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Victor Taelin 2024-02-21 22:10:51 -03:00
parent 37fb440ea9
commit e4b262f9d1
32 changed files with 416 additions and 90 deletions
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71
book/A.kind2 Normal file
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@ -0,0 +1,71 @@
//TRY-0
//-----
//A.one : A = ~λP λnew (new Nat.zero)
//A.bad : A = ~λP λnew (new (Nat.succ Nat.zero) ?UE)
//A : * =
//$self
//∀(P: ∀(x: A) *)
//∀(new: ∀(tag: Nat)
//let R = λx(*)
//let zero = (P A.one)
//let succ = λp∀(x:Empty)*
//(~tag R succ zero))
//(P self)
//A.elim : ∀(a: A) ∀(P: ∀(x: A) *) ∀(t: (P A.one)) (P a) =
//λa λP λt
//(~a P λtag(~tag λx(~x λx(*) λp(Empty) (P A.one)) λp(?B) t))
// TRY-1
// -----
A.one : A = ~λP λnew (new #0)
A.bad : A = ~λP λnew (new #1 ?UE)
A.sel
: ∀(P: ∀(x: A) *)
∀(k: #U60)
*
= λP λk #match tag = k {
#0: (P A.one)
#+: ∀(e: Empty) *
}: *
A : * =
$self
∀(P: ∀(x: A) *)
∀(new: ∀(tag: #U60) (A.sel P tag))
(P self)
A.match : ∀(a: A) ∀(P: ∀(x: A) *) ∀(t: (P A.one)) (P a) =
λa λP λt
(~a P λtag #match tag = tag {
#0: t
#+: λx (~x λx(*))
}: (A.sel P tag))
// TRY-2
// -----
//A.one
//: A
//= ~ λP λnew (new #0 Unit.one)
//A : * = (Sigma #U60 λtag #match tag = tag {
//#0: Unit
//#+: Empty
//}: *)
//A.match : ∀(a: A) ∀(P: ∀(x: A) *) ∀(t: (P A.one)) (P a) =
//λa λP λt
//(~a P λx #match x = x {
//#0: λb ?A
//#+: λb ?B
//}: ∀(b: (#match x = x { #0: Unit #+: Empty }: *))
//(P (Sigma.new #U60 λtag(#match tag = tag { #0: Unit #+: Empty }: *) x b)))
//(P (Sigma.new #U60 Unit b))

5
book/Empty.absurd.kind2 Normal file
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@ -0,0 +1,5 @@
Empty.absurd
: ∀(e: Empty)
∀(P: *)
P
= λe λP (~e λx(P))

5
book/Empty.kind2 Normal file
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@ -0,0 +1,5 @@
Empty
: *
= $self
∀(P: ∀(x: Empty) *)
(P self)

7
book/Kind.Book.to_hvm.go.kind2
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@ -6,12 +6,13 @@ Kind.Book.to_hvm.go
let cons = λhead λtail
let P = λx String.Concatenator
let new = λhead.fst λhead.snd λnil
((Kind.Text.show.go "F."
((Kind.Text.show.go head.fst)
((Kind.Text.show.go " = "
((Kind.Term.to_hvm.go head.snd Nat.zero
((Kind.Term.to_hvm.go head.snd Nat.zero Bool.true Nat.zero
((Kind.Text.show.go String.newline
((Kind.Book.to_hvm.go tail
nil)))))))))
nil)))))))))))
(~head P new)
let nil = λnil nil
(~book P cons nil)
(~book P cons nil)

2
book/Kind.Book.to_hvm.kind2
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@ -2,4 +2,4 @@ Kind.Book.to_hvm
: ∀(book: Kind.Book)
String
= λbook
(String.Concatenator.build (Kind.Book.to_hvm.go book))
(String.Concatenator.build (Kind.Book.to_hvm.go book))

9
book/Kind.Book.to_hvm.prelude.kind2 Normal file
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@ -0,0 +1,9 @@
Kind.Book.to_hvm.prelude
: String
= `
(U60.match 0 z s) = z
(U60.match n z s) = (s (- n 1))
(Str String.nil) = λP λcons λnil nil
(Str (String.cons x xs)) = λP λcons λnil (cons x (Str xs))
`

2
book/Kind.Term.parser.mat.kind2
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@ -16,4 +16,4 @@ Kind.Term.parser.mat
(Kind.Term.parser.bind Unit (Parser.text ":") λ_
(Kind.Term.parser.bind Kind.PreTerm Kind.Term.parser λp
(Kind.Term.parser.pure λscp
(Kind.mat nam (x scp) (z scp) λx(s (Kind.Scope.extend nam x scp)) λx(p (Kind.Scope.extend nam x scp)))))))))))))))))))
(Kind.mat nam (x scp) (z scp) λx(s (Kind.Scope.extend (String.concat nam "-1") x scp)) λx(p (Kind.Scope.extend nam x scp)))))))))))))))))))

4
book/Kind.Term.show.go.kind2
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@ -80,7 +80,7 @@ Kind.Term.show.go
((Kind.Text.show.go " { #0: ")
((Kind.Term.show.go z dep)
((Kind.Text.show.go "; #+: ")
((Kind.Term.show.go (s (Kind.var nam dep)) (Nat.succ dep))
((Kind.Term.show.go (s (Kind.var (String.concat nam "-1") dep)) (Nat.succ dep))
((Kind.Text.show.go " }: ")
((Kind.Term.show.go (p (Kind.var nam dep)) (Nat.succ dep))
nil))))))))))
@ -96,4 +96,4 @@ Kind.Term.show.go
let var = λnam λidx λnil
((Kind.Text.show.go nam)
nil)
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var)
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var)

138
book/Kind.Term.to_hvm.go.kind2
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@ -1,73 +1,113 @@
Kind.Term.to_hvm.go
: ∀(term: Kind.Term)
∀(dep: Nat)
∀(inc: Bool)
∀(tab: Nat)
String.Concatenator
= λterm λdep
= λterm λdep λinc λtab
let P = λx String.Concatenator
let all = λnam λinp λbod
(Kind.Text.show.go "0")
let all = λnam λinp λbod λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "0")
nil))
let lam = λnam λbod λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "λ")
((Kind.Text.show.go (U60.name (U60.from_nat dep)))
//((Kind.Text.show.go (U60.name (U60.from_nat dep)))
((Kind.Text.show.go (String.cons '_' nam))
((Kind.Text.show.go " "
((Kind.Term.to_hvm.go (bod (Kind.var nam dep)) (Nat.succ dep))
nil)))))
let app = λfun λarg λnil
((Kind.Text.show.go "(")
((Kind.Term.to_hvm.go fun dep)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go arg dep)
((Kind.Text.show.go ")")
nil)))))
let ann = λval λtyp
(Kind.Term.to_hvm.go val dep)
let slf = λnam λbod
(Kind.Text.show.go "0")
let ins = λval
(Kind.Term.to_hvm.go val dep)
let ref = λnam λval
(Kind.Text.show.go nam)
let def = λnam λval λbod λnil
((Kind.Text.show.go "let ")
((Kind.Text.show.go nam)
((Kind.Text.show.go " = ")
((Kind.Term.to_hvm.go val dep)
((Kind.Text.show.go "; ")
((Kind.Term.to_hvm.go (bod (Kind.var nam dep)) (Nat.succ dep))
((Kind.Term.to_hvm.go (bod (Kind.var nam dep)) (Nat.succ dep) Bool.true tab)
nil))))))
let set =
(Kind.Text.show.go "0")
let u60 =
(Kind.Text.show.go "0")
let num = λval
(U60.show.go val)
let app = λfun λarg λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "(")
((Kind.Term.to_hvm.go fun dep Bool.true tab)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go arg dep Bool.true tab)
((Kind.Text.show.go ")")
nil))))))
let ann = λval λtyp λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Term.to_hvm.go val dep Bool.true tab)
nil))
let slf = λnam λbod λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "0")
nil))
let ins = λval λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Term.to_hvm.go val dep Bool.true tab)
nil))
let ref = λnam λval λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "(F.")
((Kind.Text.show.go nam)
((Kind.Text.show.go ")")
nil))))
let def = λnam λval λbod λnil
let tab = ((~inc λx∀(x:Nat)Nat Nat.succ λx(x)) tab)
((Kind.Text.show.go String.newline)
((Kind.Text.show.go (String.indent tab))
((Kind.Text.show.go "let ")
//((Kind.Text.show.go (U60.name (U60.from_nat dep)))
((Kind.Text.show.go (String.cons '_' nam))
((Kind.Text.show.go " = ")
((Kind.Term.to_hvm.go val dep Bool.true tab)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go (bod (Kind.var nam dep)) (Nat.succ dep) Bool.false tab)
nil))))))))
let set = λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "0")
nil))
let u60 = λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "0")
nil))
let num = λval λnil
((Kind.Term.to_hvm.nl inc tab)
((U60.show.go val)
nil))
let op2 = λopr λfst λsnd λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "(")
((Kind.Oper.show.go opr) // TODO: Kind.Oper.to_hvm
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go fst dep)
((Kind.Term.to_hvm.go fst dep Bool.true tab)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go snd dep)
((Kind.Term.to_hvm.go snd dep Bool.true tab)
((Kind.Text.show.go ")")
nil)))))))
nil))))))))
let mat = λnam λx λz λs λp λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "(U60.match ")
((Kind.Term.to_hvm.go x dep)
((Kind.Term.to_hvm.go x dep Bool.true tab)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go z dep)
((Kind.Term.to_hvm.go z dep Bool.true tab)
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go (s (Kind.var (String.concat nam "_1") dep)) (Nat.succ dep))
((Kind.Text.show.go " ")
((Kind.Term.to_hvm.go (p (Kind.var nam dep)) (Nat.succ dep))
((Kind.Text.show.go "λ")
((Kind.Text.show.go (String.cons '_' (String.concat nam "_1")))
//((Kind.Text.show.go (U60.name (U60.from_nat dep)))
((Kind.Text.show.go "(")
((Kind.Term.to_hvm.go (s (Kind.var (String.concat nam "_1") dep)) (Nat.succ dep) Bool.true tab)
((Kind.Text.show.go ")")
nil)))))))))
((Kind.Text.show.go ")")
nil))))))))))))
let txt = λtxt λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "(Str ")
((Kind.Text.show.go String.quote)
((Kind.Text.show.go txt)
((Kind.Text.show.go String.quote)
nil)))
let hol = λnam λctx
(Kind.Text.show.go "0")
let var = λnam λidx
(Kind.Text.show.go (U60.name (U60.from_nat idx)))
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var)
((Kind.Text.show.go ")")
nil))))))
let hol = λnam λctx λnil
((Kind.Term.to_hvm.nl inc tab)
((Kind.Text.show.go "0")
nil))
let var = λnam λidx λnil
((Kind.Term.to_hvm.nl inc tab)
//((Kind.Text.show.go (U60.name (U60.from_nat idx)))
((Kind.Text.show.go (String.cons '_' nam))
nil))
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var)

10
book/Kind.Term.to_hvm.nl.kind2 Normal file
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@ -0,0 +1,10 @@
Kind.Term.to_hvm.nl
: ∀(inc: Bool)
∀(tab: Nat)
String.Concatenator
= λinc λtab
let P = λx(String.Concatenator)
let true = λnil (nil)
let false = λnil ((Kind.Text.show.go String.newline) ((Kind.Text.show.go (String.indent tab)) nil))
(~inc P true false)

2
book/Kind.ann.kind2
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@ -4,4 +4,4 @@ Kind.ann
Kind.Term
= λval λtyp
~λP λall λlam λapp λann λslf λins λref λdef λset λu60 λnum λop2 λmat λtxt λhol λvar
(ann val typ)
(ann val typ)

2
book/Kind.app.kind2
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@ -4,4 +4,4 @@ Kind.app
Kind.Term
= λfun λarg
~λP λall λlam λapp λann λslf λins λref λdef λset λu60 λnum λop2 λmat λtxt λhol λvar
(app fun arg)
(app fun arg)

2
book/Kind.if.def.kind2
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@ -22,4 +22,4 @@ Kind.if.def
let txt = λlit λY λN (N (Kind.txt lit))
let hol = λnam λctx λY λN (N (Kind.hol nam ctx))
let var = λnam λidx λY λN (N (Kind.var nam idx))
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var Y N)
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var Y N)

2
book/Kind.if.slf.kind2
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@ -22,4 +22,4 @@ Kind.if.slf
let txt = λlit λY λN (N (Kind.txt lit))
let hol = λnam λctx λY λN (N (Kind.hol nam ctx))
let var = λnam λidx λY λN (N (Kind.var nam idx))
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var Y N)
(~term P all lam app ann slf ins ref def set u60 num op2 mat txt hol var Y N)

2
book/Kind.set.kind2
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@ -1,4 +1,4 @@
Kind.set
: Kind.Term
= ~λP λall λlam λapp λann λslf λins λref λdef λset λu60 λnum λop2 λmat λtxt λhol λvar
(set)
(set)

2
book/Kind.u60.kind2
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@ -1,4 +1,4 @@
Kind.u60
: Kind.Term
= ~λP λall λlam λapp λann λslf λins λref λdef λset λu60 λnum λop2 λmat λtxt λhol λvar
u60
u60

14
book/List.begin.kind2 Normal file
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@ -0,0 +1,14 @@
// Removes the last element
List.begin
: ∀(A: *)
∀(list: (List A))
(List A)
= λA λlist
let P = λx(List A)
let cons = λx0 λxs
let P = λx(List A)
let cons = λx1 λxs (List.cons A x0 (List.begin A (List.cons A x1 xs)))
let nil = (List.nil A)
(~xs P cons nil)
let nil = (List.nil A)
(~list P cons nil)

71
book/QBool.kind2 Normal file
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@ -0,0 +1,71 @@
// Ideal:
// QBool.true : QBool = ~λP (#0, λx x)
// QBool.false : QBool = ~λP (#1, λx x)
//
// QBool : * =
// $self
// ∀(P: ∀(x: QBool) *)
// Σ(t: #U60)
// ∀(x: match t {
// 0: (P QBool.true)
// 1: (P QBool.false)
// +: Empty
// })
// (P self)
//
// QBool.match
// : ∀(a: QBool)
// ∀(P: ∀(x: QBool) *)
// ∀(t: (P QBool.true))
// ∀(f: (P QBool.false))
// (P a)
// = λa λP λt λf
// let (tag, val) = (~a P)
// #match tag = tag {
// #0: (val t)
// #1: (val f)
// #+: (val λe (Empty.absurd e *))
// }
QBool.true : QBool =
~λP ~λS λp (p #0 λx x)
QBool.false : QBool =
~λP ~λS λp (p #1 λx x)
QBool : * =
$self
∀(P: ∀(x: QBool) *)
(Sigma #U60 λt
∀(x: #match t = t {
#0: (P QBool.true)
#+: #match t = t-1 {
#0: (P QBool.false)
#+: ∀(x: Empty) *
}: *
}: *)
(P self))
QBool.match
: ∀(a: QBool)
∀(P: ∀(x: QBool) *)
∀(t: (P QBool.true))
∀(f: (P QBool.false))
(P a)
= λa λP λt λf
(~(~a P) λx(P a) λtag #match tag = tag {
#0: λx (x t)
#+: λx ((#match tag-1 = tag-1 {
#0: λx (x f)
#+: λx (x λe (Empty.absurd e *))
}: ∀(x: ∀(x: #match tag-1 = tag-1 {
#0: (P QBool.false)
#+: ∀(x: Empty) *
}: *) (P a)) (P a)) x)
}: ∀(x: (∀(x: #match tag = tag {
#0: (P QBool.true)
#+: #match tag-1 = tag-1 {
#0: (P QBool.false)
#+: ∀(x: Empty) *
}: *
}: *) (P a))) (P a))

11
book/QUnit.kind2 Normal file
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@ -0,0 +1,11 @@
QUnit.one : QUnit =
~λP ~λSP λnew (new #0 λone one)
QUnit : * =
$self
∀(P: ∀(x: QUnit) *)
(Sigma #U60 λtag
#match tag = tag {
#0: ∀(one: (P QUnit.one)) (P self)
#+: Empty
}: *)

9
book/Sigma.kind2 Normal file
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@ -0,0 +1,9 @@
Sigma
: ∀(A: *)
∀(B: ∀(x: A) *)
*
= λA λB
$self
∀(P: ∀(x: (Sigma A B)) *)
∀(new: ∀(a: A) ∀(b: (B a)) (P (Sigma.new A B a b)))
(P self)

9
book/Sigma.new.kind2 Normal file
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@ -0,0 +1,9 @@
Sigma.new
: ∀(A: *)
∀(B: ∀(x: A) *)
∀(a: A)
∀(b: (B a))
(Sigma A B)
= λA λB λa λb
~λP λnew (new a b)

5
book/String.begin.kind2 Normal file
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@ -0,0 +1,5 @@
String.begin
: ∀(str: String)
String
= λstr
(List.begin Char str)

8
book/String.indent.kind2 Normal file
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@ -0,0 +1,8 @@
String.indent
: ∀(tab: Nat)
String
= λtab
let P = λx(String)
let succ = λtab.pred (String.cons ' ' (String.cons ' ' (String.indent tab.pred)))
let zero = String.nil
(~tab P succ zero)

16
book/String.unpar.kind2 Normal file
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@ -0,0 +1,16 @@
// If first char is '(', remove first and last
// FIXME: check if last matches
String.unpar
: ∀(fst: Char)
∀(lst: Char)
∀(str: String)
String
= λfst λlst λstr
let P = λx(String)
let cons = λhead λtail
let P = λx∀(head:Char)∀(tail:String)String
let true = λheadλtail(String.begin tail)
let false = λheadλtail(String.cons head tail)
((~(Char.equal head fst) P true false) head tail)
let nil = String.nil
(~str P cons nil)

11
book/U60.match.kind2 Normal file
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@ -0,0 +1,11 @@
U60.match
: ∀(x: #U60)
∀(P: ∀(x: #U60) *)
∀(s: ∀(x: #U60) (P #(+ #1 x)))
∀(z: (P #0))
(P x)
= λx λP λs λz
#match self = x {
#0: z
#+: (s self-1)
}: (P self)

7
book/Unit.match.kind2 Normal file
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@ -0,0 +1,7 @@
Unit.match
: ∀(x: Unit)
∀(P: ∀(x: Unit) *)
∀(o: (P Unit.one))
(P x)
= λx λP λo
(~x P o)

4
book/compile.kind2 Normal file
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@ -0,0 +1,4 @@
compile : String = (Kind.Book.to_hvm (Kind.Book.parse `test9
: String
= (String.unpar '(' ')' "((foo))")
`))

5
book/oxi.kind2
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@ -1,5 +0,0 @@
oxi
: ∀(b: Bool)
(Equal Bool b (Bool.not (Bool.not b)))
= λb
(~b ?P ?T ?F)

14
book/test10.kind2 Normal file
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@ -0,0 +1,14 @@
// exp : ∀(n: Nat) Nat = λn λm λP λs λz (m ∀(x:P)P (n P))
_EXP = (Kind.all "n" _Nat λn(Kind.all "m" _Nat λm(_Nat)))
_exp = (Kind.lam "n" λn(Kind.lam "m" λm(Kind.lam "P" λP(Kind.app (Kind.app m (Kind.all "x" P λx(P))) (Kind.app n P)))))
// C2 : Nat = λs λz (s (s z))
_C2 = _Nat
_c2 = (Kind.lam "P" λP(Kind.lam "s" λs(Kind.lam "z" λz(Kind.app s (Kind.app s z)))))
// Checks if `(work 2^4)` is propositionally equal to `true`
test10
: String
= let term = (Kind.app (Kind.app _exp _c2) _c2)
(Kind.Term.show (Kind.normal Bool.true term Nat.zero) Nat.zero)

17
book/test7.kind2
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@ -1,6 +1,21 @@
test7.book
: String
= `Test : Kind.Term = (Kind.lam "f" λf(Kind.lam "x" λx(Kind.app f (Kind.app f x))))`
= `
// exp : ∀(n: Nat) Nat = λn λm λP λs λz (m ∀(x:P)P (n P))
_EXP = (Kind.all "n" _Nat λn(Kind.all "m" _Nat λm(_Nat)))
_exp = (Kind.lam "n" λn(Kind.lam "m" λm(Kind.lam "P" λP(Kind.app (Kind.app m (Kind.all "x" P λx(P))) (Kind.app n P)))))
// C2 : Nat = λs λz (s (s z))
_C2 = _Nat
_c2 = (Kind.lam "P" λP(Kind.lam "s" λs(Kind.lam "z" λz(Kind.app s (Kind.app s z)))))
// Checks if (work 2^4) is propositionally equal to true
test10
: String
= let term = (Kind.app (Kind.app _exp _c2) _c2)
(Kind.Term.show (Kind.normal Bool.true term Nat.zero) Nat.zero)
`
test7
: String

3
book/test9.kind2 Normal file
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@ -0,0 +1,3 @@
test9
: String
= (String.unpar '(' ')' "((foo))")

37
kind2.hvm1
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@ -123,9 +123,10 @@
(Reduce.op2 r RSH (Num fst) (Num snd)) = (Num (>> fst snd))
(Reduce.op2 r opr fst snd) = (Op2 opr fst snd)
(Reduce.mat r nam (Num 0) z s p) = (Reduce r z)
(Reduce.mat r nam (Num n) z s p) = (Reduce r (s (Num (- n 1))))
(Reduce.mat r nam val z s p) = (Mat nam val z s p)
(Reduce.mat r nam (Num 0) z s p) = (Reduce r z)
(Reduce.mat r nam (Num n) z s p) = (Reduce r (s (Num (- n 1))))
(Reduce.mat r nam (Op2 ADD (Num 1) k) z s p) = (Reduce r (s k))
(Reduce.mat r nam val z s p) = (Mat nam val z s p)
(Reduce.txt r (String.cons x xs)) = (Reduce 1 (App (App Book.String.cons (Num x)) (Txt xs)))
(Reduce.txt r String.nil) = (Reduce 1 Book.String.nil)
@ -154,25 +155,14 @@
// --------
// Check if two terms are identical. If not...
(Equal a b dep) = (Equal.unify.a a λx(x) b dep)
//(Equal a b dep) = (Equal.minor (Identical a b dep) a b dep)
// ...
(Equal.unify.a (App a.fun a.arg) as b dep) = (Equal.unify.a a.fun λk(as (App k a.arg)) b dep)
(Equal.unify.a (Hol a.nam a.ctx) as b dep) = (Debug dep ["Found: ?" a.nam " = " (Show b dep)] 1)
(Equal.unify.a a as b dep) = (Equal.unify.b (as a) b λx(x) dep)
// ...
(Equal.unify.b a (App b.fun b.arg) bs dep) = (Equal.unify.b a b.fun λk(bs (App k b.arg)) dep)
(Equal.unify.b a (Hol b.nam b.ctx) bs dep) = (Debug dep ["Found: ?" b.nam " = " (Show a dep)] 1)
(Equal.unify.b a b bs dep) = let b = (bs b); (Equal.minor (Identical a b dep) a b dep)
(Equal a b dep) = (Equal.minor (Identical a b dep) a b dep)
// Check if they're identical after a minor weak reduction. If not...
(Equal.minor 0 a b dep) = (Equal.major (Identical (Reduce 0 a) (Reduce 0 b) dep) a b dep)
(Equal.minor 0 a b dep) = let a = (Reduce 0 a); let b = (Reduce 0 b); (Equal.major (Identical a b dep) a b dep)
(Equal.minor 1 a b dep) = 1
// Check if they're identical after a major weak reduction. If not...
(Equal.major 0 a b dep) = (Equal.enter (Identical (Reduce 1 a) (Reduce 1 b) dep) a b dep)
(Equal.major 0 a b dep) = let a = (Reduce 1 a); let b = (Reduce 1 b); (Equal.enter (Identical a b dep) a b dep)
(Equal.major 1 a b dep) = 1
// Check if they become identical after reducing fields.
@ -197,12 +187,15 @@
(Comparer rec (Ann a.val a.typ) b dep) = (rec a.val b dep)
(Comparer rec a (Ann b.val b.typ) dep) = (rec a b.val dep)
(Comparer rec (Hol a.nam a.ctx) (Hol b.nam b.ctx) dep) = (Same a.nam b.nam)
(Comparer rec (Hol a.nam a.ctx) b dep) = (Debug dep ["Found: ?" a.nam " = " (Show (Normal 0 b dep) dep)] 1)
(Comparer rec a (Hol b.nam b.ctx) dep) = (Debug dep ["Found: ?" b.nam " = " (Show (Normal 0 a dep) dep)] 1)
(Comparer rec U60 U60 dep) = 1
(Comparer rec (Num a.val) (Num b.val) dep) = (== a.val b.val)
(Comparer rec (Op2 a.opr a.fst a.snd) (Op2 b.opr b.fst b.snd) dep) = (& (rec a.fst a.snd dep) (rec b.fst b.snd dep))
(Comparer rec (Op2 a.opr a.fst a.snd) (Op2 b.opr b.fst b.snd) dep) = (& (rec a.fst b.fst dep) (rec a.snd b.snd dep))
(Comparer rec (Mat a.nam a.x a.z a.s a.p) (Mat b.nam b.x b.z b.s b.p) dep) = (& (rec a.x b.x dep) (& (rec a.z b.z dep) (& (rec (a.s (Var (Concat a.nam "-1") dep)) (b.s (Var (Concat b.nam "-1") dep)) dep) (rec (a.p (Var a.nam dep)) (b.p (Var b.nam dep)) dep))))
(Comparer rec (Txt a.txt) (Txt b.txt) dep) = (Same a.txt b.txt)
(Comparer rec a b dep) = 0
//(Comparer rec a b dep) = (HVM.log (NOP (Show a dep) (Show b dep)) 0)
// Type-Checking
// -------------
@ -322,7 +315,7 @@
(Show (All nam inp bod) dep) = (Join ["∀(" nam ": " (Show inp dep) ") " (Show (bod (Var nam dep)) (+ dep 1))])
(Show (Lam nam bod) dep) = (Join ["λ" nam " " (Show (bod (Var nam dep)) (+ dep 1))])
(Show (App fun arg) dep) = (Join ["(" (Show.prune (Show fun dep)) " " (Show arg dep) ")"])
(Show (App fun arg) dep) = (Join ["(" (Show.unwrap (Show fun dep)) " " (Show arg dep) ")"])
(Show (Ann val typ) dep) = (Join ["{" (Show val dep) ": " (Show typ dep) "}"])
(Show (Slf nam bod) dep) = (Join ["$" nam " " (Show (bod (Var nam dep)) (+ dep 1))])
(Show (Ins val) dep) = (Join ["~" (Show val dep)])
@ -332,7 +325,7 @@
(Show U60 dep) = "#U60"
(Show (Num val) dep) = (Join ["#" (U60.show val)])
(Show (Op2 opr fst snd) dep) = (Join ["#(" (Op2.show opr) " " (Show fst dep) " " (Show snd dep) ")"])
(Show (Mat nam x z s p) dep) = (Join ["match " nam " = " (Show x dep) " { #0 => " (Show z dep) "; #+ => " (Show (s (Var (Concat nam "-1") dep)) (+ dep 1)) " }: " (Show (p (Var nam dep)) dep)])
(Show (Mat nam x z s p) dep) = (Join ["#match " nam " = " (Show x dep) " { #0: " (Show z dep) " #+: " (Show (s (Var (Concat nam "-1") dep)) (+ dep 1)) " }: " (Show (p (Var nam dep)) dep)])
(Show (Txt txt) dep) = (Join [Quote txt Quote])
(Show (Hol nam ctx) dep) = (Join ["?" nam])
(Show (Var nam idx) dep) = (Join [nam])
@ -344,8 +337,8 @@
(Show.trim (String.cons ' ' xs)) = xs
(Show.trim str) = str
(Show.prune (String.cons '(' xs)) = (Show.begin xs)
(Show.prune str) = str
(Show.unwrap (String.cons '(' xs)) = (Show.begin xs)
(Show.unwrap str) = str
(Show.begin (String.cons x (String.cons y String.nil))) = (String.cons x String.nil)
(Show.begin (String.cons x xs)) = (String.cons x (Show.begin xs))