IMPLEMENTATION Recursion

IMPORT Nat COMPLETELY
IMPORT Denotation COMPLETELY
IMPORT Char COMPLETELY

DEF plus == \\m,n . IF n = 0
		      THEN m
		      ELSE plus(succ(m), pred(n))
		    FI

DEF sum == \\m,n. IF m>n THEN 0
                         ELSE m + sum(m+1,n)
                  FI

DEF in? == \\c,d. IF d = "" THEN false
                  ELSE IF d ! 0 = c THEN true 
                                    ELSE in?(c,delete(d,0,0))
                       FI
                  FI

DEF mult == \\a,b. IF a>0 THEN b+mult(a-1,b) ELSE 0 FI
/* Alternativ: IF a>1 THEN b+mult(a-1,b) ELSE b FI */

DEF sumEven == \\m,n. IF m>n THEN 0
                      ELSE IF m%2=0 THEN m + sumEven(m+1,n)
                           ELSE sumEven(m+1,n) FI FI

DEF count == \\c,d. IF d = "" THEN 0
                    ELSE IF d ! 0 = c THEN 1+count(c,delete(d,0,0))
                         ELSE count(c,delete(d,0,0)) FI FI

DEF countDigits == \\d. IF d = "" THEN 0
                        ELSE IF digit?(d!0) THEN 1+countDigits(delete(d,0,0))
                             ELSE countDigits(delete(d,0,0)) FI FI



/* TUT-Examples following */

FUN h : nat ** nat -> nat ** nat
DEF h == \\m,n. (h1(m,n), h2(m,n))

FUN h1 : nat ** nat -> nat
DEF h1 == \\m,n. IF m < n THEN 0 ELSE h1(m-n,n) + 1 FI

FUN h2 : nat ** nat -> nat
DEF h2 == \\m,n. IF m < n THEN m ELSE h2(m-n,n) FI


FUN f : nat ** nat -> nat
DEF f == \\a,b. IF a > b THEN f1(a,b,a)
                         ELSE f1(b,a,b)
                FI

FUN f1 : nat ** nat ** nat -> nat
DEF f1 == \\a,b,z. IF mod(a,b) = 0 THEN a
                                   ELSE f1(a+z,b,z)
                   FI

FUN g : nat ** nat -> nat
DEF g == \\a,b. IF b = 0 THEN a
                         ELSE g(b,mod(a,b))
                FI