant (name :: names) "y"; - val T = mk_tupleT (map fastype_of out_ts); - val U = fastype_of success_t; - val U' = dest_predT compfuns U; - val v = Free (name, T); - val v' = Free (name', T); - in - lambda v (fst (Datatype.make_case - (ProofContext.init thy) false [] v - [(mk_tuple out_ts, - if null eqs'' then success_t - else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $ - foldr1 HOLogic.mk_conj eqs'' $ success_t $ - mk_bot compfuns U'), - (v', mk_bot compfuns U')])) - end; - -(*FIXME function can be removed*) -fun mk_funcomp f t = - let - val names = Term.add_free_names t []; - val Ts = binder_types (fastype_of t); - val vs = map Free - (Name.variant_list names (replicate (length Ts) "x") ~~ Ts) - in - fold_rev lambda vs (f (list_comb (t, vs))) - end; -(* -fun compile_param_ext thy compfuns modes (NONE, t) = t - | compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) = - let - val (vs, u) = strip_abs t - val (ivs, ovs) = split_mode is vs - val (f, args) = strip_comb u - val (params, args') = chop (length ms) args - val (inargs, outargs) = split_mode is' args' - val b = length vs - val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b) - val outp_perm = - snd (split_mode is perm) - |> map (fn i => i - length (filter (fn x => x < i) is')) - val names = [] -- TODO - val out_names = Name.variant_list names (replicate (length outargs) "x") - val f' = case f of - Const (name, T) => - if AList.defined op = modes name then - mk_predfun_of thy compfuns (name, T) (iss, is') - else error "compile param: Not an inductive predicate with correct mode" - | Free (name, T) => Free (name, param_funT_of compfuns T (SOME is')) - val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f'))) - val out_vs = map Free (out_names ~~ outTs) - val params' = map (compile_param thy modes) (ms ~~ params) - val f_app = list_comb (f', params' @ inargs) - val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm))) - val match_t = compile_match thy compfuns [] [] out_vs single_t - in list_abs (ivs, - mk_bind compfuns (f_app, match_t)) - end - | compile_param_ext _ _ _ _ = error "compile params" -*) - -fun compile_param size thy compfuns (NONE, t) = t - | compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) = - let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, args') = chop (length ms) args - val params' = map (compile_param size thy compfuns) (ms ~~ params) - val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of - val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of - val f' = - case f of - Const (name, T) => - mk_fun_of compfuns thy (name, T) (iss, is') - | Free (name, T) => Free (name, funT_of compfuns (iss, is') T) - | _ => error ("PredicateCompiler: illegal parameter term") - in list_comb (f', params' @ args') end - -fun compile_expr size thy ((Mode (mode, is, ms)), t) = - case strip_comb t of - (Const (name, T), params) => - let - val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params) - val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of - in - list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params') - end - | (Free (name, T), args) => - let - val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of - in - list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args) - end; - -fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) = - case strip_comb t of - (Const (name, T), params) => - let - val params' = map (compile_param size thy compfuns) (ms ~~ params) - in - list_comb (mk_generator_of compfuns thy (name, T) mode, params') - end - | (Free (name, T), args) => - list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args) - -(** specific rpred functions -- move them to the correct place in this file *) - -(* uncommented termify code; causes more trouble than expected at first *) -(* -fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t)) - | mk_valtermify_term (Free (x, T)) = Free (x, termifyT T) - | mk_valtermify_term (t1 $ t2) = - let - val T = fastype_of t1 - val (T1, T2) = dest_funT T - val t1' = mk_valtermify_term t1 - val t2' = mk_valtermify_term t2 - in - Const ("Code_Evaluation.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2' - end - | mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term" -*) - -fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) = - let - fun check_constrt t (names, eqs) = - if is_constrt thy t then (t, (names, eqs)) else - let - val s = Name.variant names "x"; - val v = Free (s, fastype_of t) - in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end; - - val (in_ts, out_ts) = split_smode is ts; - val (in_ts', (all_vs', eqs)) = - fold_map check_constrt in_ts (all_vs, []); - - fun compile_prems out_ts' vs names [] = - let - val (out_ts'', (names', eqs')) = - fold_map check_constrt out_ts' (names, []); - val (out_ts''', (names'', constr_vs)) = fold_map distinct_v - out_ts'' (names', map (rpair []) vs); - in - (* termify code: - compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' - (mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts))) - *) - compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' - (final_term out_ts) - end - | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) = - let - val vs' = distinct (op =) (flat (vs :: map term_vs out_ts)); - val (out_ts', (names', eqs)) = - fold_map check_constrt out_ts (names, []) - val (out_ts'', (names'', constr_vs')) = fold_map distinct_v - out_ts' ((names', map (rpair []) vs)) - val (compiled_clause, rest) = case p of - Prem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us; - val args = case size of - NONE => in_ts - | SOME size_t => in_ts @ [size_t] - val u = lift_pred compfuns - (list_comb (compile_expr size thy (mode, t), args)) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Negprem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us - val u = lift_pred compfuns - (mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts))) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Sidecond t => - let - val rest = compile_prems [] vs' names'' ps; - in - (mk_if compfuns t, rest) - end - | GeneratorPrem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us; - val args = case size of - NONE => in_ts - | SOME size_t => in_ts @ [size_t] - val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Generator (v, T) => - let - val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"}) - val rest = compile_prems [Free (v, T)] vs' names'' ps; - in - (u, rest) - end - in - compile_match thy compfuns constr_vs' eqs out_ts'' - (mk_bind compfuns (compiled_clause, rest)) - end - val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps; - in - mk_bind compfuns (mk_single compfuns inp, prem_t) - end - -fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls = - let - val (Ts1, (Us1, Us2)) = split_mode mode (binder_types T) - val funT_of = if use_size then sizelim_funT_of else funT_of - val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1 - val xnames = Name.variant_list (all_vs @ param_vs) - (map (fn i => "x" ^ string_of_int i) (snd mode)); - val size_name = Name.variant (all_vs @ param_vs @ xnames) "size" - (* termify code: val xs = map2 (fn s => fn T => Free (s, termifyT T)) xnames Us1; *) - val xs = map2 (fn s => fn T => Free (s, T)) xnames Us1; - val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1' - val size = Free (size_name, @{typ "code_numeral"}) - val decr_size = - if use_size then - SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"}) - $ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"})) - else - NONE - val cl_ts = - map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts)) - thy all_vs param_vs mode (mk_tuple xs)) moded_cls; - val t = foldr1 (mk_sup compfuns) cl_ts - val T' = mk_predT compfuns (mk_tupleT Us2) - val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T') - $ HOLogic.mk_eq (size, @{term "0 :: code_numeral"}) - $ mk_bot compfuns (dest_predT compfuns T') $ t - val fun_const = mk_fun_of compfuns thy (s, T) mode - val eq = if use_size then - (list_comb (fun_const, params @ xs @ [size]), size_t) - else - (list_comb (fun_const, params @ xs), t) - in - HOLogic.mk_Trueprop (HOLogic.mk_eq eq) - end; - -(* special setup for simpset *) -val HOL_basic_ss' = HOL_basic_ss setSolver - (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac)) - -(* Definition of executable functions and their intro and elim rules *) - -fun print_arities arities = tracing ("Arities:\n" ^ - cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^ - space_implode " -> " (map - (fn NONE => "X" | SOME k' => string_of_int k') - (ks @ [SOME k]))) arities)); - -fun mk_Eval_of ((x, T), NONE) names = (x, names) - | mk_Eval_of ((x, T), SOME mode) names = let - val Ts = binder_types T - val argnames = Name.variant_list names - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); - val args = map Free (argnames ~~ Ts) - val (inargs, outargs) = split_smode mode args - val r = PredicateCompFuns.mk_Eval (list_comb (x, inargs), mk_tuple outargs) - val t = fold_rev lambda args r -in - (t, argnames @ names) -end; - -fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy = -let - val Ts = binder_types (fastype_of pred) - val funtrm = Const (mode_id, funT) - val argnames = Name.variant_list [] - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); - val (Ts1, Ts2) = chop (length iss) Ts; - val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1 - val args = map Free (argnames ~~ (Ts1' @ Ts2)) - val (params, ioargs) = chop (length iss) args - val (inargs, outargs) = split_smode is ioargs - val param_names = Name.variant_list argnames - (map (fn i => "p" ^ string_of_int i) (1 upto (length iss))) - val param_vs = map Free (param_names ~~ Ts1) - val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) [] - val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ ioargs)) - val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ ioargs)) - val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params') - val funargs = params @ inargs - val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), - if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs)) - val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), - mk_tuple outargs)) - val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI) - val simprules = [defthm, @{thm eval_pred}, - @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}] - val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1 - val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y"]) [] introtrm (fn {...} => unfolddef_tac) - val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)); - val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P) - val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac) -in - (introthm, elimthm) -end; - -fun create_constname_of_mode thy prefix name mode = - let - fun string_of_mode mode = if null mode then "0" - else space_implode "_" (map string_of_int mode) - val HOmode = space_implode "_and_" - (fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) []) - in - (Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^ - (if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode)) - end; - -fun create_definitions preds (name, modes) thy = - let - val compfuns = PredicateCompFuns.compfuns - val T = AList.lookup (op =) preds name |> the - fun create_definition (mode as (iss, is)) thy = let - val mode_cname = create_constname_of_mode thy "" name mode - val mode_cbasename = Long_Name.base_name mode_cname - val Ts = binder_types T - val (Ts1, Ts2) = chop (length iss) Ts - val (Us1, Us2) = split_smode is Ts2 - val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1 - val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2)) - val names = Name.variant_list [] - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); - val xs = map Free (names ~~ (Ts1' @ Ts2)); - val (xparams, xargs) = chop (length iss) xs; - val (xins, xouts) = split_smode is xargs - val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names - fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t - | mk_split_lambda [x] t = lambda x t - | mk_split_lambda xs t = - let - fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t)) - | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t)) - in - mk_split_lambda' xs t - end; - val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts - (list_comb (Const (name, T), xparams' @ xargs))) - val lhs = list_comb (Const (mode_cname, funT), xparams @ xins) - val def = Logic.mk_equals (lhs, predterm) - val ([definition], thy') = thy |> - Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |> - PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])] - val (intro, elim) = - create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy' - in thy' |> add_predfun name mode (mode_cname, definition, intro, elim) - |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd - |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd - |> Theory.checkpoint - end; - in - fold create_definition modes thy - end; - -fun sizelim_create_definitions preds (name, modes) thy = - let - val T = AList.lookup (op =) preds name |> the - fun create_definition mode thy = - let - val mode_cname = create_constname_of_mode thy "sizelim_" name mode - val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T - in - thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] - |> set_sizelim_function_name name mode mode_cname - end; - in - fold create_definition modes thy - end; - -fun rpred_create_definitions preds (name, modes) thy = - let - val T = AList.lookup (op =) preds name |> the - fun create_definition mode thy = - let - val mode_cname = create_constname_of_mode thy "gen_" name mode - val funT = sizelim_funT_of RPredCompFuns.compfuns mode T - in - thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] - |> set_generator_name name mode mode_cname - end; - in - fold create_definition modes thy - end; - -(* Proving equivalence of term *) - -fun is_Type (Type _) = true - | is_Type _ = false - -(* returns true if t is an application of an datatype constructor *) -(* which then consequently would be splitted *) -(* else false *) -fun is_constructor thy t = - if (is_Type (fastype_of t)) then - (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of - NONE => false - | SOME info => (let - val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info) - val (c, _) = strip_comb t - in (case c of - Const (name, _) => name mem_string constr_consts - | _ => false) end)) - else false - -(* MAJOR FIXME: prove_params should be simple - - different form of introrule for parameters ? *) -fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1) - | prove_param thy (m as SOME (Mode (mode, is, ms)), t) = - let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, _) = chop (length ms) args - val f_tac = case f of - Const (name, T) => simp_tac (HOL_basic_ss addsimps - (@{thm eval_pred}::(predfun_definition_of thy name mode):: - @{thm "Product_Type.split_conv"}::[])) 1 - | Free _ => TRY (rtac @{thm refl} 1) - | Abs _ => error "prove_param: No valid parameter term" - in - REPEAT_DETERM (etac @{thm thin_rl} 1) - THEN REPEAT_DETERM (rtac @{thm ext} 1) - THEN print_tac "prove_param" - THEN f_tac - THEN print_tac "after simplification in prove_args" - THEN (EVERY (map (prove_param thy) (ms ~~ params))) - THEN (REPEAT_DETERM (atac 1)) - end - -fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) = - case strip_comb t of - (Const (name, T), args) => - let - val introrule = predfun_intro_of thy name mode - val (args1, args2) = chop (length ms) args - in - rtac @{thm bindI} 1 - THEN print_tac "before intro rule:" - (* for the right assumption in first position *) - THEN rotate_tac premposition 1 - THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule) - THEN rtac introrule 1 - THEN print_tac "after intro rule" - (* work with parameter arguments *) - THEN (atac 1) - THEN (print_tac "parameter goal") - THEN (EVERY (map (prove_param thy) (ms ~~ args1))) - THEN (REPEAT_DETERM (atac 1)) - end - | _ => rtac @{thm bindI} 1 THEN atac 1 - -fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st; - -fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st - -fun prove_match thy (out_ts : term list) = let - fun get_case_rewrite t = - if (is_constructor thy t) then let - val case_rewrites = (#case_rewrites (Datatype.the_info thy - ((fst o dest_Type o fastype_of) t))) - in case_rewrites @ maps get_case_rewrite (snd (strip_comb t)) end - else [] - val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: maps get_case_rewrite out_ts -(* replace TRY by determining if it necessary - are there equations when calling compile match? *) -in - (* make this simpset better! *) - asm_simp_tac (HOL_basic_ss' addsimps simprules) 1 - THEN print_tac "after prove_match:" - THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1 - THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))) - THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))) - THEN print_tac "after if simplification" -end; - -(* corresponds to compile_fun -- maybe call that also compile_sidecond? *) - -fun prove_sidecond thy modes t = - let - fun preds_of t nameTs = case strip_comb t of - (f as Const (name, T), args) => - if AList.defined (op =) modes name then (name, T) :: nameTs - else fold preds_of args nameTs - | _ => nameTs - val preds = preds_of t [] - val defs = map - (fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T))))) - preds - in - (* remove not_False_eq_True when simpset in prove_match is better *) - simp_tac (HOL_basic_ss addsimps @{thm not_False_eq_True} :: @{thm eval_pred} :: defs) 1 - (* need better control here! *) - end - -fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) = - let - val (in_ts, clause_out_ts) = split_smode is ts; - fun prove_prems out_ts [] = - (prove_match thy out_ts) - THEN asm_simp_tac HOL_basic_ss' 1 - THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1) - | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = - let - val premposition = (find_index (equal p) clauses) + nargs - val rest_tac = (case p of Prem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems out_ts''' ps - in - print_tac "before clause:" - THEN asm_simp_tac HOL_basic_ss 1 - THEN print_tac "before prove_expr:" - THEN prove_expr thy (mode, t, us) premposition - THEN print_tac "after prove_expr:" - THEN rec_tac - end - | Negprem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems out_ts''' ps - val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) - val (_, params) = strip_comb t - in - rtac @{thm bindI} 1 - THEN (if (is_some name) then - simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 - THEN rtac @{thm not_predI} 1 - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN (REPEAT_DETERM (atac 1)) - (* FIXME: work with parameter arguments *) - THEN (EVERY (map (prove_param thy) (param_modes ~~ params))) - else - rtac @{thm not_predI'} 1) - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN rec_tac - end - | Sidecond t => - rtac @{thm bindI} 1 - THEN rtac @{thm if_predI} 1 - THEN print_tac "before sidecond:" - THEN prove_sidecond thy modes t - THEN print_tac "after sidecond:" - THEN prove_prems [] ps) - in (prove_match thy out_ts) - THEN rest_tac - end; - val prems_tac = prove_prems in_ts moded_ps - in - rtac @{thm bindI} 1 - THEN rtac @{thm singleI} 1 - THEN prems_tac - end; - -fun select_sup 1 1 = [] - | select_sup _ 1 = [rtac @{thm supI1}] - | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1)); - -fun prove_one_direction thy clauses preds modes pred mode moded_clauses = - let - val T = the (AList.lookup (op =) preds pred) - val nargs = length (binder_types T) - nparams_of thy pred - val pred_case_rule = the_elim_of thy pred - in - REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})) - THEN etac (predfun_elim_of thy pred mode) 1 - THEN etac pred_case_rule 1 - THEN (EVERY (map - (fn i => EVERY' (select_sup (length moded_clauses) i) i) - (1 upto (length moded_clauses)))) - THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses)) - THEN print_tac "proved one direction" - end; - -(** Proof in the other direction **) - -fun prove_match2 thy out_ts = let - fun split_term_tac (Free _) = all_tac - | split_term_tac t = - if (is_constructor thy t) then let - val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t) - val num_of_constrs = length (#case_rewrites info) - (* special treatment of pairs -- because of fishing *) - val split_rules = case (fst o dest_Type o fastype_of) t of - "*" => [@{thm prod.split_asm}] - | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm") - val (_, ts) = strip_comb t - in - (Splitter.split_asm_tac split_rules 1) -(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1) - THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *) - THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2)) - THEN (EVERY (map split_term_tac ts)) - end - else all_tac - in - split_term_tac (mk_tuple out_ts) - THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2)))) - end - -(* VERY LARGE SIMILIRATIY to function prove_param --- join both functions -*) -(* TODO: remove function *) - -fun prove_param2 thy (NONE, t) = all_tac - | prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, _) = chop (length ms) args - val f_tac = case f of - Const (name, T) => full_simp_tac (HOL_basic_ss addsimps - (@{thm eval_pred}::(predfun_definition_of thy name mode) - :: @{thm "Product_Type.split_conv"}::[])) 1 - | Free _ => all_tac - | _ => error "prove_param2: illegal parameter term" - in - print_tac "before simplification in prove_args:" - THEN f_tac - THEN print_tac "after simplification in prove_args" - THEN (EVERY (map (prove_param2 thy) (ms ~~ params))) - end - - -fun prove_expr2 thy (Mode (mode, is, ms), t) = - (case strip_comb t of - (Const (name, T), args) => - etac @{thm bindE} 1 - THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))) - THEN print_tac "prove_expr2-before" - THEN (debug_tac (Syntax.string_of_term_global thy - (prop_of (predfun_elim_of thy name mode)))) - THEN (etac (predfun_elim_of thy name mode) 1) - THEN print_tac "prove_expr2" - THEN (EVERY (map (prove_param2 thy) (ms ~~ args))) - THEN print_tac "finished prove_expr2" - | _ => etac @{thm bindE} 1) - -(* FIXME: what is this for? *) -(* replace defined by has_mode thy pred *) -(* TODO: rewrite function *) -fun prove_sidecond2 thy modes t = let - fun preds_of t nameTs = case strip_comb t of - (f as Const (name, T), args) => - if AList.defined (op =) modes name then (name, T) :: nameTs - else fold preds_of args nameTs - | _ => nameTs - val preds = preds_of t [] - val defs = map - (fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T))))) - preds - in - (* only simplify the one assumption *) - full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1 - (* need better control here! *) - THEN print_tac "after sidecond2 simplification" - end - -fun prove_clause2 thy modes pred (iss, is) (ts, ps) i = - let - val pred_intro_rule = nth (intros_of thy pred) (i - 1) - val (in_ts, clause_out_ts) = split_smode is ts; - fun prove_prems2 out_ts [] = - print_tac "before prove_match2 - last call:" - THEN prove_match2 thy out_ts - THEN print_tac "after prove_match2 - last call:" - THEN (etac @{thm singleE} 1) - THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) - THEN (asm_full_simp_tac HOL_basic_ss' 1) - THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) - THEN (asm_full_simp_tac HOL_basic_ss' 1) - THEN SOLVED (print_tac "state before applying intro rule:" - THEN (rtac pred_intro_rule 1) - (* How to handle equality correctly? *) - THEN (print_tac "state before assumption matching") - THEN (REPEAT (atac 1 ORELSE - (CHANGED (asm_full_simp_tac HOL_basic_ss' 1) - THEN print_tac "state after simp_tac:")))) - | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = - let - val rest_tac = (case p of - Prem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems2 out_ts''' ps - in - (prove_expr2 thy (mode, t)) THEN rec_tac - end - | Negprem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems2 out_ts''' ps - val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) - val (_, params) = strip_comb t - in - print_tac "before neg prem 2" - THEN etac @{thm bindE} 1 - THEN (if is_some name then - full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 - THEN etac @{thm not_predE} 1 - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params))) - else - etac @{thm not_predE'} 1) - THEN rec_tac - end - | Sidecond t => - etac @{thm bindE} 1 - THEN etac @{thm if_predE} 1 - THEN prove_sidecond2 thy modes t - THEN prove_prems2 [] ps) - in print_tac "before prove_match2:" - THEN prove_match2 thy out_ts - THEN print_tac "after prove_match2:" - THEN rest_tac - end; - val prems_tac = prove_prems2 in_ts ps - in - print_tac "starting prove_clause2" - THEN etac @{thm bindE} 1 - THEN (etac @{thm singleE'} 1) - THEN (TRY (etac @{thm Pair_inject} 1)) - THEN print_tac "after singleE':" - THEN prems_tac - end; - -fun prove_other_direction thy modes pred mode moded_clauses = - let - fun prove_clause clause i = - (if i < length moded_clauses then etac @{thm supE} 1 else all_tac) - THEN (prove_clause2 thy modes pred mode clause i) - in - (DETERM (TRY (rtac @{thm unit.induct} 1))) - THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all}))) - THEN (rtac (predfun_intro_of thy pred mode) 1) - THEN (REPEAT_DETERM (rtac @{thm refl} 2)) - THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses)))) - end; - -(** proof procedure **) - -fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) = - let - val ctxt = ProofContext.init thy - val clauses = the (AList.lookup (op =) clauses pred) - in - Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term - (if !do_proofs then - (fn _ => - rtac @{thm pred_iffI} 1 - THEN prove_one_direction thy clauses preds modes pred mode moded_clauses - THEN print_tac "proved one direction" - THEN prove_other_direction thy modes pred mode moded_clauses - THEN print_tac "proved other direction") - else (fn _ => mycheat_tac thy 1)) - end; - -(* composition of mode inference, definition, compilation and proof *) - -(** auxillary combinators for table of preds and modes **) - -fun map_preds_modes f preds_modes_table = - map (fn (pred, modes) => - (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table - -fun join_preds_modes table1 table2 = - map_preds_modes (fn pred => fn mode => fn value => - (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1 - -fun maps_modes preds_modes_table = - map (fn (pred, modes) => - (pred, map (fn (mode, value) => value) modes)) preds_modes_table - -fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses = - map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred - (the (AList.lookup (op =) preds pred))) moded_clauses - -fun prove thy clauses preds modes moded_clauses compiled_terms = - map_preds_modes (prove_pred thy clauses preds modes) - (join_preds_modes moded_clauses compiled_terms) - -fun prove_by_skip thy _ _ _ _ compiled_terms = - map_preds_modes (fn pred => fn mode => fn t => Drule.standard (Skip_Proof.make_thm thy t)) - compiled_terms - -fun prepare_intrs thy prednames = - let - val intrs = maps (intros_of thy) prednames - |> map (Logic.unvarify o prop_of) - val nparams = nparams_of thy (hd prednames) - val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name) - val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs) - val _ $ u = Logic.strip_imp_concl (hd intrs); - val params = List.take (snd (strip_comb u), nparams); - val param_vs = maps term_vs params - val all_vs = terms_vs intrs - fun dest_prem t = - (case strip_comb t of - (v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t - | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of - Prem (ts, t) => Negprem (ts, t) - | Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t))) - | Sidecond t => Sidecond (c $ t)) - | (c as Const (s, _), ts) => - if is_registered thy s then - let val (ts1, ts2) = chop (nparams_of thy s) ts - in Prem (ts2, list_comb (c, ts1)) end - else Sidecond t - | _ => Sidecond t) - fun add_clause intr (clauses, arities) = - let - val _ $ t = Logic.strip_imp_concl intr; - val (Const (name, T), ts) = strip_comb t; - val (ts1, ts2) = chop nparams ts; - val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr); - val (Ts, Us) = chop nparams (binder_types T) - in - (AList.update op = (name, these (AList.lookup op = clauses name) @ - [(ts2, prems)]) clauses, - AList.update op = (name, (map (fn U => (case strip_type U of - (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs) - | _ => NONE)) Ts, - length Us)) arities) - end; - val (clauses, arities) = fold add_clause intrs ([], []); - in (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) end; - -(** main function of predicate compiler **) - -fun add_equations_of steps prednames thy = - let - val _ = tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...") - val (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) = - prepare_intrs thy prednames - val _ = tracing "Infering modes..." - val moded_clauses = #infer_modes steps thy extra_modes arities param_vs clauses - val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses - val _ = print_modes modes - val _ = print_moded_clauses thy moded_clauses - val _ = tracing "Defining executable functions..." - val thy' = fold (#create_definitions steps preds) modes thy - |> Theory.checkpoint - val _ = tracing "Compiling equations..." - val compiled_terms = - (#compile_preds steps) thy' all_vs param_vs preds moded_clauses - val _ = print_compiled_terms thy' compiled_terms - val _ = tracing "Proving equations..." - val result_thms = #prove steps thy' clauses preds (extra_modes @ modes) - moded_clauses compiled_terms - val qname = #qname steps - (* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *) - val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute - (fn thm => Context.mapping (Code.add_eqn thm) I)))) - val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss - [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms), - [attrib thy ])] thy)) - (maps_modes result_thms) thy' - |> Theory.checkpoint - in - thy'' - end - -fun extend' value_of edges_of key (G, visited) = - let - val (G', v) = case try (Graph.get_node G) key of - SOME v => (G, v) - | NONE => (Graph.new_node (key, value_of key) G, value_of key) - val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited) - (G', key :: visited) - in - (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited') - end; - -fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, [])) - -fun gen_add_equations steps names thy = - let - val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy - |> Theory.checkpoint; - fun strong_conn_of gr keys = - Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr) - val scc = strong_conn_of (PredData.get thy') names - val thy'' = fold_rev - (fn preds => fn thy => - if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy) - scc thy' |> Theory.checkpoint - in thy'' end - -(* different instantiantions of the predicate compiler *) - -val add_equations = gen_add_equations - {infer_modes = infer_modes false, - create_definitions = create_definitions, - compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false, - prove = prove, - are_not_defined = (fn thy => forall (null o modes_of thy)), - qname = "equation"} - -val add_sizelim_equations = gen_add_equations - {infer_modes = infer_modes false, - create_definitions = sizelim_create_definitions, - compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true, - prove = prove_by_skip, - are_not_defined = (fn thy => fn preds => true), (* TODO *) - qname = "sizelim_equation" - } - -val add_quickcheck_equations = gen_add_equations - {infer_modes = infer_modes_with_generator, - create_definitions = rpred_create_definitions, - compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true, - prove = prove_by_skip, - are_not_defined = (fn thy => fn preds => true), (* TODO *) - qname = "rpred_equation"} - -(** user interface **) - -(* generation of case rules from user-given introduction rules *) - -fun mk_casesrule ctxt nparams introrules = - let - val intros = map (Logic.unvarify o prop_of) introrules - val (pred, (params, args)) = strip_intro_concl nparams (hd intros) - val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt - val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT)) - val (argnames, ctxt2) = Variable.variant_fixes - (map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1 - val argvs = map2 (curry Free) argnames (map fastype_of args) - fun mk_case intro = - let - val (_, (_, args)) = strip_intro_concl nparams intro - val prems = Logic.strip_imp_prems intro - val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args) - val frees = (fold o fold_aterms) - (fn t as Free _ => - if member (op aconv) params t then I else insert (op aconv) t - | _ => I) (args @ prems) [] - in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end - val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs)) - val cases = map mk_case intros - in Logic.list_implies (assm :: cases, prop) end; - -(* code_pred_intro attribute *) - -fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I); - -val code_pred_intros_attrib = attrib add_intro; - -local - -(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *) -(* TODO: must create state to prove multiple cases *) -fun generic_code_pred prep_const raw_const lthy = - let - val thy = ProofContext.theory_of lthy - val const = prep_const thy raw_const - val lthy' = LocalTheory.theory (PredData.map - (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy - |> LocalTheory.checkpoint - val thy' = ProofContext.theory_of lthy' - val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy') - fun mk_cases const = - let - val nparams = nparams_of thy' const - val intros = intros_of thy' const - in mk_casesrule lthy' nparams intros end - val cases_rules = map mk_cases preds - val cases = - map (fn case_rule => RuleCases.Case {fixes = [], - assumes = [("", Logic.strip_imp_prems case_rule)], - binds = [], cases = []}) cases_rules - val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases - val lthy'' = lthy' - |> fold Variable.auto_fixes cases_rules - |> ProofContext.add_cases true case_env - fun after_qed thms goal_ctxt = - let - val global_thms = ProofContext.export goal_ctxt - (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms) - in - goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const]) - end - in - Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy'' - end; - -structure P = OuterParse - -in - -val code_pred = generic_code_pred (K I); -val code_pred_cmd = generic_code_pred Code.read_const - -val setup = PredData.put (Graph.empty) #> - Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro)) - "adding alternative introduction rules for code generation of inductive predicates" -(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib) - "adding alternative elimination rules for code generation of inductive predicates"; - *) - (*FIXME name discrepancy in attribs and ML code*) - (*FIXME intros should be better named intro*) - (*FIXME why distinguished attribute for cases?*) - -val _ = OuterSyntax.local_theory_to_proof "code_pred" - "prove equations for predicate specified by intro/elim rules" - OuterKeyword.thy_goal (P.term_group >> code_pred_cmd) - -end - -(*FIXME -- Naming of auxiliary rules necessary? -- add default code equations P x y z = P_i_i_i x y z -*) - -(* transformation for code generation *) - -val eval_ref = Unsynchronized.ref (NONE : (unit -> term Predicate.pred) option); - -(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*) -fun analyze_compr thy t_compr = - let - val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t - | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr); - val (body, Ts, fp) = HOLogic.strip_psplits split; - val (pred as Const (name, T), all_args) = strip_comb body; - val (params, args) = chop (nparams_of thy name) all_args; - val user_mode = map_filter I (map_index - (fn (i, t) => case t of Bound j => if j < length Ts then NONE - else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*) - val modes = filter (fn Mode (_, is, _) => is = user_mode) - (modes_of_term (all_modes_of thy) (list_comb (pred, params))); - val m = case modes - of [] => error ("No mode possible for comprehension " - ^ Syntax.string_of_term_global thy t_compr) - | [m] => m - | m :: _ :: _ => (warning ("Multiple modes possible for comprehension " - ^ Syntax.string_of_term_global thy t_compr); m); - val (inargs, outargs) = split_smode user_mode args; - val t_pred = list_comb (compile_expr NONE thy (m, list_comb (pred, params)), inargs); - val t_eval = if null outargs then t_pred else let - val outargs_bounds = map (fn Bound i => i) outargs; - val outargsTs = map (nth Ts) outargs_bounds; - val T_pred = HOLogic.mk_tupleT outargsTs; - val T_compr = HOLogic.mk_ptupleT fp Ts; - val arrange_bounds = map_index I outargs_bounds - |> sort (prod_ord (K EQUAL) int_ord) - |> map fst; - val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split - (Term.list_abs (map (pair "") outargsTs, - HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds))) - in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end - in t_eval end; - -fun eval thy t_compr = - let - val t = analyze_compr thy t_compr; - val T = dest_predT PredicateCompFuns.compfuns (fastype_of t); - val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t; - in (T, Code_ML.eval NONE ("Predicate_Compile.eval_ref", eval_ref) Predicate.map thy t' []) end; - -fun values ctxt k t_compr = - let - val thy = ProofContext.theory_of ctxt; - val (T, t) = eval thy t_compr; - val setT = HOLogic.mk_setT T; - val (ts, _) = Predicate.yieldn k t; - val elemsT = HOLogic.mk_set T ts; - in if k = ~1 orelse length ts < k then elemsT - else Const (@{const_name Lattices.sup}, setT --> setT --> setT) $ elemsT $ t_compr - end; - -fun values_cmd modes k raw_t state = - let - val ctxt = Toplevel.context_of state; - val t = Syntax.read_term ctxt raw_t; - val t' = values ctxt k t; - val ty' = Term.type_of t'; - val ctxt' = Variable.auto_fixes t' ctxt; - val p = PrintMode.with_modes modes (fn () => - Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk, - Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) (); - in Pretty.writeln p end; - -local structure P = OuterParse in - -val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) []; - -val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag - (opt_modes -- Scan.optional P.nat ~1 -- P.term - >> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep - (values_cmd modes k t))); - -end; - -end; -