src/CCL/Term.thy
changeset 0 a5a9c433f639
child 289 78541329ff35
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/Term.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,131 @@
+(*  Title: 	CCL/terms.thy
+    ID:         $Id$
+    Author: 	Martin Coen
+    Copyright   1993  University of Cambridge
+
+Definitions of usual program constructs in CCL.
+
+*)
+
+Term = CCL +
+
+consts
+
+  one        ::	      "i"
+
+  if         ::       "[i,i,i]=>i"           ("(3if _/ then _/ else _)" [] 60)
+
+  inl,inr    ::	      "i=>i"
+  when       ::	      "[i,i=>i,i=>i]=>i" 
+
+  split      ::	      "[i,[i,i]=>i]=>i"
+  fst,snd,   
+  thd        ::       "i=>i"
+
+  zero       ::	      "i"
+  succ       ::	      "i=>i"
+  ncase      ::	      "[i,i,i=>i]=>i"
+  nrec       ::	      "[i,i,[i,i]=>i]=>i"
+
+  nil        ::       "i"                    ("([])")
+  "."        ::       "[i,i]=>i"             (infixr 80)
+  lcase      ::	      "[i,i,[i,i]=>i]=>i"
+  lrec       ::	      "[i,i,[i,i,i]=>i]=>i"
+
+  let        ::       "[i,i=>i]=>i"
+  letrec     ::       "[[i,i=>i]=>i,(i=>i)=>i]=>i"
+  letrec2    ::       "[[i,i,i=>i=>i]=>i,(i=>i=>i)=>i]=>i"
+  letrec3    ::       "[[i,i,i,i=>i=>i=>i]=>i,(i=>i=>i=>i)=>i]=>i"  
+
+  "@let"     ::       "[id,i,i]=>i"             ("(3let _ be _/ in _)" [] 60)
+  "@letrec"  ::       "[id,id,i,i]=>i"          ("(3letrec _ _ be _/ in _)"  [] 60)
+  "@letrec2" ::       "[id,id,id,i,i]=>i"       ("(3letrec _ _ _ be _/ in _)"  [] 60)
+  "@letrec3" ::       "[id,id,id,id,i,i]=>i"    ("(3letrec _ _ _ _ be _/ in _)"  [] 60)
+
+  napply    :: "[i=>i,i,i]=>i"      ("(_ ^ _ ` _)")
+
+rules
+
+  one_def                    "one == true"
+  if_def     "if b then t else u  == case(b,t,u,% x y.bot,%v.bot)"
+  inl_def                 "inl(a) == <true,a>"
+  inr_def                 "inr(b) == <false,b>"
+  when_def           "when(t,f,g) == split(t,%b x.if b then f(x) else g(x))"
+  split_def           "split(t,f) == case(t,bot,bot,f,%u.bot)"
+  fst_def                 "fst(t) == split(t,%x y.x)"
+  snd_def                 "snd(t) == split(t,%x y.y)"
+  thd_def                 "thd(t) == split(t,%x p.split(p,%y z.z))"
+  zero_def                  "zero == inl(one)"
+  succ_def               "succ(n) == inr(n)"
+  ncase_def         "ncase(n,b,c) == when(n,%x.b,%y.c(y))"
+  nrec_def          " nrec(n,b,c) == letrec g x be ncase(x,b,%y.c(y,g(y))) in g(n)"
+  nil_def	              "[] == inl(one)"
+  cons_def                   "h.t == inr(<h,t>)"
+  lcase_def         "lcase(l,b,c) == when(l,%x.b,%y.split(y,c))"
+  lrec_def           "lrec(l,b,c) == letrec g x be lcase(x,b,%h t.c(h,t,g(t))) in g(l)"
+
+  let_def  "let x be t in f(x) == case(t,f(true),f(false),%x y.f(<x,y>),%u.f(lam x.u(x)))"
+  letrec_def    
+  "letrec g x be h(x,g) in b(g) == b(%x.fix(%f.lam x.h(x,%y.f`y))`x)"
+
+  letrec2_def  "letrec g x y be h(x,y,g) in f(g)== \
+\               letrec g' p be split(p,%x y.h(x,y,%u v.g'(<u,v>))) \
+\                          in f(%x y.g'(<x,y>))"
+
+  letrec3_def  "letrec g x y z be h(x,y,z,g) in f(g) == \
+\             letrec g' p be split(p,%x xs.split(xs,%y z.h(x,y,z,%u v w.g'(<u,<v,w>>)))) \
+\                          in f(%x y z.g'(<x,<y,z>>))"
+
+  napply_def "f ^n` a == nrec(n,a,%x g.f(g))"
+
+end
+
+ML
+
+(** Quantifier translations: variable binding **)
+
+fun let_tr [Free(id,T),a,b] = Const("let",dummyT) $ a $ absfree(id,T,b);
+fun let_tr' [a,Abs(id,T,b)] =
+     let val (id',b') = variant_abs(id,T,b)
+     in Const("@let",dummyT) $ Free(id',T) $ a $ b' end;
+
+fun letrec_tr [Free(f,S),Free(x,T),a,b] = 
+      Const("letrec",dummyT) $ absfree(x,T,absfree(f,S,a)) $ absfree(f,S,b);
+fun letrec2_tr [Free(f,S),Free(x,T),Free(y,U),a,b] = 
+      Const("letrec2",dummyT) $ absfree(x,T,absfree(y,U,absfree(f,S,a))) $ absfree(f,S,b);
+fun letrec3_tr [Free(f,S),Free(x,T),Free(y,U),Free(z,V),a,b] = 
+      Const("letrec3",dummyT) $ absfree(x,T,absfree(y,U,absfree(z,U,absfree(f,S,a)))) $ absfree(f,S,b);
+
+fun letrec_tr' [Abs(x,T,Abs(f,S,a)),Abs(ff,SS,b)] =
+     let val (f',b')  = variant_abs(ff,SS,b)
+         val (_,a'') = variant_abs(f,S,a)
+         val (x',a')  = variant_abs(x,T,a'')
+     in Const("@letrec",dummyT) $ Free(f',SS) $ Free(x',T) $ a' $ b' end;
+fun letrec2_tr' [Abs(x,T,Abs(y,U,Abs(f,S,a))),Abs(ff,SS,b)] =
+     let val (f',b') = variant_abs(ff,SS,b)
+         val ( _,a1) = variant_abs(f,S,a)
+         val (y',a2) = variant_abs(y,U,a1)
+         val (x',a') = variant_abs(x,T,a2)
+     in Const("@letrec2",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ a' $ b'
+      end;
+fun letrec3_tr' [Abs(x,T,Abs(y,U,Abs(z,V,Abs(f,S,a)))),Abs(ff,SS,b)] =
+     let val (f',b') = variant_abs(ff,SS,b)
+         val ( _,a1) = variant_abs(f,S,a)
+         val (z',a2) = variant_abs(z,V,a1)
+         val (y',a3) = variant_abs(y,U,a2)
+         val (x',a') = variant_abs(x,T,a3)
+     in Const("@letrec3",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ Free(z',V) $ a' $ b'
+      end;
+
+val  parse_translation=
+    [("@let",       let_tr),
+     ("@letrec",    letrec_tr),
+     ("@letrec2",   letrec2_tr),
+     ("@letrec3",   letrec3_tr)
+    ];
+val print_translation=
+    [("let",       let_tr'),
+     ("letrec",    letrec_tr'),
+     ("letrec2",   letrec2_tr'),
+     ("letrec3",   letrec3_tr')
+    ];