Left type-level programming aside for now
This commit is contained in:
Georges Dupéron
parent
5888eff68b
commit
8bb879dc16
198
deques.ml
198
deques.ml
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@ -194,204 +194,6 @@ module DequesColorsStack = struct
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end
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open DequesColorsStack
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module TypeLevelFunctions1 = struct
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(* TODO: bundle together the stack and an on-demand infinite stack of free variables *)
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(* This should not be exported in the sig. *)
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module Private = struct
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(* stack of type-level operands *)
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type start = ()
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type ('head, 'tail) stk = Stk of 'head * 'tail (* constraint 'tail = ('a,'b) stk *)
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(* internal: quote a type and place it on the stack *)
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type 't _typ = Typ of 't
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end
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open Private
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(* unwrap the single element on the stack *)
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type 'stk return = 'returned constraint 'stk = (start, 'returned _typ) stk
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(* quote a type and place it on the stack *)
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type ('stk, 't) typ = ('stk, 't _typ) stk
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(* type-level booleans *)
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type ('stk, 'freevar) tru = ('stk, ('a * 'b * 'b)) stk constraint 'freevar = 'a * 'b
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type ('stk, 'freevar) fals = ('stk, ('a * 'b * 'b)) stk constraint 'freevar = 'a * 'b
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(* type-level conditional *)
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type 'stk ifelse = ('tail, 'tresult) stk
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constraint 'tcondition = 'tthen * 'telse * 'tresult
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constraint 'stk = ((('tail, 'tcondition) stk, 'tthen) stk, 'telse) stk
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(* type-level duplication of a boolean
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We prefer not to allow duplication of a quoted type, as there would be no
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way to avoid using the same polymorphic variables in both occurrences. *)
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(* TODO: use if to duplicate! *)
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type 'stk dup = ('stk, 'head) stk constraint 'stk = ('tail, 'head) stk
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(* type 'x push = 'a * 'b constraint 'x = 'a * 'b *)
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(* type ('tcondition, 'tthen, 'telse) ifelse = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *)
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type s = ((((start, 't) tru, string) typ), int) typ ifelse return
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end
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(* Unification in the HM type system, along with OCaml's constraint keyword,
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allows us to describe relations between types. The type-level functions
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below are using this in a way that is reminiscent of Prolog's
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predicates. We try to put the results on the left-hand side of the equals
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sign, even though a use of the constraint keyword establishes an unordered
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relation between two types. This explains why it is possible to write
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constraint 'x = ('hd, 'tl) push to indicate that 'x is the result, and the
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equivalent constraint ('hd, 'tl) push = 'x to indicate that 'hd and 'tl are
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expected to be extracted from a known 'x. *)
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module T = struct
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(* TODO: bundle together the stack and an on-demand infinite stack of free variables *)
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(* This should not be exported in the sig. *)
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module Private = struct
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(* stack of type-level operands *)
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type ('tl, 'hd, 'fv) _stack = Stack of 'tl * 'hd * 'fv
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type ('stack, 'freevars) _state = State of 'stack * 'freevars (* constraint 'tail = ('a,'b) state *)
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type __start = ()
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type 'freevars _start = (__start, 'freevars) _state
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(* internal: quote a type and place it on the stack *)
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type 't _typ = Typ of 't
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type 't _polytyp = PolyTyp of 't
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(* Push a new type-level value onto the stack *)
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(* 'fv denotes the free variables in 'v, which will be bound to a dummy
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type if the value 'v is dropped from the stack. *)
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type ('state, 'v, 'fv) _push = (('stack, 'v, 'fv) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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(* fetch the value on top of the the stack and its free variables *)
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type 'state _peekv = 'v
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constraint (('stack, 'v, 'fv) _stack, 'freevars) _state = 'state
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type 'state _peekfv = 'fv
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constraint (('stack, 'v, 'fv) _stack, 'freevars) _state = 'state
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(* drop the value on top of the the stack *)
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(* type closed_freevar = [`FreeVar of (closed_freevar * closed_freevar)] *)
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type closed_freevar1 = [`FreeVar of unit * unit]
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(* 'x serves as a handled. If is is not unified with anything, it does not
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cause any harm. If it is unified with ('u * 'u * 'v * 'v * 'w * 'w), it
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causes three pairs of types to unify, thereby closing a local type
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variable and propagating that close order down to the two children. *)
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type 'dummy close_freevars = ('u * 'u * 'v * 'v * 'w * 'w) constraint ('u * 'v * 'w) = 'dummy
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type ('a, 'x) _fv = [`FreeVar of 'a * 'x]
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constraint ( 'a * closed_freevar1
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* unit * unit (* ignored *)
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* unit * unit (* ignored *)) = 'x
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type ('a, 'b, 'x) _fvs = [`FreeVar of ('a * 'b) * 'x]
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constraint ( unit * unit (* ignored *)
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* 'a * [`FreeVar of 'one * 'dummy1 close_freevars]
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* 'b * [`FreeVar of 'two * 'dummy2 close_freevars]) = 'x
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(*TODO: possibly need to bind: 'one 'two 'dummy1 'dummy2 *)
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type no_freevar = closed_freevar1
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type 'state _pop = ('tail, 'freevars) _state
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constraint (('tail, 'v, 'fv) _stack, 'freevars) _state = 'state
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type 'state _discard = ('tail, 'freevars) _state
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constraint (('tail, 'v, 'fv) _stack, 'freevars) _state = 'state
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constraint 'fv = [`FreeVar of 'fv_ * 'dummy close_freevars]
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end
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open Private
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(* Instantiate a new free variable. *)
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type ('state, 'freevar) _freevar = ('stack, 'new_freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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constraint 'new_freevars * 'freevar = 'freevars
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(* Unwrap the single element on the stack. *)
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type 'state return = 'returned
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constraint 'state = ((__start, 'returned _typ, 'fvs) _stack, closed_freevar1) _state
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constraint 'fvs = [`FreeVar of 'fvs_ * 'dummy close_freevars]
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(* Quote a type and place it on the stack. *)
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type ('state, 't) typ = (('stack, 't _typ, no_freevar) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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(* Quote a polymorphic type and place it on the stack. *)
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(* 'x should be a free variable on the caller's site,
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'xt should be 'x t where t is the polymorphic type to quote. *)
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type ('state, 'x, 'xt) polytyp = (('stack, ('xt * 'x) _polytyp, ('x, 'fv) _fv) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = ('state, 'x * 'fv) _freevar
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(* type-level booleans *)
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type 'state tru = ('state2, ('a * 'b * 'a * 'b), (('a, 'fva) _fv, ('b, 'fvb) _fv, 'fvab) _fvs) _push
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constraint 'state2 = ('state, 'a * 'b * 'fva * 'fvb * 'fvab) _freevar
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type 'state fals = ('state2, ('a * 'b * 'b * 'a), (('a, 'fva) _fv, ('b, 'fvb) _fv, 'fvab) _fvs) _push
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constraint 'state2 = ('state, 'a * 'b * 'fva * 'fvb * 'fvab) _freevar
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type ('x, 'y) _cons = Cons of 'x * 'y
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type 'state cons = ('state2 _pop _pop,
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('state2 _pop _peekv, 'state2 _peekv) _cons,
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('state2 _pop _peekfv, 'state2 _peekfv, 'fv) _fvs) _push
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constraint 'state2 = ('state, 'fv) _freevar
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type 'state uncons = (('state _pop, 'x, 'fvx) _push, 'y, 'fvy) _push
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constraint ('x, 'y) _cons = 'state _peekv
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constraint ('fvx, 'fvy, 'fvxy) _fvs = 'state _peekfv
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constraint 'fvxy = ( unit * unit (* ignored *)
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* 'a * [`FreeVar of 'one * 'dummy1 close_freevars]
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* 'b * [`FreeVar of 'two * 'dummy2 close_freevars])
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(* type-level conditional *)
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type 'state ifelse = (('tail, 'tresult, 'fvr) _stack, 'freevars) _state
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constraint 'state = (((('tail, 'tcondition, 'fvc) _stack, 'tthen, 'fvt) _stack, 'telse, 'fve) _stack, 'freevars) _state
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constraint 'tcondition = ([`v_fv of 'tthen * 'fvt])
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* ([`v_fv of 'telse * 'fve])
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* ([`v_fv of 'tresult * 'fvr])
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* ([`v_fv of 'tdiscard * 'fvd])
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(* Since the discarded value may contain some free variables, we need to
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bind them to some dummy value. *)
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constraint 'fvd = [`FreeVar of 'fvd_ * 'dummy close_freevars]
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constraint 'fvc = [`FreeVar of 'fvab * 'x]
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constraint 'x = unit (* release the 'x of 'fvc, since the condition was used *)
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(* type-level duplication of a boolean
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We prefer not to allow duplication of a quoted type, as there would be no
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way to avoid using the same polymorphic variables in both occurrences. *)
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type 'state dup = 'state tru tru cons fals fals cons ifelse uncons
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type 'state exch = (('state _pop _pop, 'state _peekv, 'state _peekfv) _push, 'state _pop _peekv, 'state _pop _peekfv) _push
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type 'state pop = 'state _discard
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(* apply a single-argument polymorphic type to an argument *)
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type 'state polyapp = 'result
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(* left-hand-side of product type is output, right-hand-side is input *)
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constraint ('result * ('state _pop)) _polytyp = 'state _peekv
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(* type 'x push = 'a * 'b constraint 'x = 'a * 'b *)
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(* type ('tcondition, 'tthen, 'telse) ifelse = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *)
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type 'state typ_string = ('state, string) typ
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type 'state typ_int = ('state, int) typ
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type 'state typ_unit = ('state, unit) typ
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end
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module TypeLevelFunctionsExamples = struct
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open T
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type 'state s = 'state typ_string typ_int ifelse return
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type s1 = 't tru s (* push true on the stack, call s => string *)
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type s2 = 't fals s (* push false on the stack, call s => int *)
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type 'state f = 'state tru typ_string
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type 'state t = 'state polyapp typ_int ifelse return
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type 'state push_f = ('state, 'x, 'x f) polytyp
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type t1 = 't push_f t (* => string *)
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type 'state u = 'state dup typ_int typ_string ifelse typ_unit exch ifelse return
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type u1 = 't tru u
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type u2 = 't fals u
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end
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(** jacm-final.pdf p.8 (584) §4.1 media 60 480 368 36 *)
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(* let rec child i d =
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if i = 0 then d
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149
deques_typelevelprogramming.ml
Normal file
149
deques_typelevelprogramming.ml
Normal file
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@ -0,0 +1,149 @@
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(* Unification in the HM type system, along with OCaml's constraint keyword,
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allows us to describe relations between types. The type-level functions
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below are using this in a way that is reminiscent of Prolog's
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predicates. We try to put the results on the left-hand side of the equals
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sign, even though a use of the constraint keyword establishes an unordered
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relation between two types. This explains why it is possible to write
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constraint 'x = ('hd, 'tl) push to indicate that 'x is the result, and the
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equivalent constraint ('hd, 'tl) push = 'x to indicate that 'hd and 'tl are
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expected to be extracted from a known 'x. *)
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module T = struct
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(* TODO: bundle together the stack and an on-demand infinite stack of free variables *)
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(* This should not be exported in the sig. *)
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module Private = struct
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(* stack of type-level operands *)
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type ('tl, 'hd, 'fv) _stack = Stack of 'tl * 'hd * 'fv
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type ('stack, 'freevars) _state = State of 'stack * 'freevars (* constraint 'tail = ('a,'b) state *)
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type __start = ()
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type 'freevars _start = (__start, 'freevars) _state
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(* internal: quote a type and place it on the stack *)
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type 't _typ = Typ of 't
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type 't _polytyp = PolyTyp of 't
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(* Push a new type-level value onto the stack *)
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(* 'fv denotes the free variables in 'v, which will be bound to a dummy
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type if the value 'v is dropped from the stack. *)
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type ('state, 'v, 'fv) _push = (('stack, 'v, 'fv) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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(* fetch the value on top of the the stack and its free variables *)
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type 'state _peekv = 'v
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constraint (('stack, 'v, 'fv) _stack, 'freevars) _state = 'state
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type 'state _peekfv = 'fv
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constraint (('stack, 'v, 'fv) _stack, 'freevars) _state = 'state
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(* drop the value on top of the the stack *)
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(* type closed_freevar = [`FreeVar of (closed_freevar * closed_freevar)] *)
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type closed_freevar1 = [`FreeVar of unit * unit]
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(* 'x serves as a handled. If is is not unified with anything, it does not
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cause any harm. If it is unified with ('u * 'u * 'v * 'v * 'w * 'w), it
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causes three pairs of types to unify, thereby closing a local type
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variable and propagating that close order down to the two children. *)
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type 'dummy close_freevars = ('u * 'u * 'v * 'v * 'w * 'w) constraint ('u * 'v * 'w) = 'dummy
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type ('a, 'x) _fv = [`FreeVar of 'a * 'x]
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constraint ( 'a * closed_freevar1
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* unit * unit (* ignored *)
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* unit * unit (* ignored *)) = 'x
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type ('a, 'b, 'x) _fvs = [`FreeVar of ('a * 'b) * 'x]
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constraint ( unit * unit (* ignored *)
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* 'a * [`FreeVar of 'one * 'dummy1 close_freevars]
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* 'b * [`FreeVar of 'two * 'dummy2 close_freevars]) = 'x
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(*TODO: possibly need to bind: 'one 'two 'dummy1 'dummy2 *)
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type no_freevar = closed_freevar1
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type 'state _pop = ('tail, 'freevars) _state
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constraint (('tail, 'v, 'fv) _stack, 'freevars) _state = 'state
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type 'state _discard = ('tail, 'freevars) _state
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constraint (('tail, 'v, 'fv) _stack, 'freevars) _state = 'state
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constraint 'fv = [`FreeVar of 'fv_ * 'dummy close_freevars]
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end
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open Private
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(* Instantiate a new free variable. *)
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type ('state, 'freevar) _freevar = ('stack, 'new_freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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constraint 'new_freevars * 'freevar = 'freevars
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(* Unwrap the single element on the stack. *)
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type 'state return = 'returned
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constraint 'state = ((__start, 'returned _typ, 'fvs) _stack, closed_freevar1) _state
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constraint 'fvs = [`FreeVar of 'fvs_ * 'dummy close_freevars]
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(* Quote a type and place it on the stack. *)
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type ('state, 't) typ = (('stack, 't _typ, no_freevar) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = 'state
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(* Quote a polymorphic type and place it on the stack. *)
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(* 'x should be a free variable on the caller's site,
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'xt should be 'x t where t is the polymorphic type to quote. *)
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type ('state, 'x, 'xt) polytyp = (('stack, ('xt * 'x) _polytyp, ('x, 'fv) _fv) _stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = ('state, 'x * 'fv) _freevar
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(* type-level booleans *)
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type 'state tru = ('state2, ('a * 'b * 'a * 'b), (('a, 'fva) _fv, ('b, 'fvb) _fv, 'fvab) _fvs) _push
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constraint 'state2 = ('state, 'a * 'b * 'fva * 'fvb * 'fvab) _freevar
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type 'state fals = ('state2, ('a * 'b * 'b * 'a), (('a, 'fva) _fv, ('b, 'fvb) _fv, 'fvab) _fvs) _push
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constraint 'state2 = ('state, 'a * 'b * 'fva * 'fvb * 'fvab) _freevar
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type ('x, 'y) _cons = Cons of 'x * 'y
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type 'state cons = ('state2 _pop _pop,
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('state2 _pop _peekv, 'state2 _peekv) _cons,
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('state2 _pop _peekfv, 'state2 _peekfv, 'fv) _fvs) _push
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constraint 'state2 = ('state, 'fv) _freevar
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type 'state uncons = (('state _pop, 'x, 'fvx) _push, 'y, 'fvy) _push
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constraint ('x, 'y) _cons = 'state _peekv
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constraint ('fvx, 'fvy, 'fvxy) _fvs = 'state _peekfv
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constraint 'fvxy = ( unit * unit (* ignored *)
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* 'a * [`FreeVar of 'one * 'dummy1 close_freevars]
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* 'b * [`FreeVar of 'two * 'dummy2 close_freevars])
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(* type-level conditional *)
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type 'state ifelse = (('tail, 'tresult, 'fvr) _stack, 'freevars) _state
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constraint 'state = (((('tail, 'tcondition, 'fvc) _stack, 'tthen, 'fvt) _stack, 'telse, 'fve) _stack, 'freevars) _state
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constraint 'tcondition = ([`v_fv of 'tthen * 'fvt])
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* ([`v_fv of 'telse * 'fve])
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* ([`v_fv of 'tresult * 'fvr])
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* ([`v_fv of 'tdiscard * 'fvd])
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(* Since the discarded value may contain some free variables, we need to
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bind them to some dummy value. *)
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constraint 'fvd = [`FreeVar of 'fvd_ * 'dummy close_freevars]
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constraint 'fvc = [`FreeVar of 'fvab * 'x]
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constraint 'x = unit (* release the 'x of 'fvc, since the condition was used *)
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(* type-level duplication of a boolean
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We prefer not to allow duplication of a quoted type, as there would be no
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way to avoid using the same polymorphic variables in both occurrences. *)
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type 'state dup = 'state tru tru cons fals fals cons ifelse uncons
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type 'state exch = (('state _pop _pop, 'state _peekv, 'state _peekfv) _push, 'state _pop _peekv, 'state _pop _peekfv) _push
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type 'state pop = 'state _discard
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(* apply a single-argument polymorphic type to an argument *)
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type 'state polyapp = 'result
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(* left-hand-side of product type is output, right-hand-side is input *)
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constraint ('result * ('state _pop)) _polytyp = 'state _peekv
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(* type 'x push = 'a * 'b constraint 'x = 'a * 'b *)
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(* type ('tcondition, 'tthen, 'telse) ifelse = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *)
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type 'state typ_string = ('state, string) typ
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type 'state typ_int = ('state, int) typ
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type 'state typ_unit = ('state, unit) typ
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end
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module TypeLevelFunctionsExamples = struct
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open T
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type 'state s = 'state typ_string typ_int ifelse return
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type s1 = 't tru s (* push true on the stack, call s => string *)
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type s2 = 't fals s (* push false on the stack, call s => int *)
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type 'state f = 'state tru typ_string
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type 'state t = 'state polyapp typ_int ifelse return
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type 'state push_f = ('state, 'x, 'x f) polytyp
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type t1 = 't push_f t (* => string *)
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type 'state u = 'state dup typ_int typ_string ifelse typ_unit exch ifelse return
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type u1 = 't tru u
|
||||
type u2 = 't fals u
|
||||
end
|
||||
Loading…
Reference in New Issue
Block a user