Explore quoting.

This commit is contained in:
Tony Garnock-Jones 2018-12-06 21:25:51 +00:00
parent b2a9b53b6c
commit fdd7eb6e94
2 changed files with 269 additions and 0 deletions

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#lang racket
(require racket/trace)
(struct DISCARD ())
(struct CAPTURE (p))
(define (q p)
(match p
[(DISCARD) `(discard)]
[(CAPTURE p) `(capture ,(q p))]
[`(discard) `('discard)]
[`(capture ,p) `('capture ,(q p))]
[`(quote ,p) `('quote ,(q p))]
[`(,pa . ,pd) `(,(q pa) . ,(q pd))]
[a a]))
(define (uq p)
(match p
[`(discard) (DISCARD)]
[`(capture ,p) (CAPTURE (uq p))]
[`(quote ,p) p]
[`(,pa . ,pd) `(,(uq pa) . ,(uq pd))]
[a a]))
;; Goal: (uq (q p)) === p
;; (define (m p v k)
;; (match* (p v)
;; [(`(discard) _) (k '())]
;; [(`(capture ,p) v) (m p v (lambda (bs) (cons v bs)))]
;; [(`(quote ,p) v) (and (equal? p v) (k '()))]
;; [(`(,pa . ,pd) `(,va . ,vd)) (m pa va (lambda (bs) (m pd vd (lambda (cs) (k (append bs cs))))))]
;; [(p v) (and (equal? p v) (k '()))]))
(define (m p v k)
(match* (p v)
[((DISCARD) _) (k '())]
[((CAPTURE p) v) (m p v (lambda (bs) (cons v bs)))]
[(`(,pa . ,pd) `(,va . ,vd)) (m pa va (lambda (bs) (m pd vd (lambda (cs) (k (append bs cs))))))]
[(p v) (and (equal? p v) (k '()))]))
;; (trace m)
(module+ test
(require rackunit)
;; (define (M p v) (m p v values))
(define (M p v) (m (uq p) v values))
(check-equal? (M `(capture 1) 1) '(1))
(check-equal? (M `(discard) 1) '())
(check-equal? (M 1 1) '())
(check-equal? (M 2 1) #f)
(check-equal? (M `(capture 2) 1) #f)
(check-equal? (M `(record (capture (discard))) `(record value)) '(value))
(check-equal? (M `(record (capture (discard))) `(record 'value)) '('value))
(check-equal? (M `(record (capture (discard))) `(record (capture (discard))))
'((capture (discard))))
(check-equal? (M `(record ('capture (discard))) `(record (capture (discard))))
'())
(check-equal? (M `(record (capture ('capture (discard)))) `(record (capture (discard))))
'((capture (discard))))
(check-equal? (M `(record (capture ('capture (discard)))) `(record value))
#f)
(check-equal? (M `(record (capture ('capture (discard)))) `(record 'value))
#f)
(check-equal? (M `(record (capture ('capture (discard)))) `(record ('capture (discard))))
#f)
(check-equal? (M `(record '(capture (discard))) `(record (capture (discard))))
'())
(check-equal? (M `(record (capture '(capture (discard)))) `(record (capture (discard))))
'((capture (discard))))
(check-equal? (M `(record (capture '(capture (discard)))) `(record value))
#f)
(check-equal? (M `(record (capture '(capture (discard)))) `(record 'value))
#f)
(check-equal? (M `(record (capture '(capture (discard)))) `(record '(capture (discard))))
#f)
(check-equal? (M `(record ('quote value)) `(record (capture (discard)))) #f)
(check-equal? (M `(record (capture ('quote value))) `(record (capture (discard)))) #f)
(check-equal? (M `(record (capture ('quote value))) `(record value)) #f)
(check-equal? (M `(record (capture ('quote value))) `(record 'value)) '('value))
(check-equal? (M `(record (capture ('quote value))) `(record 'notvalue)) #f)
(check-equal? (M `(record ('quote value)) `(record 'value)) '())
(check-equal? (M `(record (capture ('quote value))) `(record ('quote value))) #f)
(check-equal? (M `(record ''value) `(record (capture (discard)))) #f)
(check-equal? (M `(record (capture ''value)) `(record (capture (discard)))) #f)
(check-equal? (M `(record (capture ''value)) `(record value)) #f)
(check-equal? (M `(record (capture ''value)) `(record 'value)) '('value))
(check-equal? (M `(record (capture ''value)) `(record 'notvalue)) #f)
(check-equal? (M `(record ''value) `(record 'value)) '())
(check-equal? (M `(record (capture ''value)) `(record ''value)) #f)
(check-equal? (q (CAPTURE 1)) `(capture 1))
(check-equal? (q (DISCARD)) `(discard))
(check-equal? (q `(capture 1)) `('capture 1))
(check-equal? (q `(discard)) `('discard))
)

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Require Import Coq.Lists.List.
Require Import Coq.Program.Equality.
Require Import Omega.
Require Import String.
Require Import Bool.
Import ListNotations.
Open Scope list_scope.
Open Scope string_scope.
Inductive label : Type := (* efficiency hack *)
| lDiscard : label
| lCapture : label
| lQuote: label
| lStr : string -> label.
Inductive value : Type :=
| vBool : bool -> value
| vSymbol : label -> value
| vRecord: value -> values -> value
| vSeq : values -> value
with values : Type :=
| vsNil : values
| vsCons : value -> values -> values.
Inductive pat : Type :=
| pDiscard : pat
| pCapture : pat -> pat
| pBool : bool -> pat
| pSymbol : label -> pat
| pRecord: pat -> pats -> pat
| pSeq : pats -> pat
with pats : Type :=
| psNil : pats
| psCons : pat -> pats -> pats.
Definition vs1 v : values := vsCons v vsNil.
Definition ps1 p : pats := psCons p psNil.
Definition vQuote v : value := vRecord (vSymbol lQuote) (vs1 v).
Lemma value_dec : forall x y : value, { x = y } + { x <> y }
with values_dec : forall xs ys : values, { xs = ys } + { xs <> ys }.
repeat decide equality.
repeat decide equality.
Defined.
Lemma pat_dec : forall x y : pat, { x = y } + { x <> y }
with pats_dec : forall xs ys : pats, { xs = ys } + { xs <> ys }.
repeat decide equality.
repeat decide equality.
Defined.
Fixpoint qp p : value :=
match p with
| pDiscard => vRecord (vSymbol lDiscard) vsNil
| pCapture p' => vRecord (vSymbol lCapture) (vs1 (qp p'))
| pBool b => vBool b
| pSymbol s => vSymbol s
| pRecord (pSymbol lDiscard) psNil => vRecord (vQuote (vSymbol lDiscard)) vsNil
| pRecord (pSymbol lCapture) (psCons p' psNil) => vRecord (vQuote (vSymbol lCapture)) (vs1 (qp p'))
| pRecord (pSymbol lQuote) (psCons p' psNil) => vRecord (vQuote (vSymbol lQuote)) (vs1 (qp p'))
| pRecord l ps => vRecord (qp l) (qps ps)
| pSeq ps => vSeq (qps ps)
end
with qps ps : values :=
match ps with
| psNil => vsNil
| psCons p' ps' => vsCons (qp p') (qps ps')
end.
Fixpoint raw_uqp v : pat :=
match v with
| vBool b => pBool b
| vSymbol s => pSymbol s
| vRecord l fs => pRecord (raw_uqp l) (raw_uqps fs)
| vSeq vs => pSeq (raw_uqps vs)
end
with raw_uqps vs : pats :=
match vs with
| vsNil => psNil
| vsCons v vs' => psCons (raw_uqp v) (raw_uqps vs')
end.
Fixpoint uqp v : pat :=
match v with
| vRecord (vSymbol lDiscard) vsNil => pDiscard
| vRecord (vSymbol lCapture) (vsCons v' vsNil) => pCapture (uqp v')
| vRecord (vSymbol lQuote) (vsCons v' vsNil) => raw_uqp v'
| vBool b => pBool b
| vSymbol s => pSymbol s
| vRecord l fs => pRecord (uqp l) (uqps fs)
| vSeq vs => pSeq (uqps vs)
end
with uqps vs : pats :=
match vs with
| vsNil => psNil
| vsCons v vs' => psCons (uqp v) (uqps vs')
end.
Lemma quoting_for_record_sensible :
forall p ps,
p <> pSymbol lDiscard ->
p <> pSymbol lCapture ->
p <> pSymbol lQuote ->
uqp (qp (pRecord p ps)) = pRecord (uqp (qp p)) (uqps (qps ps)).
Proof.
destruct p; try reflexivity.
destruct l; try congruence; reflexivity.
intros; destruct p; try reflexivity.
destruct l; try reflexivity; destruct p0; try reflexivity.
destruct p0; try reflexivity.
destruct p0; try reflexivity.
Qed.
Theorem quoting_sensible : forall p, uqp (qp p) = p
with quoting_list_sensible : forall ps, uqps (qps ps) = ps.
Proof.
clear quoting_sensible.
induction p; try reflexivity.
remember (qp (pCapture p)) as p'; simpl in Heqp'; rewrite Heqp'; simpl; rewrite IHp; reflexivity.
remember (pat_dec p (pSymbol lDiscard)) as HisDiscard; inversion HisDiscard.
remember (pats_dec p0 psNil) as HisEmpty; inversion HisEmpty.
rewrite H, H0; reflexivity.
rewrite H; remember p0 as p0'; destruct p0'.
congruence.
simpl.
rewrite Heqp0'.
rewrite <- quoting_list_sensible with (ps := p0).
rewrite <- Heqp0'.
reflexivity.
remember (pat_dec p (pSymbol lCapture)) as HisCapture; inversion HisCapture;
[ rewrite H0; clear H0 | ].
remember p0 as p0'; destruct p0'; [ reflexivity | ].
rewrite Heqp0'.
destruct p0';
[ simpl | unfold qp];
rewrite <- quoting_list_sensible with (ps := p0) at 2;
rewrite <- Heqp0';
reflexivity.
remember (pat_dec p (pSymbol lQuote)) as HisQuote; inversion HisQuote;
[ rewrite H1; clear H1 | ].
remember p0 as p0'; destruct p0'; [ reflexivity | ].
rewrite Heqp0'.
destruct p0';
[ simpl | unfold qp];
rewrite <- quoting_list_sensible with (ps := p0) at 2;
rewrite <- Heqp0';
reflexivity.
rewrite quoting_for_record_sensible; try assumption.
rewrite <- IHp at 2.
rewrite <- quoting_list_sensible with (ps := p0) at 2.
reflexivity.
rewrite <- quoting_list_sensible with (ps := p) at 2; reflexivity.
clear quoting_list_sensible.
induction ps; try reflexivity.
simpl.
rewrite quoting_sensible.
f_equal.
apply IHps.
Qed.