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boyer_no_exc.ml
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boyer_no_exc.ml
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(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the Q Public License version 1.0. *)
(* *)
(***********************************************************************)
(* $Id: boyer.ml 7017 2005-08-12 09:22:04Z xleroy $ *)
(* Manipulations over terms *)
type term =
| Var of int
| Prop of head * term list
and head =
{ name : string
; mutable props : (term * term) list
}
let rec print_term = function
| Var v ->
print_string "v";
print_int v
| Prop (head, argl) ->
print_string "(";
print_string head.name;
List.iter
(fun t ->
print_string " ";
print_term t)
argl;
print_string ")"
let lemmas = ref ([] : head list)
(* Replacement for property lists *)
let get name =
let rec get_rec = function
| hd1 :: hdl -> if hd1.name = name then hd1 else get_rec hdl
| [] ->
let entry = { name; props = [] } in
lemmas := entry :: !lemmas;
entry
in
get_rec !lemmas
let add_lemma = function
| Prop (_, [ (Prop (headl, _) as left); right ]) ->
headl.props <- (left, right) :: headl.props
| _ -> assert false
(* Substitutions *)
type subst = Bind of int * term
let get_binding v list =
let rec get_rec = function
| [] -> None
| Bind (w, t) :: rest -> if v = w then Some t else get_rec rest
in
get_rec list
let apply_subst alist term =
let rec as_rec = function
| Var v -> (
match get_binding v alist with
| Some t -> t
| None -> term)
| Prop (head, argl) -> Prop (head, List.map as_rec argl)
in
as_rec term
exception Unify
let rec unify term1 term2 = unify1 term1 term2 []
and unify1 term1 term2 unify_subst =
match term2 with
| Var v -> (
match get_binding v unify_subst with
| Some t when t = term1 -> Some unify_subst
| Some _ -> None
| None -> Some (Bind (v, term1) :: unify_subst))
| Prop (head2, argl2) -> (
match term1 with
| Var _ -> None
| Prop (head1, argl1) ->
if head1 == head2 then unify1_lst argl1 argl2 unify_subst else None)
and unify1_lst l1 l2 unify_subst =
match l1, l2 with
| [], [] -> Some unify_subst
| h1 :: r1, h2 :: r2 -> (
match unify1 h1 h2 unify_subst with
| Some unify_subst -> unify1_lst r1 r2 unify_subst
| None -> None)
| _ -> None
let rec rewrite = function
| Var _ as term -> term
| Prop (head, argl) ->
rewrite_with_lemmas (Prop (head, List.map rewrite argl)) head.props
and rewrite_with_lemmas term lemmas =
match lemmas with
| [] -> term
| (t1, t2) :: rest -> (
match unify term t1 with
| Some unify_subst -> rewrite (apply_subst unify_subst t2)
| None -> rewrite_with_lemmas term rest)
type cterm =
| CVar of int
| CProp of string * cterm list
let rec cterm_to_term = function
| CVar v -> Var v
| CProp (p, l) -> Prop (get p, List.map cterm_to_term l)
let add t = add_lemma (cterm_to_term t)
let _ =
add
(CProp
( "equal"
, [ CProp ("compile", [ CVar 5 ])
; CProp
( "reverse"
, [ CProp ("codegen", [ CProp ("optimize", [ CVar 5 ]); CProp ("nil", []) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("eqp", [ CVar 23; CVar 24 ])
; CProp ("equal", [ CProp ("fix", [ CVar 23 ]); CProp ("fix", [ CVar 24 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("gt", [ CVar 23; CVar 24 ]); CProp ("lt", [ CVar 24; CVar 23 ]) ] ));
add
(CProp
( "equal"
, [ CProp ("le", [ CVar 23; CVar 24 ]); CProp ("ge", [ CVar 24; CVar 23 ]) ] ));
add
(CProp
( "equal"
, [ CProp ("ge", [ CVar 23; CVar 24 ]); CProp ("le", [ CVar 24; CVar 23 ]) ] ));
add
(CProp
( "equal"
, [ CProp ("boolean", [ CVar 23 ])
; CProp
( "or"
, [ CProp ("equal", [ CVar 23; CProp ("true", []) ])
; CProp ("equal", [ CVar 23; CProp ("false", []) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("iff", [ CVar 23; CVar 24 ])
; CProp
( "and"
, [ CProp ("implies", [ CVar 23; CVar 24 ])
; CProp ("implies", [ CVar 24; CVar 23 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("even1", [ CVar 23 ])
; CProp
( "if"
, [ CProp ("zerop", [ CVar 23 ])
; CProp ("true", [])
; CProp ("odd", [ CProp ("sub1", [ CVar 23 ]) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("countps_", [ CVar 11; CVar 15 ])
; CProp ("countps_loop", [ CVar 11; CVar 15; CProp ("zero", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("fact_", [ CVar 8 ])
; CProp ("fact_loop", [ CVar 8; CProp ("one", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("reverse_", [ CVar 23 ])
; CProp ("reverse_loop", [ CVar 23; CProp ("nil", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("divides", [ CVar 23; CVar 24 ])
; CProp ("zerop", [ CProp ("remainder", [ CVar 24; CVar 23 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("assume_true", [ CVar 21; CVar 0 ])
; CProp ("cons", [ CProp ("cons", [ CVar 21; CProp ("true", []) ]); CVar 0 ])
] ));
add
(CProp
( "equal"
, [ CProp ("assume_false", [ CVar 21; CVar 0 ])
; CProp ("cons", [ CProp ("cons", [ CVar 21; CProp ("false", []) ]); CVar 0 ])
] ));
add
(CProp
( "equal"
, [ CProp ("tautology_checker", [ CVar 23 ])
; CProp ("tautologyp", [ CProp ("normalize", [ CVar 23 ]); CProp ("nil", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("falsify", [ CVar 23 ])
; CProp ("falsify1", [ CProp ("normalize", [ CVar 23 ]); CProp ("nil", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("prime", [ CVar 23 ])
; CProp
( "and"
, [ CProp ("not", [ CProp ("zerop", [ CVar 23 ]) ])
; CProp
( "not"
, [ CProp ("equal", [ CVar 23; CProp ("add1", [ CProp ("zero", []) ]) ])
] )
; CProp ("prime1", [ CVar 23; CProp ("sub1", [ CVar 23 ]) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("and", [ CVar 15; CVar 16 ])
; CProp
( "if"
, [ CVar 15
; CProp ("if", [ CVar 16; CProp ("true", []); CProp ("false", []) ])
; CProp ("false", [])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("or", [ CVar 15; CVar 16 ])
; CProp
( "if"
, [ CVar 15
; CProp ("true", [])
; CProp ("if", [ CVar 16; CProp ("true", []); CProp ("false", []) ])
; CProp ("false", [])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("not", [ CVar 15 ])
; CProp ("if", [ CVar 15; CProp ("false", []); CProp ("true", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("implies", [ CVar 15; CVar 16 ])
; CProp
( "if"
, [ CVar 15
; CProp ("if", [ CVar 16; CProp ("true", []); CProp ("false", []) ])
; CProp ("true", [])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("fix", [ CVar 23 ])
; CProp ("if", [ CProp ("numberp", [ CVar 23 ]); CVar 23; CProp ("zero", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("if", [ CProp ("if", [ CVar 0; CVar 1; CVar 2 ]); CVar 3; CVar 4 ])
; CProp
( "if"
, [ CVar 0
; CProp ("if", [ CVar 1; CVar 3; CVar 4 ])
; CProp ("if", [ CVar 2; CVar 3; CVar 4 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("zerop", [ CVar 23 ])
; CProp
( "or"
, [ CProp ("equal", [ CVar 23; CProp ("zero", []) ])
; CProp ("not", [ CProp ("numberp", [ CVar 23 ]) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("plus", [ CProp ("plus", [ CVar 23; CVar 24 ]); CVar 25 ])
; CProp ("plus", [ CVar 23; CProp ("plus", [ CVar 24; CVar 25 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CProp ("plus", [ CVar 0; CVar 1 ]); CProp ("zero", []) ])
; CProp ("and", [ CProp ("zerop", [ CVar 0 ]); CProp ("zerop", [ CVar 1 ]) ])
] ));
add
(CProp ("equal", [ CProp ("difference", [ CVar 23; CVar 23 ]); CProp ("zero", []) ]));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("plus", [ CVar 0; CVar 1 ]); CProp ("plus", [ CVar 0; CVar 2 ]) ]
)
; CProp ("equal", [ CProp ("fix", [ CVar 1 ]); CProp ("fix", [ CVar 2 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp
("equal", [ CProp ("zero", []); CProp ("difference", [ CVar 23; CVar 24 ]) ])
; CProp ("not", [ CProp ("gt", [ CVar 24; CVar 23 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CVar 23; CProp ("difference", [ CVar 23; CVar 24 ]) ])
; CProp
( "and"
, [ CProp ("numberp", [ CVar 23 ])
; CProp
( "or"
, [ CProp ("equal", [ CVar 23; CProp ("zero", []) ])
; CProp ("zerop", [ CVar 24 ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "meaning"
, [ CProp ("plus_tree", [ CProp ("append", [ CVar 23; CVar 24 ]) ]); CVar 0 ]
)
; CProp
( "plus"
, [ CProp ("meaning", [ CProp ("plus_tree", [ CVar 23 ]); CVar 0 ])
; CProp ("meaning", [ CProp ("plus_tree", [ CVar 24 ]); CVar 0 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "meaning"
, [ CProp ("plus_tree", [ CProp ("plus_fringe", [ CVar 23 ]) ]); CVar 0 ] )
; CProp ("fix", [ CProp ("meaning", [ CVar 23; CVar 0 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("append", [ CProp ("append", [ CVar 23; CVar 24 ]); CVar 25 ])
; CProp ("append", [ CVar 23; CProp ("append", [ CVar 24; CVar 25 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("reverse", [ CProp ("append", [ CVar 0; CVar 1 ]) ])
; CProp
("append", [ CProp ("reverse", [ CVar 1 ]); CProp ("reverse", [ CVar 0 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("times", [ CVar 23; CProp ("plus", [ CVar 24; CVar 25 ]) ])
; CProp
( "plus"
, [ CProp ("times", [ CVar 23; CVar 24 ])
; CProp ("times", [ CVar 23; CVar 25 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("times", [ CProp ("times", [ CVar 23; CVar 24 ]); CVar 25 ])
; CProp ("times", [ CVar 23; CProp ("times", [ CVar 24; CVar 25 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CProp ("times", [ CVar 23; CVar 24 ]); CProp ("zero", []) ])
; CProp ("or", [ CProp ("zerop", [ CVar 23 ]); CProp ("zerop", [ CVar 24 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("exec", [ CProp ("append", [ CVar 23; CVar 24 ]); CVar 15; CVar 4 ])
; CProp
("exec", [ CVar 24; CProp ("exec", [ CVar 23; CVar 15; CVar 4 ]); CVar 4 ])
] ));
add
(CProp
( "equal"
, [ CProp ("mc_flatten", [ CVar 23; CVar 24 ])
; CProp ("append", [ CProp ("flatten", [ CVar 23 ]); CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp ("member", [ CVar 23; CProp ("append", [ CVar 0; CVar 1 ]) ])
; CProp
( "or"
, [ CProp ("member", [ CVar 23; CVar 0 ])
; CProp ("member", [ CVar 23; CVar 1 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("member", [ CVar 23; CProp ("reverse", [ CVar 24 ]) ])
; CProp ("member", [ CVar 23; CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp ("length", [ CProp ("reverse", [ CVar 23 ]) ])
; CProp ("length", [ CVar 23 ])
] ));
add
(CProp
( "equal"
, [ CProp ("member", [ CVar 0; CProp ("intersect", [ CVar 1; CVar 2 ]) ])
; CProp
( "and"
, [ CProp ("member", [ CVar 0; CVar 1 ])
; CProp ("member", [ CVar 0; CVar 2 ])
] )
] ));
add
(CProp ("equal", [ CProp ("nth", [ CProp ("zero", []); CVar 8 ]); CProp ("zero", []) ]));
add
(CProp
( "equal"
, [ CProp ("exp", [ CVar 8; CProp ("plus", [ CVar 9; CVar 10 ]) ])
; CProp
( "times"
, [ CProp ("exp", [ CVar 8; CVar 9 ]); CProp ("exp", [ CVar 8; CVar 10 ]) ]
)
] ));
add
(CProp
( "equal"
, [ CProp ("exp", [ CVar 8; CProp ("times", [ CVar 9; CVar 10 ]) ])
; CProp ("exp", [ CProp ("exp", [ CVar 8; CVar 9 ]); CVar 10 ])
] ));
add
(CProp
( "equal"
, [ CProp ("reverse_loop", [ CVar 23; CVar 24 ])
; CProp ("append", [ CProp ("reverse", [ CVar 23 ]); CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp ("reverse_loop", [ CVar 23; CProp ("nil", []) ])
; CProp ("reverse", [ CVar 23 ])
] ));
add
(CProp
( "equal"
, [ CProp ("count_list", [ CVar 25; CProp ("sort_lp", [ CVar 23; CVar 24 ]) ])
; CProp
( "plus"
, [ CProp ("count_list", [ CVar 25; CVar 23 ])
; CProp ("count_list", [ CVar 25; CVar 24 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("append", [ CVar 0; CVar 1 ])
; CProp ("append", [ CVar 0; CVar 2 ])
] )
; CProp ("equal", [ CVar 1; CVar 2 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "plus"
, [ CProp ("remainder", [ CVar 23; CVar 24 ])
; CProp ("times", [ CVar 24; CProp ("quotient", [ CVar 23; CVar 24 ]) ])
] )
; CProp ("fix", [ CVar 23 ])
] ));
add
(CProp
( "equal"
, [ CProp
("power_eval", [ CProp ("big_plus", [ CVar 11; CVar 8; CVar 1 ]); CVar 1 ])
; CProp ("plus", [ CProp ("power_eval", [ CVar 11; CVar 1 ]); CVar 8 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "power_eval"
, [ CProp ("big_plus", [ CVar 23; CVar 24; CVar 8; CVar 1 ]); CVar 1 ] )
; CProp
( "plus"
, [ CVar 8
; CProp
( "plus"
, [ CProp ("power_eval", [ CVar 23; CVar 1 ])
; CProp ("power_eval", [ CVar 24; CVar 1 ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("remainder", [ CVar 24; CProp ("one", []) ]); CProp ("zero", []) ] ));
add
(CProp
( "equal"
, [ CProp ("lt", [ CProp ("remainder", [ CVar 23; CVar 24 ]); CVar 24 ])
; CProp ("not", [ CProp ("zerop", [ CVar 24 ]) ])
] ));
add (CProp ("equal", [ CProp ("remainder", [ CVar 23; CVar 23 ]); CProp ("zero", []) ]));
add
(CProp
( "equal"
, [ CProp ("lt", [ CProp ("quotient", [ CVar 8; CVar 9 ]); CVar 8 ])
; CProp
( "and"
, [ CProp ("not", [ CProp ("zerop", [ CVar 8 ]) ])
; CProp
( "or"
, [ CProp ("zerop", [ CVar 9 ])
; CProp ("not", [ CProp ("equal", [ CVar 9; CProp ("one", []) ]) ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("lt", [ CProp ("remainder", [ CVar 23; CVar 24 ]); CVar 23 ])
; CProp
( "and"
, [ CProp ("not", [ CProp ("zerop", [ CVar 24 ]) ])
; CProp ("not", [ CProp ("zerop", [ CVar 23 ]) ])
; CProp ("not", [ CProp ("lt", [ CVar 23; CVar 24 ]) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("power_eval", [ CProp ("power_rep", [ CVar 8; CVar 1 ]); CVar 1 ])
; CProp ("fix", [ CVar 8 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "power_eval"
, [ CProp
( "big_plus"
, [ CProp ("power_rep", [ CVar 8; CVar 1 ])
; CProp ("power_rep", [ CVar 9; CVar 1 ])
; CProp ("zero", [])
; CVar 1
] )
; CVar 1
] )
; CProp ("plus", [ CVar 8; CVar 9 ])
] ));
add
(CProp
( "equal"
, [ CProp ("gcd", [ CVar 23; CVar 24 ]); CProp ("gcd", [ CVar 24; CVar 23 ]) ] ));
add
(CProp
( "equal"
, [ CProp ("nth", [ CProp ("append", [ CVar 0; CVar 1 ]); CVar 8 ])
; CProp
( "append"
, [ CProp ("nth", [ CVar 0; CVar 8 ])
; CProp
( "nth"
, [ CVar 1
; CProp ("difference", [ CVar 8; CProp ("length", [ CVar 0 ]) ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("difference", [ CProp ("plus", [ CVar 23; CVar 24 ]); CVar 23 ])
; CProp ("fix", [ CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp ("difference", [ CProp ("plus", [ CVar 24; CVar 23 ]); CVar 23 ])
; CProp ("fix", [ CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "difference"
, [ CProp ("plus", [ CVar 23; CVar 24 ])
; CProp ("plus", [ CVar 23; CVar 25 ])
] )
; CProp ("difference", [ CVar 24; CVar 25 ])
] ));
add
(CProp
( "equal"
, [ CProp ("times", [ CVar 23; CProp ("difference", [ CVar 2; CVar 22 ]) ])
; CProp
( "difference"
, [ CProp ("times", [ CVar 2; CVar 23 ])
; CProp ("times", [ CVar 22; CVar 23 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("remainder", [ CProp ("times", [ CVar 23; CVar 25 ]); CVar 25 ])
; CProp ("zero", [])
] ));
add
(CProp
( "equal"
, [ CProp
( "difference"
, [ CProp ("plus", [ CVar 1; CProp ("plus", [ CVar 0; CVar 2 ]) ]); CVar 0 ]
)
; CProp ("plus", [ CVar 1; CVar 2 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "difference"
, [ CProp ("add1", [ CProp ("plus", [ CVar 24; CVar 25 ]) ]); CVar 25 ] )
; CProp ("add1", [ CVar 24 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "lt"
, [ CProp ("plus", [ CVar 23; CVar 24 ])
; CProp ("plus", [ CVar 23; CVar 25 ])
] )
; CProp ("lt", [ CVar 24; CVar 25 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "lt"
, [ CProp ("times", [ CVar 23; CVar 25 ])
; CProp ("times", [ CVar 24; CVar 25 ])
] )
; CProp
( "and"
, [ CProp ("not", [ CProp ("zerop", [ CVar 25 ]) ])
; CProp ("lt", [ CVar 23; CVar 24 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("lt", [ CVar 24; CProp ("plus", [ CVar 23; CVar 24 ]) ])
; CProp ("not", [ CProp ("zerop", [ CVar 23 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp
( "gcd"
, [ CProp ("times", [ CVar 23; CVar 25 ])
; CProp ("times", [ CVar 24; CVar 25 ])
] )
; CProp ("times", [ CVar 25; CProp ("gcd", [ CVar 23; CVar 24 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("value", [ CProp ("normalize", [ CVar 23 ]); CVar 0 ])
; CProp ("value", [ CVar 23; CVar 0 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("flatten", [ CVar 23 ])
; CProp ("cons", [ CVar 24; CProp ("nil", []) ])
] )
; CProp
( "and"
, [ CProp ("nlistp", [ CVar 23 ]); CProp ("equal", [ CVar 23; CVar 24 ]) ] )
] ));
add
(CProp
( "equal"
, [ CProp ("listp", [ CProp ("gother", [ CVar 23 ]) ])
; CProp ("listp", [ CVar 23 ])
] ));
add
(CProp
( "equal"
, [ CProp ("samefringe", [ CVar 23; CVar 24 ])
; CProp
("equal", [ CProp ("flatten", [ CVar 23 ]); CProp ("flatten", [ CVar 24 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("greatest_factor", [ CVar 23; CVar 24 ]); CProp ("zero", []) ] )
; CProp
( "and"
, [ CProp
( "or"
, [ CProp ("zerop", [ CVar 24 ])
; CProp ("equal", [ CVar 24; CProp ("one", []) ])
] )
; CProp ("equal", [ CVar 23; CProp ("zero", []) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("greatest_factor", [ CVar 23; CVar 24 ]); CProp ("one", []) ] )
; CProp ("equal", [ CVar 23; CProp ("one", []) ])
] ));
add
(CProp
( "equal"
, [ CProp ("numberp", [ CProp ("greatest_factor", [ CVar 23; CVar 24 ]) ])
; CProp
( "not"
, [ CProp
( "and"
, [ CProp
( "or"
, [ CProp ("zerop", [ CVar 24 ])
; CProp ("equal", [ CVar 24; CProp ("one", []) ])
] )
; CProp ("not", [ CProp ("numberp", [ CVar 23 ]) ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("times_list", [ CProp ("append", [ CVar 23; CVar 24 ]) ])
; CProp
( "times"
, [ CProp ("times_list", [ CVar 23 ]); CProp ("times_list", [ CVar 24 ]) ] )
] ));
add
(CProp
( "equal"
, [ CProp ("prime_list", [ CProp ("append", [ CVar 23; CVar 24 ]) ])
; CProp
( "and"
, [ CProp ("prime_list", [ CVar 23 ]); CProp ("prime_list", [ CVar 24 ]) ] )
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CVar 25; CProp ("times", [ CVar 22; CVar 25 ]) ])
; CProp
( "and"
, [ CProp ("numberp", [ CVar 25 ])
; CProp
( "or"
, [ CProp ("equal", [ CVar 25; CProp ("zero", []) ])
; CProp ("equal", [ CVar 22; CProp ("one", []) ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("ge", [ CVar 23; CVar 24 ])
; CProp ("not", [ CProp ("lt", [ CVar 23; CVar 24 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CVar 23; CProp ("times", [ CVar 23; CVar 24 ]) ])
; CProp
( "or"
, [ CProp ("equal", [ CVar 23; CProp ("zero", []) ])
; CProp
( "and"
, [ CProp ("numberp", [ CVar 23 ])
; CProp ("equal", [ CVar 24; CProp ("one", []) ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("remainder", [ CProp ("times", [ CVar 24; CVar 23 ]); CVar 24 ])
; CProp ("zero", [])
] ));
add
(CProp
( "equal"
, [ CProp ("equal", [ CProp ("times", [ CVar 0; CVar 1 ]); CProp ("one", []) ])
; CProp
( "and"
, [ CProp ("not", [ CProp ("equal", [ CVar 0; CProp ("zero", []) ]) ])
; CProp ("not", [ CProp ("equal", [ CVar 1; CProp ("zero", []) ]) ])
; CProp ("numberp", [ CVar 0 ])
; CProp ("numberp", [ CVar 1 ])
; CProp ("equal", [ CProp ("sub1", [ CVar 0 ]); CProp ("zero", []) ])
; CProp ("equal", [ CProp ("sub1", [ CVar 1 ]); CProp ("zero", []) ])
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "lt"
, [ CProp ("length", [ CProp ("delete", [ CVar 23; CVar 11 ]) ])
; CProp ("length", [ CVar 11 ])
] )
; CProp ("member", [ CVar 23; CVar 11 ])
] ));
add
(CProp
( "equal"
, [ CProp ("sort2", [ CProp ("delete", [ CVar 23; CVar 11 ]) ])
; CProp ("delete", [ CVar 23; CProp ("sort2", [ CVar 11 ]) ])
] ));
add (CProp ("equal", [ CProp ("dsort", [ CVar 23 ]); CProp ("sort2", [ CVar 23 ]) ]));
add
(CProp
( "equal"
, [ CProp
( "length"
, [ CProp
( "cons"
, [ CVar 0
; CProp
( "cons"
, [ CVar 1
; CProp
( "cons"
, [ CVar 2
; CProp
( "cons"
, [ CVar 3
; CProp
( "cons"
, [ CVar 4
; CProp ("cons", [ CVar 5; CVar 6 ])
] )
] )
] )
] )
] )
] )
; CProp ("plus", [ CProp ("six", []); CProp ("length", [ CVar 6 ]) ])
] ));
add
(CProp
( "equal"
, [ CProp
( "difference"
, [ CProp ("add1", [ CProp ("add1", [ CVar 23 ]) ]); CProp ("two", []) ] )
; CProp ("fix", [ CVar 23 ])
] ));
add
(CProp
( "equal"
, [ CProp
( "quotient"
, [ CProp ("plus", [ CVar 23; CProp ("plus", [ CVar 23; CVar 24 ]) ])
; CProp ("two", [])
] )
; CProp ("plus", [ CVar 23; CProp ("quotient", [ CVar 24; CProp ("two", []) ]) ])
] ));
add
(CProp
( "equal"
, [ CProp ("sigma", [ CProp ("zero", []); CVar 8 ])
; CProp
( "quotient"
, [ CProp ("times", [ CVar 8; CProp ("add1", [ CVar 8 ]) ])
; CProp ("two", [])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("plus", [ CVar 23; CProp ("add1", [ CVar 24 ]) ])
; CProp
( "if"
, [ CProp ("numberp", [ CVar 24 ])
; CProp ("add1", [ CProp ("plus", [ CVar 23; CVar 24 ]) ])
; CProp ("add1", [ CVar 23 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "equal"
, [ CProp ("difference", [ CVar 23; CVar 24 ])
; CProp ("difference", [ CVar 25; CVar 24 ])
] )
; CProp
( "if"
, [ CProp ("lt", [ CVar 23; CVar 24 ])
; CProp ("not", [ CProp ("lt", [ CVar 24; CVar 25 ]) ])
; CProp
( "if"
, [ CProp ("lt", [ CVar 25; CVar 24 ])
; CProp ("not", [ CProp ("lt", [ CVar 24; CVar 23 ]) ])
; CProp
( "equal"
, [ CProp ("fix", [ CVar 23 ]); CProp ("fix", [ CVar 25 ]) ] )
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp
( "meaning"
, [ CProp ("plus_tree", [ CProp ("delete", [ CVar 23; CVar 24 ]) ]); CVar 0 ]
)
; CProp
( "if"
, [ CProp ("member", [ CVar 23; CVar 24 ])
; CProp
( "difference"
, [ CProp ("meaning", [ CProp ("plus_tree", [ CVar 24 ]); CVar 0 ])
; CProp ("meaning", [ CVar 23; CVar 0 ])
] )
; CProp ("meaning", [ CProp ("plus_tree", [ CVar 24 ]); CVar 0 ])
] )
] ));
add
(CProp
( "equal"
, [ CProp ("times", [ CVar 23; CProp ("add1", [ CVar 24 ]) ])
; CProp
( "if"
, [ CProp ("numberp", [ CVar 24 ])
; CProp
( "plus"
, [ CVar 23
; CProp ("times", [ CVar 23; CVar 24 ])
; CProp ("fix", [ CVar 23 ])
] )
] )
] ));
add
(CProp
( "equal"
, [ CProp ("nth", [ CProp ("nil", []); CVar 8 ])