proofs/kernel_read_witness.bend source

proofs/kernel_read_witness.bend on the hub · documented module

import Baseimport ../kernel_gemm.bend as Gemmimport ../kernel_rows.bend as Rowsimport ../kernel_tile.bend as Tileimport ../traversal_loop.bend as Loopimport ./storage_witness.bend as Witness# The k loop returns every owner it received. Index, context and the erased# accumulators are whatever the steps produced.type Looped<-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,-state: Gemm.Loop> is Data:  Looped{index: U32,context: Gemm.Context,-accumulators: Rows.Rows<Tile.Tile8>,    equation: {state == Gemm.Loop{input,weights,bias,output,index,context,accumulators} : Gemm.Loop}}def after_input(-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,+index: U32,+context: Gemm.Context,  -accumulators: Rows.Rows<Tile.Tile8>,-samples: Rows.Rows<F32>,+address: U32,read: Witness.Read<Tile.Tile8,input,Array.get(Tile.Tile8,input,address)>) ->  Looped<input,weights,bias,output,Gemm.with_input(weights,bias,output,index,context,accumulators,samples,Array.get(Tile.Tile8,input,address))>:  Witness.Read{value,equation} = read  %Equal.sym(Array<Tile.Tile8> & Tile.Tile8,Array.get(Tile.Tile8,input,address),(input,value),equation) :    Looped<input,weights,bias,output,Gemm.with_input(weights,bias,output,index,context,accumulators,samples,_)>  Looped{(index + 1 : U32),context,Gemm.update(accumulators,value,samples),{==}}def after_weights(~upper: Bool,-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,+index: U32,+context: Gemm.Context,  +input_base: U32,-accumulators: Rows.Rows<Tile.Tile8>,+address: U32,input_evidence: Witness.ArrayWitness<Tile.Tile8,input>,  read: Witness.Read<Tile.Tile8,weights,Array.get(Tile.Tile8,weights,address)>) ->  Looped<input,weights,bias,output,Gemm.with_weights(~upper,input,bias,output,index,context,input_base,accumulators,Array.get(Tile.Tile8,weights,address))>:  Witness.Read{value,equation} = read  %Equal.sym(Array<Tile.Tile8> & Tile.Tile8,Array.get(Tile.Tile8,weights,address),(weights,value),equation) :    Looped<input,weights,bias,output,Gemm.with_weights(~upper,input,bias,output,index,context,input_base,accumulators,_)>  after_input(input,weights,bias,output,index,context,accumulators,Rows.half(upper,value),(input_base + index : U32),    Witness.observed(Tile.Tile8,input,(input_base + index : U32),input_evidence))def step_at(~upper: Bool,-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,+index: U32,context: Gemm.Context,  -accumulators: Rows.Rows<Tile.Tile8>,+input_evidence: Witness.ArrayWitness<Tile.Tile8,input>,+weight_evidence: Witness.ArrayWitness<Tile.Tile8,weights>) ->  Looped<input,weights,bias,output,Gemm.step(~upper,Gemm.Loop{input,weights,bias,output,index,context,accumulators})>:  Gemm.Context{+row,+position,+rows,+columns,+input_base,+weight_base} = context  after_weights(~upper,input,weights,bias,output,index,Gemm.Context{row,position,rows,columns,input_base,weight_base},input_base,accumulators,    (weight_base + index : U32),input_evidence,Witness.observed(Tile.Tile8,weights,(weight_base + index : U32),weight_evidence))def step(~upper: Bool,-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,-state: Gemm.Loop,  +input_evidence: Witness.ArrayWitness<Tile.Tile8,input>,+weight_evidence: Witness.ArrayWitness<Tile.Tile8,weights>,  evidence: Looped<input,weights,bias,output,state>) -> Looped<input,weights,bias,output,Gemm.step(~upper,state)>:  Looped{+index,+context,accumulators,equation} = evidence  %Equal.sym(Gemm.Loop,state,Gemm.Loop{input,weights,bias,output,index,context,accumulators},equation) :    Looped<input,weights,bias,output,Gemm.step(~upper,_)>  step_at(~upper,input,weights,bias,output,index,context,accumulators,input_evidence,weight_evidence)def run(~upper: Bool,count: Nat,-input: Array<Tile.Tile8>,-weights: Array<Tile.Tile8>,-bias: Array<F32>,-output: Array<F32>,-state: Gemm.Loop,  +input_evidence: Witness.ArrayWitness<Tile.Tile8,input>,+weight_evidence: Witness.ArrayWitness<Tile.Tile8,weights>,  evidence: Looped<input,weights,bias,output,state>) ->  Looped<input,weights,bias,output,Loop.run(~Gemm.Loop,~Gemm.step(~upper),count,state)>:  match count:    case 0n: evidence    case 1n+rest:      run(~upper,rest,input,weights,bias,output,Gemm.step(~upper,state),input_evidence,weight_evidence,        step(~upper,input,weights,bias,output,state,input_evidence,weight_evidence,evidence))