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Georges Dupéron
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122
deques.ml
122
deques.ml
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@ -218,7 +218,7 @@ module TypeLevelFunctions1 = struct
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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 tif = ('tail, 'tresult) stk
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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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@ -230,9 +230,9 @@ module TypeLevelFunctions1 = struct
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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) tif = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *)
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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 tif return
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type s = ((((start, 't) tru, string) typ), int) typ ifelse return
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end
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@ -251,74 +251,106 @@ end
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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 TypeLevelFunctions = struct
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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 ('hd, 'tl) stack = Stack of 'hd * 'tl
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type ('stack, 'freevars) state = State of 'stack * 'freevars (* constraint 'tail = ('a,'b) state *)
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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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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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type ('state, 'v) _push = (('stack, 'v) 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 *)
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type 'state _peek = 'v
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constraint (('stack, 'v) stack, 'freevars) _state = 'state
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(* drop the value on top of the the stack *)
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type 'state _drop = ('tail, 'freevars) _state
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constraint (('tail, 'v) stack, 'freevars) _state = 'state
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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 close_freevars = ()
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type 'state return = 'returned constraint 'state = ((_start, 'returned _typ) stack, close_freevars) state
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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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(* quote a type and place it on the stack *)
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type ('state, 't) typ = (('stack, 't _typ) stack, 'freevars) state constraint ('stack, 'freevars) state = 'state
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(* Unwrap the single element on the stack. *)
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type close_freevars = ()
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type 'state return = 'returned constraint 'state = ((__start, 'returned _typ) stack, close_freevars) _state
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(* Quote a type and place it on the stack. *)
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type ('state, 't) typ = (('stack, 't _typ) stack, 'freevars) _state 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) stack, 'freevars) _state
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constraint ('stack, 'freevars) _state = ('state, 'x) freevar
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(* type-level booleans *)
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type 'state tru = (('stack, ('a * 'b * 'a)) stack, 'new_freevars) state
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constraint ('stack, 'freevars) state = 'state
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constraint 'freevars = 'new_freevars * 'freevar
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constraint 'freevar = 'a * 'b
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type 'state fals = (('stack, ('a * 'b * 'b)) stack, 'new_freevars) state
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constraint ('stack, 'freevars) state = 'state
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constraint 'freevars = 'new_freevars * 'freevar
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constraint 'freevar = 'a * 'b
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type 'state tru = ('state2, ('a * 'b * 'a)) _push
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constraint 'state2 = ('state, 'a * 'b) freevar
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type 'state fals = ('state2, ('a * 'b * 'b)) _push
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constraint 'state2 = ('state, 'a * 'b) freevar
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type ('x, 'y) _cons = Cons of 'x * 'y
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type 'state cons = ('state _drop _drop, ('state _peek, 'state _drop _peek) _cons) _push
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type 'state uncons = (('state _drop, 'x) _push, 'y) _push
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constraint ('x, 'y) _cons = 'state _peek
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(* type-level conditional *)
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type 'state tif = (('tail, 'tresult) stack, 'freevars) state
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type 'state ifelse = (('tail, 'tresult) stack, 'freevars) _state
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constraint 'tcondition = 'tthen * 'telse * 'tresult
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constraint 'state = (((('tail, 'tcondition) stack, 'tthen) stack, 'telse) stack, 'freevars) state
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constraint 'state = (((('tail, 'tcondition) stack, 'tthen) stack, 'telse) stack, 'freevars) _state
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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 'state dup = ('state, 'head) state constraint 'state = ('tail, 'head) state *)
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(* type 'state dup = 'state tru tru cons fals fals cons ifelse uncons *)
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type 'state dup = 'state tru
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type 'state exch = (('state _drop _drop, 'state _peek) _push, 'state _drop _peek) _push
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type 'state pop = 'state _drop
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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 _drop)) _polytyp = 'state _peek
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(* type 'x push = 'a * 'b constraint 'x = 'a * 'b *)
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(* type ('tcondition, 'tthen, 'telse) tif = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *)
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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 'arg s = 'result
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constraint 'state = 'freevars start
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constraint 'result = 'bool typ_string typ_int tif return
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constraint 'bool * 'state = 'arg
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type 'state tt = ('state tru * 'state)
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type 'state ff = ('state fals * 'state)
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type s1 = 'state tt s
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type s2 = 'state ff s
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type z = ('freevars start, string) typ return
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type 'state xs = 'state typ_string typ_int tif return
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type xs1 = 't tru xs
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type xs2 = 't fals xs
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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
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type 'state u = 'state tru dup typ_int typ_string ifelse typ_unit ifelse return
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type u1 = 't u
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(* type u2 = 't fals u *)
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end
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@ -378,7 +410,7 @@ end
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* constraint [`State of 'stk * 'freevars] = 'tail
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* constraint 'tail * 'tcondition * 'stk * 'freevars = 'arg
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*
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* type 'state tif = ('tail * 'tresult * int * string) psh
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* type 'state ifelse = ('tail * 'tresult * int * string) psh
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* (\* constraint ('tail, 'tcondition) push = 'state *\)
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* (\* type ('state, 'elt) push = [`State of ('elt * 'stk) * 'freevars] *\)
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* constraint 'state = ('tail * 'tcondition * int * string) psh
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@ -397,9 +429,9 @@ end
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* type 'state dup = ('state, 'head) push constraint 'state = ('tail, 'head) push
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*
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* (\* type 'x push = 'a * 'b constraint 'x = 'a * 'b *\)
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* (\* type ('tcondition, 'tthen, 'telse) tif = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *\)
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* (\* type ('tcondition, 'tthen, 'telse) ifelse = 'tresult constraint 'tcondition = 'tthen * 'telse * 'tresult *\)
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*
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* (\* type s = ((((start, 't) tru, string) typ), int) typ tif return *\)
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* (\* type s = ((((start, 't) tru, string) typ), int) typ ifelse return *\)
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* end *)
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