diff -r 000000000000 -r a5a9c433f639 src/CCL/term.thy --- /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) == " + inr_def "inr(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()" + 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(),%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'())) \ +\ in f(%x y.g'())" + + 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'(>)))) \ +\ in f(%x y z.g'(>))" + + 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') + ];