--- a/ex/MT.thy Fri Apr 14 11:23:33 1995 +0200
+++ b/ex/MT.thy Wed Jun 21 15:12:40 1995 +0200
@@ -102,9 +102,9 @@
e_var_inj "e_var(ev1) = e_var(ev2) ==> ev1 = ev2"
e_fn_inj "fn ev1 => e1 = fn ev2 => e2 ==> ev1 = ev2 & e1 = e2"
e_fix_inj
- " fix ev11e(v12) = e1 = fix ev21(ev22) = e2 ==> \
-\ ev11 = ev21 & ev12 = ev22 & e1 = e2 \
-\ "
+ " fix ev11e(v12) = e1 = fix ev21(ev22) = e2 ==>
+ ev11 = ev21 & ev12 = ev22 & e1 = e2
+ "
e_app_inj "e11 @ e12 = e21 @ e22 ==> e11 = e21 & e12 = e22"
(* All constructors are distinct *)
@@ -123,14 +123,14 @@
(* Strong elimination, induction on expressions *)
e_ind
- " [| !!ev. P(e_var(ev)); \
-\ !!c. P(e_const(c)); \
-\ !!ev e. P(e) ==> P(fn ev => e); \
-\ !!ev1 ev2 e. P(e) ==> P(fix ev1(ev2) = e); \
-\ !!e1 e2. P(e1) ==> P(e2) ==> P(e1 @ e2) \
-\ |] ==> \
-\ P(e) \
-\ "
+ " [| !!ev. P(e_var(ev));
+ !!c. P(e_const(c));
+ !!ev e. P(e) ==> P(fn ev => e);
+ !!ev1 ev2 e. P(e) ==> P(fix ev1(ev2) = e);
+ !!e1 e2. P(e1) ==> P(e2) ==> P(e1 @ e2)
+ |] ==>
+ P(e)
+ "
(* Types - same scheme as for expressions *)
@@ -144,8 +144,8 @@
(* Strong elimination, induction on types *)
t_ind
- "[| !!p. P(t_const(p)); !!t1 t2. P(t1) ==> P(t2) ==> P(t_fun(t1,t2)) |] \
-\ ==> P(t)"
+ "[| !!p. P(t_const(p)); !!t1 t2. P(t1) ==> P(t2) ==> P(t_fun(t1,t2)) |]
+ ==> P(t)"
(* Values - same scheme again *)
@@ -154,8 +154,8 @@
v_const_inj "v_const(c1) = v_const(c2) ==> c1 = c2"
v_clos_inj
- " v_clos(<|ev1,e1,ve1|>) = v_clos(<|ev2,e2,ve2|>) ==> \
-\ ev1 = ev2 & e1 = e2 & ve1 = ve2"
+ " v_clos(<|ev1,e1,ve1|>) = v_clos(<|ev2,e2,ve2|>) ==>
+ ev1 = ev2 & e1 = e2 & ve1 = ve2"
(* All constructors are distinct *)
@@ -194,26 +194,26 @@
*)
eval_fun_def
- " eval_fun(s) == \
-\ { pp. \
-\ (? ve c. pp=<<ve,e_const(c)>,v_const(c)>) | \
-\ (? ve x. pp=<<ve,e_var(x)>,ve_app(ve,x)> & x:ve_dom(ve)) |\
-\ (? ve e x. pp=<<ve,fn x => e>,v_clos(<|x,e,ve|>)>)| \
-\ ( ? ve e x f cl. \
-\ pp=<<ve,fix f(x) = e>,v_clos(cl)> & \
-\ cl=<|x, e, ve+{f |-> v_clos(cl)} |> \
-\ ) | \
-\ ( ? ve e1 e2 c1 c2. \
-\ pp=<<ve,e1 @ e2>,v_const(c_app(c1,c2))> & \
-\ <<ve,e1>,v_const(c1)>:s & <<ve,e2>,v_const(c2)>:s \
-\ ) | \
-\ ( ? ve vem e1 e2 em xm v v2. \
-\ pp=<<ve,e1 @ e2>,v> & \
-\ <<ve,e1>,v_clos(<|xm,em,vem|>)>:s & \
-\ <<ve,e2>,v2>:s & \
-\ <<vem+{xm |-> v2},em>,v>:s \
-\ ) \
-\ }"
+ " eval_fun(s) ==
+ { pp.
+ (? ve c. pp=<<ve,e_const(c)>,v_const(c)>) |
+ (? ve x. pp=<<ve,e_var(x)>,ve_app(ve,x)> & x:ve_dom(ve)) |
+ (? ve e x. pp=<<ve,fn x => e>,v_clos(<|x,e,ve|>)>)|
+ ( ? ve e x f cl.
+ pp=<<ve,fix f(x) = e>,v_clos(cl)> &
+ cl=<|x, e, ve+{f |-> v_clos(cl)} |>
+ ) |
+ ( ? ve e1 e2 c1 c2.
+ pp=<<ve,e1 @ e2>,v_const(c_app(c1,c2))> &
+ <<ve,e1>,v_const(c1)>:s & <<ve,e2>,v_const(c2)>:s
+ ) |
+ ( ? ve vem e1 e2 em xm v v2.
+ pp=<<ve,e1 @ e2>,v> &
+ <<ve,e1>,v_clos(<|xm,em,vem|>)>:s &
+ <<ve,e2>,v2>:s &
+ <<vem+{xm |-> v2},em>,v>:s
+ )
+ }"
eval_rel_def "eval_rel == lfp(eval_fun)"
eval_def "ve |- e ---> v == <<ve,e>,v>:eval_rel"
@@ -224,18 +224,18 @@
*)
elab_fun_def
- "elab_fun(s) == \
-\ { pp. \
-\ (? te c t. pp=<<te,e_const(c)>,t> & c isof t) | \
-\ (? te x. pp=<<te,e_var(x)>,te_app(te,x)> & x:te_dom(te)) | \
-\ (? te x e t1 t2. pp=<<te,fn x => e>,t1->t2> & <<te+{x |=> t1},e>,t2>:s) | \
-\ (? te f x e t1 t2. \
-\ pp=<<te,fix f(x)=e>,t1->t2> & <<te+{f |=> t1->t2}+{x |=> t1},e>,t2>:s \
-\ ) | \
-\ (? te e1 e2 t1 t2. \
-\ pp=<<te,e1 @ e2>,t2> & <<te,e1>,t1->t2>:s & <<te,e2>,t1>:s \
-\ ) \
-\ }"
+ "elab_fun(s) ==
+ { pp.
+ (? te c t. pp=<<te,e_const(c)>,t> & c isof t) |
+ (? te x. pp=<<te,e_var(x)>,te_app(te,x)> & x:te_dom(te)) |
+ (? te x e t1 t2. pp=<<te,fn x => e>,t1->t2> & <<te+{x |=> t1},e>,t2>:s) |
+ (? te f x e t1 t2.
+ pp=<<te,fix f(x)=e>,t1->t2> & <<te+{f |=> t1->t2}+{x |=> t1},e>,t2>:s
+ ) |
+ (? te e1 e2 t1 t2.
+ pp=<<te,e1 @ e2>,t2> & <<te,e1>,t1->t2>:s & <<te,e2>,t1>:s
+ )
+ }"
elab_rel_def "elab_rel == lfp(elab_fun)"
elab_def "te |- e ===> t == <<te,e>,t>:elab_rel"
@@ -243,36 +243,36 @@
(* The original correspondence relation *)
isof_env_def
- " ve isofenv te == \
-\ ve_dom(ve) = te_dom(te) & \
-\ ( ! x. \
-\ x:ve_dom(ve) --> \
-\ (? c.ve_app(ve,x) = v_const(c) & c isof te_app(te,x)) \
-\ ) \
-\ "
+ " ve isofenv te ==
+ ve_dom(ve) = te_dom(te) &
+ ( ! x.
+ x:ve_dom(ve) -->
+ (? c.ve_app(ve,x) = v_const(c) & c isof te_app(te,x))
+ )
+ "
isof_app "[| c1 isof t1->t2; c2 isof t1 |] ==> c_app(c1,c2) isof t2"
(* The extented correspondence relation *)
hasty_fun_def
- " hasty_fun(r) == \
-\ { p. \
-\ ( ? c t. p = <v_const(c),t> & c isof t) | \
-\ ( ? ev e ve t te. \
-\ p = <v_clos(<|ev,e,ve|>),t> & \
-\ te |- fn ev => e ===> t & \
-\ ve_dom(ve) = te_dom(te) & \
-\ (! ev1.ev1:ve_dom(ve) --> <ve_app(ve,ev1),te_app(te,ev1)> : r) \
-\ ) \
-\ } \
-\ "
+ " hasty_fun(r) ==
+ { p.
+ ( ? c t. p = <v_const(c),t> & c isof t) |
+ ( ? ev e ve t te.
+ p = <v_clos(<|ev,e,ve|>),t> &
+ te |- fn ev => e ===> t &
+ ve_dom(ve) = te_dom(te) &
+ (! ev1.ev1:ve_dom(ve) --> <ve_app(ve,ev1),te_app(te,ev1)> : r)
+ )
+ }
+ "
hasty_rel_def "hasty_rel == gfp(hasty_fun)"
hasty_def "v hasty t == <v,t> : hasty_rel"
hasty_env_def
- " ve hastyenv te == \
-\ ve_dom(ve) = te_dom(te) & \
-\ (! x. x: ve_dom(ve) --> ve_app(ve,x) hasty te_app(te,x))"
+ " ve hastyenv te ==
+ ve_dom(ve) = te_dom(te) &
+ (! x. x: ve_dom(ve) --> ve_app(ve,x) hasty te_app(te,x))"
end