author  lcp 
Thu, 06 Apr 1995 10:53:21 +0200  
changeset 999  9bf3816298d0 
parent 22  41dc6b189412 
child 1474  3f7d67927fe2 
permissions  rwrr 
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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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Gave tighter priorities to SUM and PROD to reduce ambiguities.
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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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parents:
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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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Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
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9bf3816298d0
Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
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diff
changeset

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"@Sigma" :: "[idt, i set, i set] => i set" ("(3SUM _:_./ _)" 
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Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
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diff
changeset

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[0,0,60] 60) 
9bf3816298d0
Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
22
diff
changeset

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9bf3816298d0
Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
22
diff
changeset

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"@>" :: "[i set, i set] => i set" ("(_ >/ _)" [54, 53] 53) 
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Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
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"@*" :: "[i set, i set] => i set" ("(_ */ _)" [56, 55] 55) 
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Gave tighter priorities to SUM and PROD to reduce ambiguities.
lcp
parents:
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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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