--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/Type.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,73 @@
+(* Title: CCL/types.thy
+ ID: $Id$
+ Author: Martin Coen
+ Copyright 1993 University of Cambridge
+
+Types in CCL are defined as sets of terms.
+
+*)
+
+Type = Term +
+
+consts
+
+ Subtype :: "['a set, 'a => o] => 'a set"
+ Bool :: "i set"
+ Unit :: "i set"
+ "+" :: "[i set, i set] => i set" (infixr 55)
+ Pi :: "[i set, i => i set] => i set"
+ Sigma :: "[i set, i => i set] => i set"
+ Nat :: "i set"
+ List :: "i set => i set"
+ Lists :: "i set => i set"
+ ILists :: "i set => i set"
+ TAll :: "(i set => i set) => i set" (binder "TALL " 55)
+ TEx :: "(i set => i set) => i set" (binder "TEX " 55)
+ Lift :: "i set => i set" ("(3[_])")
+
+ SPLIT :: "[i, [i, i] => i set] => i set"
+
+ "@Pi" :: "[idt, i set, i set] => i set" ("(3PROD _:_./ _)" [] 60)
+ "@Sigma" :: "[idt, i set, i set] => i set" ("(3SUM _:_./ _)" [] 60)
+ "@->" :: "[i set, i set] => i set" ("(_ ->/ _)" [54, 53] 53)
+ "@*" :: "[i set, i set] => i set" ("(_ */ _)" [56, 55] 55)
+ "@Subtype" :: "[idt, 'a set, o] => 'a set" ("(1{_: _ ./ _})")
+
+translations
+ "PROD x:A. B" => "Pi(A, %x. B)"
+ "SUM x:A. B" => "Sigma(A, %x. B)"
+ "{x: A. B}" == "Subtype(A, %x. B)"
+
+rules
+
+ Subtype_def "{x:A.P(x)} == {x.x:A & P(x)}"
+ Unit_def "Unit == {x.x=one}"
+ Bool_def "Bool == {x.x=true | x=false}"
+ Plus_def "A+B == {x. (EX a:A.x=inl(a)) | (EX b:B.x=inr(b))}"
+ Pi_def "Pi(A,B) == {x.EX b.x=lam x.b(x) & (ALL x:A.b(x):B(x))}"
+ Sigma_def "Sigma(A,B) == {x.EX a:A.EX b:B(a).x=<a,b>}"
+ Nat_def "Nat == lfp(% X.Unit + X)"
+ List_def "List(A) == lfp(% X.Unit + A*X)"
+
+ Lists_def "Lists(A) == gfp(% X.Unit + A*X)"
+ ILists_def "ILists(A) == gfp(% X.{} + A*X)"
+
+ Tall_def "TALL X.B(X) == Inter({X.EX Y.X=B(Y)})"
+ Tex_def "TEX X.B(X) == Union({X.EX Y.X=B(Y)})"
+ Lift_def "[A] == A Un {bot}"
+
+ SPLIT_def "SPLIT(p,B) == Union({A.EX x y.p=<x,y> & A=B(x,y)})"
+
+end
+
+
+ML
+
+val parse_translation =
+ [("@->", ndependent_tr "Pi"),
+ ("@*", ndependent_tr "Sigma")];
+
+val print_translation =
+ [("Pi", dependent_tr' ("@Pi", "@->")),
+ ("Sigma", dependent_tr' ("@Sigma", "@*"))];
+