--- a/src/HOLCF/ex/Witness.ML Mon May 12 14:24:31 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,113 +0,0 @@
-open Witness;
-
-(* -------------------------------------------------------------------- *)
-(* classes cplus, cminus, ctimes, cdiv introduce
- characteristic constants o+ o- o* o/
-
- "circ":: "one -> one -> one"
-
- is the witness for o+ o- o* o/
-
- No characteristic axioms are to be checked
-*)
-
-(* -------------------------------------------------------------------- *)
-(* classes per and qpo introduce characteristic constants
- ".=" :: "'a::per -> 'a -> tr" (cinfixl 55)
- ".<=" :: "'a::qpo -> 'a -> tr" (cinfixl 55)
-
- The witness for these is
-
- "bullet":: "one -> one -> tr" (cinfixl 55)
-
- the classes equiv, eq, impose additional axioms
-*)
-
-(* -------------------------------------------------------------------- *)
-(*
-
-characteristic axioms of class per:
-
-strict_per "(UU .= x) = UU & (x .= UU) = UU"
-total_per "[|x ~= UU; y ~= UU|] ==> (x .= y) ~= UU"
-flat_per "flat (UU::'a::per)"
-
-sym_per "(x .= y) = (y .= x)"
-trans_per "[|(x .= y)=TT; (y .= z)=TT |] ==> (x .= z)=TT"
-
- --------------------------------------------------------------------
-
-characteristic axioms of class equiv:
-
-refl_per "[|(x::'a::equiv) ~= UU|] ==> (x .= x)=TT"
-
- --------------------------------------------------------------------
-
-characteristic axioms of class eq:
-
-weq "[|(x::'a::eq)~=UU; y~=UU|] ==> (x=y --> (x.=y)=TT) & (x~=y --> Çx.=yÈ)"
-
-
- --------------------------------------------------------------------
-
-*)
-
-(* strict_per, strict_qpo *)
-goalw thy [bullet_def] "(UU bullet x) = UU & (x bullet UU) = UU";
-by (simp_tac (!simpset addsimps [flift1_def,flift2_def,o_def]) 1);
-by (lift.induct_tac "x" 1);
-auto();
-result();
-
-(* total_per, total_qpo *)
-val prems = goal thy "[|x~=UU; y~=UU|] ==> (x bullet y) ~= UU";
-by (subgoal_tac "x~=UU&y~=UU-->(x bullet y) ~= UU" 1);
-by (cut_facts_tac prems 1);
-by (fast_tac HOL_cs 1);
-by (simp_tac (!simpset addsimps [bullet_def,flift1_def,flift2_def,o_def]) 1);
-by (lift.induct_tac "x" 1);
-by (fast_tac HOL_cs 1);
-by (lift.induct_tac "y" 1);
-auto();
-result();
-
-(* flat_per *)
-
-goal thy "flat (x::one)";
-by (rtac flat_flat 1);
-result();
-
-(* sym_per *)
-goalw thy [bullet_def] "(x bullet y) = (y bullet x)";
-by (simp_tac (!simpset addsimps [bullet_def,flift1_def,flift2_def,o_def]) 1);
-by (lift.induct_tac "x" 1);
-by (lift.induct_tac "y" 2);
-by (lift.induct_tac "y" 1);
-auto();
-result();
-
-(* trans_per, trans_qpo *)
-val prems = goal thy "[|(x bullet y)=TT; (y bullet z)=TT|] ==>(x bullet z)=TT";
-by (subgoal_tac "(x bullet y)=TT&(y bullet z)=TT-->(x bullet z)=TT" 1);
-by (cut_facts_tac prems 1);
-by (fast_tac HOL_cs 1);
-by (simp_tac (!simpset addsimps [bullet_def,flift1_def,flift2_def,o_def]) 1);
-by (lift.induct_tac "x" 1);
-by (lift.induct_tac "y" 2);
-by (lift.induct_tac "y" 1);
-by (lift.induct_tac "z" 4);
-by (lift.induct_tac "z" 3);
-by (lift.induct_tac "z" 2);
-by (lift.induct_tac "z" 1);
-auto();
-result();
-
-(* refl_per *)
-val prems = goal thy "x ~= UU ==> (x bullet x)=TT";
-by (subgoal_tac "x ~= UU --> (x bullet x)=TT" 1);
-by (cut_facts_tac prems 1);
-by (fast_tac HOL_cs 1);
-by (simp_tac (!simpset addsimps [bullet_def,flift1_def,flift2_def,o_def]) 1);
-by (lift.induct_tac "x" 1);
-auto();
-qed "refl_per_one";
--- a/src/HOLCF/ex/Witness.thy Mon May 12 14:24:31 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,24 +0,0 @@
-(* Title: FOCUS/Witness.thy
- ID: $Id$
- Author: Franz Regensburger
- Copyright 1995 Technical University Munich
-
-Witnesses for introduction of type cleasse in theory Classlib
-
-The type one of HOLCF/One.thy is a witness for all the introduced classes.
-
-the trivial instance for ++ -- ** // is circ
-the trivial instance for .= and .<= is bullet
-
-*)
-
-Witness = HOLCF +
-
-ops curried
- "bullet":: "one -> one -> tr" (cinfixl 55)
-
-defs
-
-bullet_def "(op bullet) Ú flift1(flift2 o (op =))"
-
-end