diff options
author | Makarius Wenzel <makarius@sketis.net> | 2008-06-14 17:16:23 +0000 |
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committer | Makarius Wenzel <makarius@sketis.net> | 2008-06-14 17:16:23 +0000 |
commit | 41fc4493a96c8a66971d293b557ba9903bf9c053 (patch) | |
tree | 574f9c8f375204cc2ef11e1c04e53f21cfae079d /etc | |
parent | faea8019ff496be6b5bf49f8257117fb1bddacef (diff) |
obsolete;
Diffstat (limited to 'etc')
-rw-r--r-- | etc/isa/completed-proof.ML | 43 | ||||
-rw-r--r-- | etc/isa/depends/Fib.ML | 106 | ||||
-rw-r--r-- | etc/isa/depends/Fib.thy | 17 | ||||
-rw-r--r-- | etc/isa/depends/Primes.ML | 197 | ||||
-rw-r--r-- | etc/isa/depends/Primes.thy | 33 | ||||
-rw-r--r-- | etc/isa/depends/Usedepends.ML | 3 | ||||
-rw-r--r-- | etc/isa/depends/Usedepends.thy | 5 | ||||
-rw-r--r-- | etc/isa/goal-matching.ML | 10 |
8 files changed, 0 insertions, 414 deletions
diff --git a/etc/isa/completed-proof.ML b/etc/isa/completed-proof.ML deleted file mode 100644 index 70cc8e18..00000000 --- a/etc/isa/completed-proof.ML +++ /dev/null @@ -1,43 +0,0 @@ -(* Test of completed proof behaviour: even if qed command is missing, - PG should close of the proof as a goalsave. - - Issue with Isabelle2002: Goals.disable_pr prevents - proof-shell-proof-completed being set because "No Subgoals!" is not - displayed. This means that processing file in one go here (or C-c - C-RET at val_) does not work properly. -*) - -(* default proof-completed-proof-behaviour for isa is 'closeany. - Also should test this file with 'closegoal, 'extend. - - (setq proof-completed-proof-behaviour 'closeany) - : close on any command after proof completed seen - (setq proof-completed-proof-behaviour 'closegoal) - : close when next goal is seen - (setq proof-completed-proof-behaviour 'extend) - : continually extend region after proof completed, until next goal. - - *) - -Goal "A & B --> B & A"; - by (rtac impI 1); - by (etac conjE 1); - by (rtac conjI 1); - by (assume_tac 1); - by (assume_tac 1); - (* qed "and_comms"; *) - -val _ = (); -val _ = (); - -Goal "A & B --> B & A"; - by (rtac impI 1); - by (etac conjE 1); - by (rtac conjI 1); - by (assume_tac 1); - by (assume_tac 1); - qed "and_comms"; - - - - diff --git a/etc/isa/depends/Fib.ML b/etc/isa/depends/Fib.ML deleted file mode 100644 index eba2f0e0..00000000 --- a/etc/isa/depends/Fib.ML +++ /dev/null @@ -1,106 +0,0 @@ -(* Title: HOL/ex/Fib - ID: $Id$ - Author: Lawrence C Paulson - Copyright 1997 University of Cambridge - -Fibonacci numbers: proofs of laws taken from - - R. L. Graham, D. E. Knuth, O. Patashnik. - Concrete Mathematics. - (Addison-Wesley, 1989) -*) - - -(** The difficulty in these proofs is to ensure that the induction hypotheses - are applied before the definition of "fib". Towards this end, the - "fib" equations are not added to the simpset and are applied very - selectively at first. -**) - -Delsimps fib.Suc_Suc; - -val [fib_Suc_Suc] = fib.Suc_Suc; -val fib_Suc3 = read_instantiate [("x", "(Suc ?n)")] fib_Suc_Suc; - -(*Concrete Mathematics, page 280*) -Goal "fib (Suc (n + k)) = fib(Suc k) * fib(Suc n) + fib k * fib n"; -by (res_inst_tac [("u","n")] fib.induct 1); -(*Simplify the LHS just enough to apply the induction hypotheses*) -by (asm_full_simp_tac - (simpset() addsimps [inst "x" "Suc(?m+?n)" fib_Suc_Suc]) 3); -by (ALLGOALS - (asm_simp_tac (simpset() addsimps - ([fib_Suc_Suc, add_mult_distrib, add_mult_distrib2])))); -qed "fib_add"; - - -Goal "fib (Suc n) ~= 0"; -by (res_inst_tac [("u","n")] fib.induct 1); -by (ALLGOALS (asm_simp_tac (simpset() addsimps [fib_Suc_Suc]))); -qed "fib_Suc_neq_0"; - -(* Also add 0 < fib (Suc n) *) -Addsimps [fib_Suc_neq_0, [neq0_conv, fib_Suc_neq_0] MRS iffD1]; - -Goal "0<n ==> 0 < fib n"; -by (rtac (not0_implies_Suc RS exE) 1); -by Auto_tac; -qed "fib_gr_0"; - -(*Concrete Mathematics, page 278: Cassini's identity. - It is much easier to prove using integers!*) -Goal "int (fib (Suc (Suc n)) * fib n) = \ -\ (if n mod 2 = 0 then int (fib(Suc n) * fib(Suc n)) - #1 \ -\ else int (fib(Suc n) * fib(Suc n)) + #1)"; -by (res_inst_tac [("u","n")] fib.induct 1); -by (simp_tac (simpset() addsimps [fib_Suc_Suc, mod_Suc]) 2); -by (simp_tac (simpset() addsimps [fib_Suc_Suc]) 1); -by (asm_full_simp_tac - (simpset() addsimps [fib_Suc_Suc, add_mult_distrib, add_mult_distrib2, - mod_Suc, zmult_int RS sym] @ zmult_ac) 1); -qed "fib_Cassini"; - - - -(** Towards Law 6.111 of Concrete Mathematics **) - -Goal "gcd(fib n, fib (Suc n)) = 1"; -by (res_inst_tac [("u","n")] fib.induct 1); -by (asm_simp_tac (simpset() addsimps [fib_Suc3, gcd_commute, gcd_add2]) 3); -by (ALLGOALS (simp_tac (simpset() addsimps [fib_Suc_Suc]))); -qed "gcd_fib_Suc_eq_1"; - -val gcd_fib_commute = - read_instantiate_sg (sign_of thy) [("m", "fib m")] gcd_commute; - -Goal "gcd(fib m, fib (n+m)) = gcd(fib m, fib n)"; -by (simp_tac (simpset() addsimps [gcd_fib_commute]) 1); -by (case_tac "m=0" 1); -by (Asm_simp_tac 1); -by (clarify_tac (claset() addSDs [not0_implies_Suc]) 1); -by (simp_tac (simpset() addsimps [fib_add]) 1); -by (asm_simp_tac (simpset() addsimps [add_commute, gcd_non_0]) 1); -by (asm_simp_tac (simpset() addsimps [gcd_non_0 RS sym]) 1); -by (asm_simp_tac (simpset() addsimps [gcd_fib_Suc_eq_1, gcd_mult_cancel]) 1); -qed "gcd_fib_add"; - -Goal "m <= n ==> gcd(fib m, fib (n-m)) = gcd(fib m, fib n)"; -by (rtac (gcd_fib_add RS sym RS trans) 1); -by (Asm_simp_tac 1); -qed "gcd_fib_diff"; - -Goal "0<m ==> gcd (fib m, fib (n mod m)) = gcd (fib m, fib n)"; -by (res_inst_tac [("n","n")] less_induct 1); -by (stac mod_if 1); -by (Asm_simp_tac 1); -by (asm_simp_tac (simpset() addsimps [gcd_fib_diff, mod_geq, - not_less_iff_le, diff_less]) 1); -qed "gcd_fib_mod"; - -(*Law 6.111*) -Goal "fib(gcd(m,n)) = gcd(fib m, fib n)"; -by (res_inst_tac [("m","m"),("n","n")] gcd_induct 1); -by (Asm_simp_tac 1); -by (asm_full_simp_tac (simpset() addsimps [gcd_non_0]) 1); -by (asm_full_simp_tac (simpset() addsimps [gcd_commute, gcd_fib_mod]) 1); -qed "fib_gcd"; diff --git a/etc/isa/depends/Fib.thy b/etc/isa/depends/Fib.thy deleted file mode 100644 index 9272ed8c..00000000 --- a/etc/isa/depends/Fib.thy +++ /dev/null @@ -1,17 +0,0 @@ -(* Title: ex/Fib - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1997 University of Cambridge - -The Fibonacci function. Demonstrates the use of recdef. -*) - -Fib = Usedepends + Divides + Primes + - -consts fib :: "nat => nat" -recdef fib "less_than" - zero "fib 0 = 0" - one "fib 1 = 1" - Suc_Suc "fib (Suc (Suc x)) = fib x + fib (Suc x)" - -end diff --git a/etc/isa/depends/Primes.ML b/etc/isa/depends/Primes.ML deleted file mode 100644 index 102419da..00000000 --- a/etc/isa/depends/Primes.ML +++ /dev/null @@ -1,197 +0,0 @@ -(* Title: HOL/ex/Primes.ML - ID: $Id$ - Author: Christophe Tabacznyj and Lawrence C Paulson - Copyright 1996 University of Cambridge - -The "divides" relation, the greatest common divisor and Euclid's algorithm - -See H. Davenport, "The Higher Arithmetic". 6th edition. (CUP, 1992) -*) - -eta_contract:=false; - -(************************************************) -(** Greatest Common Divisor **) -(************************************************) - -(*** Euclid's Algorithm ***) - - -val [gcd_eq] = gcd.simps; - - -val prems = goal thy - "[| !!m. P m 0; \ -\ !!m n. [| 0<n; P n (m mod n) |] ==> P m n \ -\ |] ==> P (m::nat) (n::nat)"; -by (res_inst_tac [("u","m"),("v","n")] gcd.induct 1); -by (case_tac "n=0" 1); -by (asm_simp_tac (simpset() addsimps prems) 1); -by Safe_tac; -by (asm_simp_tac (simpset() addsimps prems) 1); -qed "gcd_induct"; - - -Goal "gcd(m,0) = m"; -by (Simp_tac 1); -qed "gcd_0"; -Addsimps [gcd_0]; - -Goal "0<n ==> gcd(m,n) = gcd (n, m mod n)"; -by (Asm_simp_tac 1); -qed "gcd_non_0"; - -Delsimps gcd.simps; - -Goal "gcd(m,1) = 1"; -by (simp_tac (simpset() addsimps [gcd_non_0]) 1); -qed "gcd_1"; -Addsimps [gcd_1]; - -(*gcd(m,n) divides m and n. The conjunctions don't seem provable separately*) -Goal "(gcd(m,n) dvd m) & (gcd(m,n) dvd n)"; -by (res_inst_tac [("m","m"),("n","n")] gcd_induct 1); -by (ALLGOALS (asm_full_simp_tac (simpset() addsimps [gcd_non_0]))); -by (blast_tac (claset() addDs [dvd_mod_imp_dvd]) 1); -qed "gcd_dvd_both"; - -bind_thm ("gcd_dvd1", gcd_dvd_both RS conjunct1); -bind_thm ("gcd_dvd2", gcd_dvd_both RS conjunct2); - - -(*Maximality: for all m,n,f naturals, - if f divides m and f divides n then f divides gcd(m,n)*) -Goal "(f dvd m) --> (f dvd n) --> f dvd gcd(m,n)"; -by (res_inst_tac [("m","m"),("n","n")] gcd_induct 1); -by (ALLGOALS (asm_full_simp_tac (simpset() addsimps[gcd_non_0, dvd_mod]))); -qed_spec_mp "gcd_greatest"; - -(*Function gcd yields the Greatest Common Divisor*) -Goalw [is_gcd_def] "is_gcd (gcd(m,n)) m n"; -by (asm_simp_tac (simpset() addsimps [gcd_greatest, gcd_dvd_both]) 1); -qed "is_gcd"; - -(*uniqueness of GCDs*) -Goalw [is_gcd_def] "[| is_gcd m a b; is_gcd n a b |] ==> m=n"; -by (blast_tac (claset() addIs [dvd_anti_sym]) 1); -qed "is_gcd_unique"; - -(*USED??*) -Goalw [is_gcd_def] - "[| is_gcd m a b; k dvd a; k dvd b |] ==> k dvd m"; -by (Blast_tac 1); -qed "is_gcd_dvd"; - -(** Commutativity **) - -Goalw [is_gcd_def] "is_gcd k m n = is_gcd k n m"; -by (Blast_tac 1); -qed "is_gcd_commute"; - -Goal "gcd(m,n) = gcd(n,m)"; -by (rtac is_gcd_unique 1); -by (rtac is_gcd 2); -by (asm_simp_tac (simpset() addsimps [is_gcd, is_gcd_commute]) 1); -qed "gcd_commute"; - -Goal "gcd(gcd(k,m),n) = gcd(k,gcd(m,n))"; -by (rtac is_gcd_unique 1); -by (rtac is_gcd 2); -by (rewtac is_gcd_def); -by (blast_tac (claset() addSIs [gcd_dvd1, gcd_dvd2] - addIs [gcd_greatest, dvd_trans]) 1); -qed "gcd_assoc"; - -Goal "gcd(0,m) = m"; -by (stac gcd_commute 1); -by (rtac gcd_0 1); -qed "gcd_0_left"; - -Goal "gcd(1,m) = 1"; -by (stac gcd_commute 1); -by (rtac gcd_1 1); -qed "gcd_1_left"; -Addsimps [gcd_0_left, gcd_1_left]; - - -(** Multiplication laws **) - -(*Davenport, page 27*) -Goal "k * gcd(m,n) = gcd(k*m, k*n)"; -by (res_inst_tac [("m","m"),("n","n")] gcd_induct 1); -by (Asm_full_simp_tac 1); -by (case_tac "k=0" 1); - by (Asm_full_simp_tac 1); -by (asm_full_simp_tac - (simpset() addsimps [mod_geq, gcd_non_0, mod_mult_distrib2]) 1); -qed "gcd_mult_distrib2"; - -Goal "gcd(m,m) = m"; -by (cut_inst_tac [("k","m"),("m","1"),("n","1")] gcd_mult_distrib2 1); -by (Asm_full_simp_tac 1); -qed "gcd_self"; -Addsimps [gcd_self]; - -Goal "gcd(k, k*n) = k"; -by (cut_inst_tac [("k","k"),("m","1"),("n","n")] gcd_mult_distrib2 1); -by (Asm_full_simp_tac 1); -qed "gcd_mult"; -Addsimps [gcd_mult]; - -Goal "[| gcd(k,n)=1; k dvd (m*n) |] ==> k dvd m"; -by (subgoal_tac "m = gcd(m*k, m*n)" 1); -by (etac ssubst 1 THEN rtac gcd_greatest 1); -by (ALLGOALS (asm_simp_tac (simpset() addsimps [gcd_mult_distrib2 RS sym]))); -qed "relprime_dvd_mult"; - -Goalw [prime_def] "[| p: prime; ~ p dvd n |] ==> gcd (p, n) = 1"; -by (cut_inst_tac [("m","p"),("n","n")] gcd_dvd_both 1); -by Auto_tac; -qed "prime_imp_relprime"; - -(*This theorem leads immediately to a proof of the uniqueness of factorization. - If p divides a product of primes then it is one of those primes.*) -Goal "[| p: prime; p dvd (m*n) |] ==> p dvd m | p dvd n"; -by (blast_tac (claset() addIs [relprime_dvd_mult, prime_imp_relprime]) 1); -qed "prime_dvd_mult"; - - -(** Addition laws **) - -Goal "gcd(m, m+n) = gcd(m,n)"; -by (res_inst_tac [("n1", "m+n")] (gcd_commute RS ssubst) 1); -by (rtac (gcd_eq RS trans) 1); -by Auto_tac; -by (asm_simp_tac (simpset() addsimps [mod_add_self1]) 1); -by (stac gcd_commute 1); -by (stac gcd_non_0 1); -by Safe_tac; -qed "gcd_add"; - -Goal "gcd(m, n+m) = gcd(m,n)"; -by (asm_simp_tac (simpset() addsimps [add_commute, gcd_add]) 1); -qed "gcd_add2"; - -Goal "gcd(m, k*m+n) = gcd(m,n)"; -by (induct_tac "k" 1); -by (asm_simp_tac (simpset() addsimps [gcd_add, add_assoc]) 2); -by (Simp_tac 1); -qed "gcd_add_mult"; - - -(** More multiplication laws **) - -Goal "gcd(m,n) dvd gcd(k*m, n)"; -by (blast_tac (claset() addIs [gcd_greatest, dvd_trans, - gcd_dvd1, gcd_dvd2]) 1); -qed "gcd_dvd_gcd_mult"; - -Goal "gcd(k,n) = 1 ==> gcd(k*m, n) = gcd(m,n)"; -by (rtac dvd_anti_sym 1); -by (rtac gcd_dvd_gcd_mult 2); -by (rtac ([relprime_dvd_mult, gcd_dvd2] MRS gcd_greatest) 1); -by (stac mult_commute 2); -by (rtac gcd_dvd1 2); -by (stac gcd_commute 1); -by (asm_simp_tac (simpset() addsimps [gcd_assoc RS sym]) 1); -qed "gcd_mult_cancel"; diff --git a/etc/isa/depends/Primes.thy b/etc/isa/depends/Primes.thy deleted file mode 100644 index fac39463..00000000 --- a/etc/isa/depends/Primes.thy +++ /dev/null @@ -1,33 +0,0 @@ -(* Title: HOL/ex/Primes.thy - ID: $Id$ - Author: Christophe Tabacznyj and Lawrence C Paulson - Copyright 1996 University of Cambridge - -The Greatest Common Divisor and Euclid's algorithm - -The "simpset" clause in the recdef declaration used to be necessary when the -two lemmas where not part of the default simpset. -*) - -Primes = Main + - - -consts - is_gcd :: [nat,nat,nat]=>bool (*gcd as a relation*) - gcd :: "nat*nat=>nat" (*Euclid's algorithm *) - coprime :: [nat,nat]=>bool - prime :: nat set - -recdef gcd "measure ((%(m,n).n) ::nat*nat=>nat)" -(* simpset "simpset() addsimps [mod_less_divisor, zero_less_eq]" *) - "gcd (m, n) = (if n=0 then m else gcd(n, m mod n))" - -defs - is_gcd_def "is_gcd p m n == p dvd m & p dvd n & - (ALL d. d dvd m & d dvd n --> d dvd p)" - - coprime_def "coprime m n == gcd(m,n) = 1" - - prime_def "prime == {p. 1<p & (ALL m. m dvd p --> m=1 | m=p)}" - -end diff --git a/etc/isa/depends/Usedepends.ML b/etc/isa/depends/Usedepends.ML deleted file mode 100644 index 7557d6e8..00000000 --- a/etc/isa/depends/Usedepends.ML +++ /dev/null @@ -1,3 +0,0 @@ -use "~/ProofGeneral/isa/depends.ML"; - - diff --git a/etc/isa/depends/Usedepends.thy b/etc/isa/depends/Usedepends.thy deleted file mode 100644 index 4f8eb516..00000000 --- a/etc/isa/depends/Usedepends.thy +++ /dev/null @@ -1,5 +0,0 @@ -(* dummy theory to load depends.ML *) -theory Usedepends = Main: -end - - diff --git a/etc/isa/goal-matching.ML b/etc/isa/goal-matching.ML deleted file mode 100644 index 843e2ca5..00000000 --- a/etc/isa/goal-matching.ML +++ /dev/null @@ -1,10 +0,0 @@ -(* - Test case sent by David von Oheimb. - Bug in matching case-insensitively meant that - the SELECT_GOAL line was considered a goal. -*) - -Goal "x"; -by (SELECT_GOAL all_tac 1); - - |