gf-book web page index and toc

gf-book/examples/chapter6/Arithm.gf

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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) ;
+
+}