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authoraarne <aarne@chalmers.se>2011-01-11 15:46:43 +0000
committeraarne <aarne@chalmers.se>2011-01-11 15:46:43 +0000
commite7439d65b0e153434d3acc07df6e2a0972ee79ca (patch)
tree36716eec18256eeb600b4a552d9cc80f8ad7f16f /book/examples/chapter6/Arithm.gf
parent276327f7f264e770478a6d8c6e683266505b0a55 (diff)
gf-book web page index and toc
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-abstract Arithm = {
- cat
- Prop ; -- proposition
- Nat ; -- natural number
- data
- Zero : Nat ; -- 0
- Succ : Nat -> Nat ; -- the successor of x
- fun
- Even : Nat -> Prop ; -- x is even
- And : Prop -> Prop -> Prop ; -- A and B
-
- cat Less Nat Nat ;
- data LessZ : (y : Nat) -> Less Zero (Succ y) ;
- data LessS : (x,y : Nat) -> Less x y -> Less (Succ x) (Succ y) ;
-
- cat Span ;
- data FromTo : (m,n : Nat) -> Less m n -> Span ;
-
- fun one : Nat ;
- def one = Succ Zero ;
-
- fun twice : Nat -> Nat ;
- def twice x = plus x x ;
-
- fun plus : Nat -> Nat -> Nat ;
- def
- plus x Zero = x ;
- plus x (Succ y) = Succ (plus x y) ;
-
-}