I am using redex-check to validate a model against another, and would like to see the intermediate (successful) results for debugging purposes. The most obvious way to do this would be to have the property-expr print the given term as a side-effect, but this is inelegant. Is there another way to look at intermediate redex-check attempts?
It looks like you have the right idea on how to do this. In fact, the example for redex-check in the docs actually does this:
(let ([R (reduction-relation
empty-lang
(--> (Σ) 0)
(--> (Σ number) number)
(--> (Σ number_1 number_2 number_3 ...)
(Σ ,(+ (term number_1) (term number_2))
number_3 ...)))])
(redex-check
empty-lang
(Σ number ...)
(printf "~s\n" (term (number ...)))
#:attempts 3
#:source R))
Writes the following result to current-output-port:
()
(0)
(2 0)
redex-check: no counterexamples in 1 attempt (with each clause)
Related
I'm trying to match against a hash table in typed racket, but I keep getting the following error. The code works fine in untyped racket and I've tried changing it up some to no effect. The error looks like it's happening somewhere after the match macro gets expanded but I'm not familiar enough with racket to understand where or how to debug the issue.
Is is possible to use the hash-table pattern in typed racket?
(match (make-hash '((a . 2) (b . 3) (c . 2)))
[(hash-table _ ...) #t])
Type Checker: Polymorphic function `hash-map' could not be applied to arguments:
Domains: HashTableTop (-> Any Any c) Any
HashTableTop (-> Any Any c)
(HashTable a b) (-> a b c) Any
(HashTable a b) (-> a b c)
Arguments: (Mutable-HashTable Symbol Integer) (All (a) (-> a * (Listof a)))
it's impossible.
in the match macro, the hash-table form expands to syntax that includes the hash-map function, viz (lambda (e) (hash-map e list)). this is correct but its type is too abstract for typed racket to infer it. for the type checker to be satisfied, we'd need:
(lambda #:forall (k v) ([e : (HashTable k v)])
(hash-map e
(λ ([k : k] [v : v])
(list k v))))
there's no practical way to specify this, so the hash-table matcher is unusable in typed racket.
if a for loop is usually best, e.g.
(for ([(k v) (make-hash '((a . 2) (b . 3) (c . 2)))] #:when (even? v))
(printf "~a and ~a~n" k v))
or else something like (hash-keys m)
otherwise, positional matching requires advanced knoweldge of typed racket. for example, the following function, hash-set/cond, takes a hash table and arguments of the form (flag k v) ... and updates (if key already in table) or inserts (if key not already in table) each k/v pair if its associated flag is truthy:
(: hash-set/cond (∀ (k v) (->* ((HashTable k v))
#:rest-star (Any k v)
(HashTable k v))))
(define (hash-set/cond ht . args)
(let loop ([ht : (HashTable k v) ht]
[args : (Rec r (U (List* Any k v r) Null)) args])
(if (null? args)
ht
(loop (if (car args)
(hash-set ht (cadr args) (caddr args))
ht)
(cdddr args)))))
e.g.
(hash-set/cond (hash 'a 20 'b "yes")
(even? 3) 'a 10 ; 3's not even, so 'a isn't modified
#t 'b "canary" ; necessarily set 'b to "canary"
'im-a-truthy-value! 'c 'new-value) ; ditto
returns #hash((a . 20) (b . "canary") (c . new-value)).
so if you end-up using typed racket a lot and want to use this kind of functionality, then it can be very useful in certain places! still, typed racket's type system can represent—but not handle—certain recursive hash table types. this is because, when checking the type of the value, hash? cannot refine the type of the hash table beyond it being a hash table with some type of key and value, i.e. hash? : (-> Any Boolean : HashTableTop) instead of (-> Any Boolean : (HashTable k v)). this makes recursing over particular recursively defined JSON schemata impossible. in these cases you must use untyped racket, though the saving grace here is that racket contracts can handle such complex definitions.
if your project is heavily based on complex hash tables, then clojure or janet are likely better language choices.
I am very new to ACL2 so I understand that some of you may feel this is such a simple solution that you would frown upon my outreach for help. I am trying to figure out how to get my code to add up to an Nth reciprocal squared (I.E if n=4 then i am looking for 1/1 + 1/4 + 1/9 + 1/16)
I have a function that will add up to n and it works and looks like this
(defun sum-up-to-n (n)
(if (zp n)
0
(+ n (sum-up-to-n (- n 1)))))
With the the Reciprocal squared looking like this
(defun sum-up-to-nSqRecip (n)
(if (zp n)
0
(+ (sum-up-to-nSqRecip (- n 1))) 1/n^2) ))
I receive this error "The body of
SUM-UP-TO-NSQRECIP contains a free occurrence of the variable symbol
|1/N^2|. Note that |1/N^2| occurs in the context of condition (NOT (ZP N))
from a surrounding IF test." and i do not know how to resolve this error.
included stuff
(encapsulate nil
(set-state-ok t)
(program)
(defun check-expect-fn (left right sexpr state)
(if (equal left right)
(mv nil (cw "check-expect succeeded: ~x0~%" sexpr) state)
(er soft nil "check-expect failed: ~x0
Expected: ~x1
Actual: ~x2" sexpr right left)))
(defmacro check-expect (&whole sexpr left right)
`(check-expect-fn ,left ,right (quote ,sexpr) state))
(logic))
(include-book "doublecheck" :uncertified-okp t :dir :teachpacks)
(include-book "arithmetic-5/top" :uncertified-okp t :dir :system)
ACL2 uses LISP syntax, which means you need prefix operators. So 1/n^2 should be (/ 1 (* n n)).
LISP allows a lot of the characters to be in a name, 1/n^2 in your example is treated as a name of a variable, which isn't binded to anything (not an input either). This is why you are receiving the "free occurrence of the variable" error.
Suppose I want to convert the following untyped code into typed racket. These functions are inspired by SICP where they show how a data structure can be constructed purely from functions.
(define (make-pair x y)
(lambda (c)
(cond
((= c 1) x)
((= c 2) y)
(error "error in input, should be 1 or 2"))))
(define (first p) (p 1))
(define (second p) (p 2))
To convert it straight to typed racket, the return value of the make-pair function seems to be (: make-pair (All (A B) (-> A B (-> Number (U A B))))). And following this, the type of first should be (: first (All (A B) (-> (-> Number (U A B)) A))). However, while implementing the function we can't call (p 1) directly now because we need some sort of occurrence typing to make sure first returns only of type A. Changing the return type of first to (U A B) works but then the burden of occurrence typing goes on the user and not in the API. So in this scenario how can we use occurrence typing inside first (that is, how to use a predicate for type variable A) so that we can safely return only the first component of the pair?
UPDATE
I tried an approach which differs a bit from above and requires the predicates for A and B to be supplied as arguments to make-pair function. Below is the code:
#lang typed/racket
(define-type FuncPair (All (A B) (List (-> Number (U A B)) (-> A Boolean) (-> B Boolean))))
(: make-pair (All (A B) (-> A B (-> A Boolean) (-> B Boolean) (FuncPair A B))))
(define (make-pair x y x-pred y-pred)
(list
(lambda ([c : Number])
(cond
((= c 1) x)
((= c 2) y)
(else (error "Wrong input!"))))
x-pred
y-pred))
(: first (All (A B) (-> (FuncPair A B) Any)))
(define (first p)
(let ([pair-fn (car p)]
[fn-pred (cadr p)])
(let ([f-value (pair-fn 1)])
(if (fn-pred f-value)
f-value
(error "Cannot get first value in pair")))))
However, this fails in the check (fn-pred f-value) condition with error expected: A
given: (U A B) in: f-value
From the untyped code at the start of your question, it seems like a pair of A and B is a function that given 1, gives back A, and given 2, gives back B. The way to express this type of function is with a case-> type:
#lang typed/racket
(define-type (Pairof A B)
(case-> [1 -> A] [2 -> B]))
The accessors can be defined the same way as your original untyped code, just by adding type annotations:
(: first : (All (A B) [(Pairof A B) -> A]))
(define (first p) (p 1))
(: second : (All (A B) [(Pairof A B) -> B]))
(define (second p) (p (ann 2 : 2)))
The type of the constructor should be:
(: make-pair : (All (A B) [A B -> (Pairof A B)]))
But the constructor doesn't quite work as-is. One thing wrong with it is that your else clause is missing the else part of it. Fixing that gives you:
(: make-pair : (All (A B) [A B -> (Pairof A B)]))
(define (make-pair x y)
(lambda (c)
(cond
[(= c 1) x]
[(= c 2) y]
[else (error "error in input, should be 1 or 2")])))
This is almost right, and if typed racket were awesome enough, it would be. Typed racket treats equal? specially for occurrence typing, but it doesn't do the same thing for =. Changing = to equal? fixes it.
(: make-pair : (All (A B) [A B -> (Pairof A B)]))
(define (make-pair x y)
(lambda (c)
(cond
[(equal? c 1) x]
[(equal? c 2) y]
[else (error "error in input, should be 1 or 2")])))
Ideally occurrence typing should work with =, but perhaps the fact that things like (= 2 2.0) return true makes that both harder to implement and less useful.
A common way of defining semantics is (for example):
return v if [some other condition]
otherwise, return error
For example, consider
(define-language simple-dispatch
(e ::= v (+ e e))
(v ::= number string)
(res ::= e err)
(E ::= hole (+ E e) (+ v E)))
We could then define the reduction relation
(define s-> (reduction-relation simple-dispatch
#:domain res
(--> (in-hole E (+ number_1 number_2))
(in-hole E ,(+ number_1 number_2)))
(--> (in-hole E (+ any any))
err)))
This is the natural way to do this, because it avoids having to write individual matchers for each of the 3 failure cases (number string, string number, string string). However, it then creates the problem that running it like this:
(apply-reduction-relation s-> (term (+ 2 2)))
Shows (correctly) that it lets you reduce both to an error or to the number 4. Is there a way to make an "except" pattern that avoids having to check all of the constituent cases?
What you want to use here is a combination of side-condition and redex-match?. Extending your reduction-relation gives:
(define s-> (reduction-relation simple-dispatch
#:domain res
(--> (in-hole E (+ number_1 number_2))
(in-hole E ,(+ (term number_1) (term number_2))))
(--> (in-hole E (+ any_1 any_2))
err
(side-condition
(not (redex-match? simple-dispatch
(+ number number)
(term (+ any_1 any_2))))))))
This just says you can take the second rule so long as the first one is not true, which is what the papers are saying implicitly, and just didn't draw out explicitly in the figure. (Note that you can use side-condition/hidden to get it to not draw the side condition when rendering the figure).
You can use this method to scale up to any number of patterns you want to disallow.
I'm trying to get a bit into Typed Racket, but I'm having some trouble getting an (admittedly rather constructed) experiment to work.
This is what I originally had:
#lang typed/racket
(: generate-list
(All (A)
((A -> A) (Integer -> A) Integer -> (Listof A))))
(define (generate-list function location-function num-items)
(let: loop : (Listof A)
((count : Integer 0)
(result : (Listof A) (list)))
(if (>= count num-items)
(reverse result)
(loop (+ count 1)
(cons (function (location-function count)) result)))))
; ---------------------------------
(: f (Number -> Number))
(define (f x) (* x x))
(: locf (Integer -> Number))
(define (locf x) x)
; ---------------------------------
(displayln (generate-list f locf 10))
Which has the output:
(0 1 4 9 16 25 36 49 64 81)
Which is nice. Then I figured I could make this a bit better documented by giving the function and location-function a defined type:
#lang typed/racket
(define-type (ListGenFunction A) (A -> A))
(define-type (ListGenLocFunction A) (Integer -> A))
(: generate-list
(All (A)
(ListGenFunction ListGenLocFunction Integer -> (Listof A))))
(define (generate-list function location-function num-items)
(let: loop : (Listof A)
((count : Integer 0)
(result : (Listof A) (list)))
(if (>= count num-items)
(reverse result)
(loop (+ count 1)
(cons (function (location-function count)) result)))))
; ----------- Numbers! ------------
(: f ListGenFunction)
(define (f x) (* x x))
(: locf ListGenLocFunction)
(define (locf x) x)
; ---------------------------------
(displayln (generate-list f locf 10))
Now here's where the problems start (and I really hope some experienced Typed Racketeers aren't facepalming too hard right now). For one, the type checker gives me an error on the line where I define f. The message is rather lengthy, but it's basically: "Type Checker: No function domains matched in function application: Types: ... in: (* x x)". I thought I defined a type that has one parameter of a generic type A that returns a generic type A? Wouldn't (* x x) work? Or is there some need to "tag" the type? (Like in C++-like languages where it's list<int> for example)
On top of that: Now my type-definition for the function generate-list has a return type of "(Listof A)". But that A is not at all declared to be the same A that the parameters with the types ListGenFunction and ListGenLocFunction expect. I kind of want to make that connection, however, so that anyone who uses that function can be sure that the types of his provided functions match the type of the returning list items.
How do I do this correctly?
PS:
I'm not sure if I described my intention in the last paragraph so that anyone can understand it. But if you take some generic pseudo-C++-like code, I want to get the following:
list<T> generate-list(LGF<T> f, LGLF<T> locf, int count) { ... }
So that all T's are exactly the same.
There are two problems here, both of which stem from the same confusion. You're using a generic type, ListGenFunction, without telling Typed Racket (or the reader of your program) what particular type you're using it with.
For example, f isn't an arbitrary ListGenFunction, it's a ListGenFunction that works specifically on numbers. So you should write:
(: f (ListGenFunction Integer))
and
(: locf (ListGenLocFunction Integer))
Similarly, you should give generate-list a type like this:
(: generate-list
(All (A)
((ListGenFunction A) (ListGenLocFunction A) Integer -> (Listof A))))
This is just like how you explicitly say that you're producing a (Listof A), not just a Listof.