author  lcp 
Thu, 30 Sep 1993 10:10:21 +0100  
changeset 14  1c0926788772 
parent 0  a5a9c433f639 
child 43  eb7ad4a7dc4f 
permissions  rwrr 
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(* Title: ZF/listfn 
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ID: $Id$ 

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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

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Copyright 1993 University of Cambridge 

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Functions for Lists in ZermeloFraenkel Set Theory 

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map is a binding operator  it applies to metalevel functions, not 

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objectlevel functions. This simplifies the final form of term_rec_conv, 

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although complicating its derivation. 

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*) 

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ListFn = List + 

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consts 

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"@" :: "[i,i]=>i" (infixr 60) 

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list_rec :: "[i, i, [i,i,i]=>i] => i" 

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map :: "[i=>i, i] => i" 

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length,rev :: "i=>i" 

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flat :: "i=>i" 

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list_add :: "i=>i" 

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1c0926788772
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hd,tl :: "i=>i" 
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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drop :: "[i,i]=>i" 
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(* List Enumeration *) 

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"[]" :: "i" ("[]") 

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"@List" :: "args => i" ("[(_)]") 

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translations 

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"[x, xs]" == "Cons(x, [xs])" 

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"[x]" == "Cons(x, [])" 

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"[]" == "Nil" 

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rules 

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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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hd_def "hd(l) == list_case(0, %x xs.x, l)" 
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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tl_def "tl(l) == list_case(Nil, %x xs.xs, l)" 
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drop_def "drop(i,l) == rec(i, l, %j r. tl(r))" 
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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list_rec_def 
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"list_rec(l,c,h) == Vrec(l, %l g.list_case(c, %x xs. h(x, xs, g`xs), l))" 

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map_def "map(f,l) == list_rec(l, Nil, %x xs r. Cons(f(x), r))" 

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length_def "length(l) == list_rec(l, 0, %x xs r. succ(r))" 

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app_def "xs@ys == list_rec(xs, ys, %x xs r. Cons(x,r))" 

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rev_def "rev(l) == list_rec(l, Nil, %x xs r. r @ [x])" 

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flat_def "flat(ls) == list_rec(ls, Nil, %l ls r. l @ r)" 

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list_add_def "list_add(l) == list_rec(l, 0, %x xs r. x#+r)" 

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end 