(* 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 _)" [0,0,60] 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" ("([])") "$" :: "[i,i]=>i" (infixr 80) lcase :: "[i,i,[i,i]=>i]=>i" lrec :: "[i,i,[i,i,i]=>i]=>i" let :: "[i,i=>i]=>i" letrec :: "[[i,i=>i]=>i,(i=>i)=>i]=>i" letrec2 :: "[[i,i,i=>i=>i]=>i,(i=>i=>i)=>i]=>i" letrec3 :: "[[i,i,i,i=>i=>i=>i]=>i,(i=>i=>i=>i)=>i]=>i" "@let" :: "[idt,i,i]=>i" ("(3let _ be _/ in _)" [0,0,60] 60) "@letrec" :: "[idt,idt,i,i]=>i" ("(3letrec _ _ be _/ in _)" [0,0,0,60] 60) "@letrec2" :: "[idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ be _/ in _)" [0,0,0,0,60] 60) "@letrec3" :: "[idt,idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ _ be _/ in _)" [0,0,0,0,0,60] 60) napply :: "[i=>i,i,i]=>i" ("(_ ^ _ ` _)" [56,56,56] 56) rules one_def "one == true" if_def "if b then t else u == case(b,t,u,% x y.bot,%v.bot)" inl_def "inl(a) == " inr_def "inr(b) == " when_def "when(t,f,g) == split(t,%b x.if b then f(x) else g(x))" split_def "split(t,f) == case(t,bot,bot,f,%u.bot)" fst_def "fst(t) == split(t,%x y.x)" snd_def "snd(t) == split(t,%x y.y)" thd_def "thd(t) == split(t,%x p.split(p,%y z.z))" zero_def "zero == inl(one)" succ_def "succ(n) == inr(n)" ncase_def "ncase(n,b,c) == when(n,%x.b,%y.c(y))" nrec_def " nrec(n,b,c) == letrec g x be ncase(x,b,%y.c(y,g(y))) in g(n)" nil_def "[] == inl(one)" cons_def "h$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') ];