src/CCL/Type.thy
author lcp
Thu, 06 Apr 1995 10:53:21 +0200
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Gave tighter priorities to SUM and PROD to reduce ambiguities.
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(*  Title:      CCL/types.thy
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    ID:         $Id$
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    Author:     Martin Coen
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    Copyright   1993  University of Cambridge
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Types in CCL are defined as sets of terms.
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*)
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Type = Term +
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consts
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  Subtype       :: "['a set, 'a => o] => 'a set"
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  Bool          :: "i set"
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  Unit          :: "i set"
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  "+"           :: "[i set, i set] => i set"         (infixr 55)
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  Pi            :: "[i set, i => i set] => i set"
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  Sigma         :: "[i set, i => i set] => i set"
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  Nat           :: "i set"
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  List          :: "i set => i set"
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  Lists         :: "i set => i set"
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  ILists        :: "i set => i set"
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  TAll          :: "(i set => i set) => i set"       (binder "TALL " 55)
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  TEx           :: "(i set => i set) => i set"       (binder "TEX " 55)
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  Lift          :: "i set => i set"                  ("(3[_])")
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  SPLIT         :: "[i, [i, i] => i set] => i set"
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  "@Pi"         :: "[idt, i set, i set] => i set"    ("(3PROD _:_./ _)"
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  				[0,0,60] 60)
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  "@Sigma"      :: "[idt, i set, i set] => i set"    ("(3SUM _:_./ _)"
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  				[0,0,60] 60)
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  "@->"         :: "[i set, i set] => i set"         ("(_ ->/ _)"  [54, 53] 53)
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  "@*"          :: "[i set, i set] => i set"         ("(_ */ _)" [56, 55] 55)
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  "@Subtype"    :: "[idt, 'a set, o] => 'a set"      ("(1{_: _ ./ _})")
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translations
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  "PROD x:A. B" => "Pi(A, %x. B)"
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  "A -> B"      => "Pi(A, _K(B))"
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  "SUM x:A. B"  => "Sigma(A, %x. B)"
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  "A * B"       => "Sigma(A, _K(B))"
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  "{x: A. B}"   == "Subtype(A, %x. B)"
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rules
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  Subtype_def "{x:A.P(x)} == {x.x:A & P(x)}"
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  Unit_def          "Unit == {x.x=one}"
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  Bool_def          "Bool == {x.x=true | x=false}"
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  Plus_def           "A+B == {x. (EX a:A.x=inl(a)) | (EX b:B.x=inr(b))}"
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  Pi_def         "Pi(A,B) == {x.EX b.x=lam x.b(x) & (ALL x:A.b(x):B(x))}"
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  Sigma_def   "Sigma(A,B) == {x.EX a:A.EX b:B(a).x=<a,b>}"
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  Nat_def            "Nat == lfp(% X.Unit + X)"
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  List_def       "List(A) == lfp(% X.Unit + A*X)"
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  Lists_def     "Lists(A) == gfp(% X.Unit + A*X)"
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  ILists_def   "ILists(A) == gfp(% X.{} + A*X)"
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  Tall_def   "TALL X.B(X) == Inter({X.EX Y.X=B(Y)})"
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  Tex_def     "TEX X.B(X) == Union({X.EX Y.X=B(Y)})"
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  Lift_def           "[A] == A Un {bot}"
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  SPLIT_def   "SPLIT(p,B) == Union({A.EX x y.p=<x,y> & A=B(x,y)})"
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end
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ML
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val print_translation =
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  [("Pi", dependent_tr' ("@Pi", "@->")),
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   ("Sigma", dependent_tr' ("@Sigma", "@*"))];
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