src/LCF/ex.ML

--- a/src/LCF/ex.ML	Thu Mar 20 10:49:44 1997 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,131 +0,0 @@
-(*  Title:      LCF/ex.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow
-    Copyright   1991  University of Cambridge
-
-Some examples from Lawrence Paulson's book Logic and Computation.
-*)
-
-
-LCF_build_completed;    (*Cause examples to fail if LCF did*)
-
-proof_timing := true;
-
-(***  Section 10.4  ***)
-
-val ex_thy =
-  thy
-  |> add_consts
-   [("P", "'a => tr", NoSyn),
-    ("G", "'a => 'a", NoSyn),
-    ("H", "'a => 'a", NoSyn),
-    ("K", "('a => 'a) => ('a => 'a)", NoSyn)]
-  |> add_axioms
-   [("P_strict", "P(UU) = UU"),
-    ("K", "K = (%h x. P(x) => x | h(h(G(x))))"),
-    ("H", "H = FIX(K)")]
-  |> add_thyname "Ex 10.4";
-
-val ax = get_axiom ex_thy;
-
-val P_strict = ax"P_strict";
-val K = ax"K";
-val H = ax"H";
-
-val ex_ss = LCF_ss addsimps [P_strict,K];
-
-
-val H_unfold = prove_goal ex_thy "H = K(H)"
- (fn _ => [stac H 1, rtac (FIX_eq RS sym) 1]);
-
-val H_strict = prove_goal ex_thy "H(UU)=UU"
- (fn _ => [stac H_unfold 1, simp_tac ex_ss 1]);
-
-val ex_ss = ex_ss addsimps [H_strict];
-
-goal ex_thy "ALL x. H(FIX(K,x)) = FIX(K,x)";
-by(induct_tac "K" 1);
-by(simp_tac ex_ss 1);
-by(simp_tac (ex_ss setloop (split_tac [COND_cases_iff])) 1);
-by(strip_tac 1);
-by(stac H_unfold 1);
-by(asm_simp_tac ex_ss 1);
-val H_idemp_lemma = topthm();
-
-val H_idemp = rewrite_rule [mk_meta_eq (H RS sym)] H_idemp_lemma;
-
-
-(***  Example 3.8  ***)
-
-val ex_thy =
-  thy
-  |> add_consts
-   [("P", "'a => tr", NoSyn),
-    ("F", "'a => 'a", NoSyn),
-    ("G", "'a => 'a", NoSyn),
-    ("H", "'a => 'b => 'b", NoSyn),
-    ("K", "('a => 'b => 'b) => ('a => 'b => 'b)", NoSyn)]
-  |> add_axioms
-   [("F_strict", "F(UU) = UU"),
-    ("K", "K = (%h x y. P(x) => y | F(h(G(x),y)))"),
-    ("H", "H = FIX(K)")]
-  |> add_thyname "Ex 3.8";
-
-val ax = get_axiom ex_thy;
-
-val F_strict = ax"F_strict";
-val K = ax"K";
-val H = ax"H";
-
-val ex_ss = LCF_ss addsimps [F_strict,K];
-
-goal ex_thy "ALL x. F(H(x::'a,y::'b)) = H(x,F(y))";
-by(stac H 1);
-by(induct_tac "K::('a=>'b=>'b)=>('a=>'b=>'b)" 1);
-by(simp_tac ex_ss 1);
-by(asm_simp_tac (ex_ss setloop (split_tac [COND_cases_iff])) 1);
-result();
-
-
-(*** Addition with fixpoint of successor ***)
-
-val ex_thy =
-  thy
-  |> add_consts
-   [("s", "'a => 'a", NoSyn),
-    ("p", "'a => 'a => 'a", NoSyn)]
-  |> add_axioms
-   [("p_strict", "p(UU) = UU"),
-    ("p_s", "p(s(x),y) = s(p(x,y))")]
-  |> add_thyname "fix ex";
-
-val ax = get_axiom ex_thy;
-
-val p_strict = ax"p_strict";
-val p_s = ax"p_s";
-
-val ex_ss = LCF_ss addsimps [p_strict,p_s];
-
-goal ex_thy "p(FIX(s),y) = FIX(s)";
-by(induct_tac "s" 1);
-by(simp_tac ex_ss 1);
-by(simp_tac ex_ss 1);
-result();
-
-
-(*** Prefixpoints ***)
-
-val asms = goal thy "[| f(p) << p; !!q. f(q) << q ==> p << q |] ==> FIX(f)=p";
-by(rewtac eq_def);
-by (rtac conjI 1);
-by(induct_tac "f" 1);
-by (rtac minimal 1);
-by(strip_tac 1);
-by (rtac less_trans 1);
-by (resolve_tac asms 2);
-by (etac less_ap_term 1);
-by (resolve_tac asms 1);
-by (rtac (FIX_eq RS eq_imp_less1) 1);
-result();
-
-maketest"END: file for LCF examples";