src/HOL/Prolog/Func.thy
author oheimb
Tue Jun 11 16:43:17 2002 +0200 (2002-06-11)
changeset 13208 965f95a3abd9
parent 12338 de0f4a63baa5
child 14981 e73f8140af78
permissions -rw-r--r--
added the usual file headers
     1 (*  Title:    HOL/Prolog/Func.thy
     2     ID:       $Id$
     3     Author:   David von Oheimb (based on a lecture on Lambda Prolog by Nadathur)
     4     License:  GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 untyped functional language, with call by value semantics 
     7 *)
     8 
     9 Func = HOHH +
    10 
    11 types tm
    12 
    13 arities tm :: type
    14 
    15 consts	abs	:: (tm => tm) => tm
    16 	app	:: tm => tm => tm
    17 
    18 	cond	:: tm => tm => tm => tm
    19 	fix	:: (tm => tm) => tm
    20 
    21 	true,
    22 	false	:: tm
    23 	"and"	:: tm => tm => tm	(infixr 999)
    24 	"eq"	:: tm => tm => tm	(infixr 999)
    25 
    26 	"0"	:: tm			("Z")
    27 	S	:: tm => tm
    28 (*
    29 	"++", "--",
    30 	"**"	:: tm => tm => tm	(infixr 999)
    31 *)
    32 	eval	:: [tm, tm] => bool
    33 
    34 arities tm :: plus
    35 arities tm :: minus
    36 arities tm :: times
    37 
    38 rules	eval "
    39 
    40 eval (abs RR) (abs RR)..
    41 eval (app F X) V :- eval F (abs R) & eval X U & eval (R U) V..
    42 
    43 eval (cond P L1 R1) D1 :- eval P true  & eval L1 D1..
    44 eval (cond P L2 R2) D2 :- eval P false & eval R2 D2..
    45 eval (fix G) W   :- eval (G (fix G)) W..
    46 
    47 eval true  true ..
    48 eval false false..
    49 eval (P and Q) true  :- eval P true  & eval Q true ..
    50 eval (P and Q) false :- eval P false | eval Q false..
    51 eval (A1 eq B1) true  :- eval A1 C1 & eval B1 C1.. 
    52 eval (A2 eq B2) false :- True..
    53 
    54 eval Z Z..
    55 eval (S N) (S M) :- eval N M..
    56 eval ( Z    + M) K     :- eval      M  K..
    57 eval ((S N) + M) (S K) :- eval (N + M) K..
    58 eval (N     - Z) K     :- eval  N      K..
    59 eval ((S N) - (S M)) K :- eval (N- M)  K..
    60 eval ( Z    * M) Z..
    61 eval ((S N) * M) K :- eval (N * M) L & eval (L + M) K"
    62 
    63 end