99 lines
2.4 KiB
OCaml
99 lines
2.4 KiB
OCaml
(****************** Equation manipulations *************)
|
|
|
|
open Terms
|
|
|
|
type rule =
|
|
{ number: int;
|
|
numvars: int;
|
|
lhs: term;
|
|
rhs: term }
|
|
|
|
(* standardizes an equation so its variables are 1,2,... *)
|
|
|
|
let mk_rule num m n =
|
|
let all_vars = union (vars m) (vars n) in
|
|
let counter = ref 0 in
|
|
let subst =
|
|
List.map (fun v -> incr counter; (v, Var !counter)) (List.rev all_vars) in
|
|
{ number = num;
|
|
numvars = !counter;
|
|
lhs = substitute subst m;
|
|
rhs = substitute subst n }
|
|
|
|
|
|
(* checks that rules are numbered in sequence and returns their number *)
|
|
|
|
let check_rules rules =
|
|
let counter = ref 0 in
|
|
List.iter (fun r -> incr counter;
|
|
if r.number <> !counter
|
|
then failwith "Rule numbers not in sequence")
|
|
rules;
|
|
!counter
|
|
|
|
|
|
let pretty_rule rule =
|
|
print_int rule.number; print_string " : ";
|
|
pretty_term rule.lhs; print_string " = "; pretty_term rule.rhs;
|
|
print_newline()
|
|
|
|
|
|
let pretty_rules rules = List.iter pretty_rule rules
|
|
|
|
(****************** Rewriting **************************)
|
|
|
|
(* Top-level rewriting. Let eq:L=R be an equation, M be a term such that L<=M.
|
|
With sigma = matching L M, we define the image of M by eq as sigma(R) *)
|
|
let reduce l m r =
|
|
substitute (matching l m) r
|
|
|
|
(* Test whether m can be reduced by l, i.e. m contains an instance of l. *)
|
|
|
|
let rec reducible l m =
|
|
try
|
|
matching l m; true
|
|
with Failure _ ->
|
|
match m with Term(_,sons) -> List.exists (reducible l) sons
|
|
| _ -> false
|
|
|
|
(* Top-level rewriting with multiple rules. *)
|
|
|
|
let rec mreduce rules m =
|
|
match rules with
|
|
[] -> failwith "mreduce"
|
|
| rule::rest ->
|
|
try
|
|
reduce rule.lhs m rule.rhs
|
|
with Failure _ ->
|
|
mreduce rest m
|
|
|
|
|
|
(* One step of rewriting in leftmost-outermost strategy,
|
|
with multiple rules. Fails if no redex is found *)
|
|
|
|
let rec mrewrite1 rules m =
|
|
try
|
|
mreduce rules m
|
|
with Failure _ ->
|
|
match m with
|
|
Var n -> failwith "mrewrite1"
|
|
| Term(f, sons) -> Term(f, mrewrite1_sons rules sons)
|
|
|
|
and mrewrite1_sons rules = function
|
|
[] -> failwith "mrewrite1"
|
|
| son::rest ->
|
|
try
|
|
mrewrite1 rules son :: rest
|
|
with Failure _ ->
|
|
son :: mrewrite1_sons rules rest
|
|
|
|
|
|
(* Iterating rewrite1. Returns a normal form. May loop forever *)
|
|
|
|
let rec mrewrite_all rules m =
|
|
try
|
|
mrewrite_all rules (mrewrite1 rules m)
|
|
with Failure _ ->
|
|
m
|
|
|